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1. Compactness of embedding between Sobolev type spaces with multiweighted derivatives Abdikalikova, Zamira PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt606",{id:"formSmash:items:resultList:0:j_idt606",widgetVar:"widget_formSmash_items_resultList_0_j_idt606",onLabel:"Abdikalikova, Zamira ",offLabel:"Abdikalikova, Zamira ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:0:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Compactness of embedding between Sobolev type spaces with multiweighted derivatives2009Inngår i: AIHT : Analysis, Inequalities and Homogenization Theory: Midnight sun conference in honor of Lars-Erik Persson, 2009Konferansepaper (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_0_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:0:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_0_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider a new Sobolev type function space called the space with multiweighted derivatives. As basis for this space serves some differential operators containing weight functions. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding between the spaces with multiweighted derivatives in different selections of weights.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:0:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 2. Embedding theorems for spaces with multiweighted derivatives Abdikalikova, Zamira PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt606",{id:"formSmash:items:resultList:1:j_idt606",widgetVar:"widget_formSmash_items_resultList_1_j_idt606",onLabel:"Abdikalikova, Zamira ",offLabel:"Abdikalikova, Zamira ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:1:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Embedding theorems for spaces with multiweighted derivatives2007Licentiatavhandling, med artikler (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_1_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:1:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_1_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This Licentiate Thesis consists of four chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we consider and analyze some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we present and prove analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are crucially for the proofs of the main results of this Licentiate Thesis. In Chapter 3 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of spaces. However, with the help of our new embedding theorems we can extend these results to the case of strong degeneration. In Chapter 4 we prove some new estimates for each function in a Tchebychev system. In order to be able to study also compactness of the embeddings from Chapter 3 such estimates are crucial. I plan to study this question in detail in my further PhD studies.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:1:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_1_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:1:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_1_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:1:j_idt869:0:fullText"});}); 3. Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives Abdikalikova, Zamira PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt606",{id:"formSmash:items:resultList:2:j_idt606",widgetVar:"widget_formSmash_items_resultList_2_j_idt606",onLabel:"Abdikalikova, Zamira ",offLabel:"Abdikalikova, Zamira ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:2:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives2009Doktoravhandling, med artikler (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_2_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:2:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_2_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This Doctoral Thesis consists of five chapters, which deal with a new Sobolev type function space called the space with multiweighted derivatives. This space is a generalization of the usual one dimensional Sobolev space. As basis for this space serves some differential operators containing weight functions.Chapter 1 is an introduction, where, in particular, the importance to study function spaces with weights is discussed and motivated. In Chapter 2 we prove some new estimates for each function in a Tchebychev system. In order to be able to study compactness of the embeddings from Chapter 3 such estimates are crucial.In Chapter 3 we rewrite and present some results of L. D. Kudryavtsev, where he investigated one dimensional Sobolev spaces. Moreover, in this chapter we rewrite and discuss some analogous results by B. L. Baidel'dinov for generalized Sobolev spaces. These results are not available in the Western literatures in this way and they are crucial for the proofs of the main results in Chapter 4. In Chapter 4 we prove some embedding theorems for these new generalized Sobolev spaces. The main results of Kudryavtsev and Baidel'dinov about characterization of the behavior of functions at a singularity take place in weak degeneration of the spaces. However, with the help of our new embedding theorems we can extend theseresults to the case of strong degeneration.The main aim of Chapter 5 is to establish boundedness and compactness of the embedding considered in Chapter 4.In Chapter 4 basically only sufficient conditions for boundedness of this embedding were obtained. In Chapter 5 we obtain necessary and sufficient conditions for boundedness and compactness of this embedding and the main results are proved in a different way.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:2:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_2_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:2:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_2_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:2:j_idt869:0:fullText"});}); 4. Compactness of embedding between spaces with multiweighted derivatives Abdikalikova, Zamiraet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_3_j_idt609",{id:"formSmash:items:resultList:3:j_idt609",widgetVar:"widget_formSmash_items_resultList_3_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Baiarystanov, Askar O.Oinarov, RyskulPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:3:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Compactness of embedding between spaces with multiweighted derivatives: the case 1 ≤ p ≤ q2009Rapport (Annet vitenskapelig)5. Summability of a Tchebysheff system of functions Abdikalikova, Zamira PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt606",{id:"formSmash:items:resultList:4:j_idt606",widgetVar:"widget_formSmash_items_resultList_4_j_idt606",onLabel:"Abdikalikova, Zamira ",offLabel:"Abdikalikova, Zamira ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_4_j_idt609",{id:"formSmash:items:resultList:4:j_idt609",widgetVar:"widget_formSmash_items_resultList_4_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kalybay, AigerimLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:4:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Summability of a Tchebysheff system of functions2007Rapport (Annet vitenskapelig)6. Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1 Abdikalikova, Zamira PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt606",{id:"formSmash:items:resultList:5:j_idt606",widgetVar:"widget_formSmash_items_resultList_5_j_idt606",onLabel:"Abdikalikova, Zamira ",offLabel:"Abdikalikova, Zamira ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt609",{id:"formSmash:items:resultList:5:j_idt609",widgetVar:"widget_formSmash_items_resultList_5_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); L.N. Gumilyov Eurasian National University.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Oinarov, RyskulL.N. Gumilyov Eurasian National University.Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:5:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 12011Inngår i: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 61, nr 1, s. 7-26Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_5_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:5:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_5_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider a new Sobolev type function space called the space with multiweighted derivatives W-p(n),(alpha) over bar, where (alpha) over bar = (alpha(0), alpha(1), ......, alpha(n)), alpha(i) is an element of R, i = 0, 1,......,n, and parallel to f parallel to W-p(n),((alpha) over bar) = parallel to D((alpha) over bar)(n)f parallel to(p) + Sigma(n-1) (i=0) vertical bar D((alpha) over bar)(i)f(1)vertical bar, D((alpha) over bar)(0)f(t) = t(alpha 0) f(t), d((alpha) over bar)(i)f(t) = t(alpha i) d/dt D-(alpha) over bar(i-1) f(t), i = 1, 2, ....., n. We establish necessary and sufficient conditions for the boundedness and compactness of the embedding W-p,(alpha) over bar(n) -> W-q,(beta) over bar,(m) when 1 <= q < p < infinity, 0 <= m < n

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:5:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 7. Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1≤ q Abdikalikova, Zamira PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt606",{id:"formSmash:items:resultList:6:j_idt606",widgetVar:"widget_formSmash_items_resultList_6_j_idt606",onLabel:"Abdikalikova, Zamira ",offLabel:"Abdikalikova, Zamira ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_6_j_idt609",{id:"formSmash:items:resultList:6:j_idt609",widgetVar:"widget_formSmash_items_resultList_6_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); L.N. Gumilyov Eurasian National University.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Oinarov, RyskulL.N. Gumilyov Eurasian National University.Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:6:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1≤ q2009Rapport (Annet vitenskapelig)8. Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions Abramovic, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt606",{id:"formSmash:items:resultList:7:j_idt606",widgetVar:"widget_formSmash_items_resultList_7_j_idt606",onLabel:"Abramovic, Shoshana ",offLabel:"Abramovic, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt609",{id:"formSmash:items:resultList:7:j_idt609",widgetVar:"widget_formSmash_items_resultList_7_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Haifa, Haifa, Israel.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT The Arctic University of Norway, Narvik, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:7:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions2017Inngår i: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 102, nr 5-6, s. 599-609Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_7_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:7:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_7_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:7:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 9. Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities Abramovich, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt606",{id:"formSmash:items:resultList:8:j_idt606",widgetVar:"widget_formSmash_items_resultList_8_j_idt606",onLabel:"Abramovich, S. ",offLabel:"Abramovich, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt609",{id:"formSmash:items:resultList:8:j_idt609",widgetVar:"widget_formSmash_items_resultList_8_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of Haifa, Haifa, Israel.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UIT The Arctic University of Norway, Narvik, Norway.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:8:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities2018Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 3, s. 759-772Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_8_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:8:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_8_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper extensions and refinements of Hermite-Hadamard and Fejer type inequalities are derived including monotonicity of some functions related to the Fejer inequality and extensions for functions, which are 1-quasiconvex and for function with bounded second derivative. We deal also with Fejer inequalities in cases that p, the weight function in Fejer inequality, is not symmetric but monotone on [a, b] .

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:8:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 10. Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 3 Abramovich, Shosana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt606",{id:"formSmash:items:resultList:9:j_idt606",widgetVar:"widget_formSmash_items_resultList_9_j_idt606",onLabel:"Abramovich, Shosana ",offLabel:"Abramovich, Shosana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt609",{id:"formSmash:items:resultList:9:j_idt609",widgetVar:"widget_formSmash_items_resultList_9_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of Haifa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:9:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 32014Inngår i: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 / [ed] Manuel Cepedello Boiso; Håkan Hedenmalm; Marinus A. Kaashoek; Alfonso Montes Rodríguez; Sergei Treil, Basel: Encyclopedia of Global Archaeology/Springer Verlag, 2014, s. 1-10Konferansepaper (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_9_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:9:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_9_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For usual Hardy type inequalities the natural “breaking point” (the parameter value where the inequality reverses) is p = 1. Recently, J. Oguntuase and L.-E. Persson proved a refined Hardy type inequality with breaking point at p = 2. In this paper we show that this refinement is not unique and can be replaced by another refined Hardy type inequality with breaking point at p = 2. Moreover, a new refined Hardy type inequality with breaking point at p = 3 is obtained. One key idea is to prove some new Jensen type inequalities related to convex or superquadratic funcions, which are also of independent interest

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:9:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 11. Some new refined Hardy type inequalities with general kernels and measures Abramovich, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt606",{id:"formSmash:items:resultList:10:j_idt606",widgetVar:"widget_formSmash_items_resultList_10_j_idt606",onLabel:"Abramovich, Shoshana ",offLabel:"Abramovich, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt609",{id:"formSmash:items:resultList:10:j_idt609",widgetVar:"widget_formSmash_items_resultList_10_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of Haifa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Krulić, KristinaFaculty of Textile Technology, University of Zagreb.Pečarić, JosipFaculty of Textile Technology, University of Zagreb.Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:10:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Some new refined Hardy type inequalities with general kernels and measures2010Inngår i: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 79, nr 1-2, s. 157-172Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_10_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:10:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_10_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We state and prove some new refined Hardy type inequalities using the notation of superquadratic and subquadratic functions with an integral operator Ak defined by, where k: Ω1 × Ω2 is a general nonnegative kernel, (Ω1, μ1) and (Ω2, μ2) are measure spaces and,. The relations to other results of this type are discussed and, in particular, some new integral identities of independent interest are obtained.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:10:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 12. Inequalities for averages of quasiconvex and superquadratic functions Abramovich, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt606",{id:"formSmash:items:resultList:11:j_idt606",widgetVar:"widget_formSmash_items_resultList_11_j_idt606",onLabel:"Abramovich, Shoshana ",offLabel:"Abramovich, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt609",{id:"formSmash:items:resultList:11:j_idt609",widgetVar:"widget_formSmash_items_resultList_11_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of Haifa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:11:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Inequalities for averages of quasiconvex and superquadratic functions2016Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, nr 2, s. 535-550Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_11_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:11:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_11_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For n ε ℤ+ we consider the difference Bn-1 (f)-Bn(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) where the sequences{ai} and {ai-ai-1} are increasing. Some lower bounds are derived when f is 1-quasiconvex and when f is a closely related superquadratic function. In particular, by using some fairly new results concerning the so called "Jensen gap", these bounds can be compared. Some applications and related results about An-1 (f)-An(f):= 1/an n-1/ηi=0 f(ai/an-1)-1/an+1 nηi=0f(ai/an) are also included.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:11:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 13. Some new estimates of the ‘Jensen gap’ Abramovich, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt606",{id:"formSmash:items:resultList:12:j_idt606",widgetVar:"widget_formSmash_items_resultList_12_j_idt606",onLabel:"Abramovich, Shoshana ",offLabel:"Abramovich, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt609",{id:"formSmash:items:resultList:12:j_idt609",widgetVar:"widget_formSmash_items_resultList_12_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of Haifa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:12:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Some new estimates of the ‘Jensen gap’2016Inngår i: Journal of inequalities and applications, ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, artikkel-id 39Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_12_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:12:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_12_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Let (μ,Ω) be a probability measure space. We consider the so-called ‘Jensen gap’ J(φ,μ,f)=∫ Ω φ(f(s))dμ(s)−φ(∫ Ω f(s)dμ(s)) for some classes of functions φ. Several new estimates and equalities are derived and compared with other results of this type. Especially the case when φ has a Taylor expansion is treated and the corresponding discrete results are pointed out.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:12:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 14. Some new scales of refined Hardy type inequalities via functions related to superquadracity Abramovich, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt606",{id:"formSmash:items:resultList:13:j_idt606",widgetVar:"widget_formSmash_items_resultList_13_j_idt606",onLabel:"Abramovich, Shoshana ",offLabel:"Abramovich, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt609",{id:"formSmash:items:resultList:13:j_idt609",widgetVar:"widget_formSmash_items_resultList_13_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Haifa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:13:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Some new scales of refined Hardy type inequalities via functions related to superquadracity2013Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, nr 3, s. 679-695Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_13_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:13:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_13_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For the Hardy type inequalities the "breaking point" (=the point where the inequality reverses) is p = 1. Recently, J. Oguntoase and L. E. Persson proved a refined Hardy type inequality with a breaking point at p = 2. In this paper we prove a new scale of refined Hardy type inequality which can have a breaking point at any p ≥ 2. The technique is to first make some further investigations for superquadratic and superterzatic functions of independent interest, among which, a new Jensen type inequality is proved

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:13:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 15. General inequalities via isotonic subadditive functionals Abramovich, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt606",{id:"formSmash:items:resultList:14:j_idt606",widgetVar:"widget_formSmash_items_resultList_14_j_idt606",onLabel:"Abramovich, Shoshana ",offLabel:"Abramovich, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt609",{id:"formSmash:items:resultList:14:j_idt609",widgetVar:"widget_formSmash_items_resultList_14_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Haifa, Department of Mathematics.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Pecaric, JosipUniversity of Zagreb.Varosanec, SanjaUniversity of Zagreb.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:14:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); General inequalities via isotonic subadditive functionals2007Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, nr 1, s. 15-28Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_14_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:14:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_14_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this manuscript a number of general inequalities for isotonic subadditive functionals on a set of positive mappings are proved and applied. In particular, it is pointed out that these inequalities both unify and generalize some general forms of the Holder, Popoviciu, Minkowski, Bellman and Power mean inequalities. Also some refinements of some of these results are proved.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:14:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 16. On some new developments of Hardy-type inequalities Abramovich, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt606",{id:"formSmash:items:resultList:15:j_idt606",widgetVar:"widget_formSmash_items_resultList_15_j_idt606",onLabel:"Abramovich, Shoshana ",offLabel:"Abramovich, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt609",{id:"formSmash:items:resultList:15:j_idt609",widgetVar:"widget_formSmash_items_resultList_15_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); University of Haifa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Samko, NatashaLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:15:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On some new developments of Hardy-type inequalities2012Inngår i: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2012, s. 739-746Konferansepaper (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_15_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:15:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_15_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper we present and discuss some new developments of Hardy-type inequalities, namely to derive (a) Hardy-type inequalities via a convexity approach, (b) refined scales of Hardy-type inequalities with other “breaking points” than p = 1 via superquadratic and superterzatic functions, (c) scales of conditions to characterize modern forms of weighted Hardy-type inequalities.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:15:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 17. On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities Abramovich, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt606",{id:"formSmash:items:resultList:16:j_idt606",widgetVar:"widget_formSmash_items_resultList_16_j_idt606",onLabel:"Abramovich, Shoshana ",offLabel:"Abramovich, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt609",{id:"formSmash:items:resultList:16:j_idt609",widgetVar:"widget_formSmash_items_resultList_16_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of Haifa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Samko, NatashaLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:16:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities2015Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 18, nr 2, s. 615-627Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_16_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:16:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_16_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper we deal with γ -quasiconvex functions when −1γ 0, to derive sometwo-sided Jensen type inequalities. We also discuss some Jensen-Steffensen type inequalitiesfor 1-quasiconvex functions. We compare Jensen type inequalities for 1-quasiconvex functionswith Jensen type inequalities for superquadratic functions and we extend the result obtained forγ -quasiconvex functions to more general classes of functions.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:16:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 18. Some new scales of refined Jensen and Hardy type inequalities Abramovich, Shoshana PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt606",{id:"formSmash:items:resultList:17:j_idt606",widgetVar:"widget_formSmash_items_resultList_17_j_idt606",onLabel:"Abramovich, Shoshana ",offLabel:"Abramovich, Shoshana ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt609",{id:"formSmash:items:resultList:17:j_idt609",widgetVar:"widget_formSmash_items_resultList_17_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of Haifa.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Samko, NatashaLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:17:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Some new scales of refined Jensen and Hardy type inequalities2014Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, nr 3, s. 1105-1114Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_17_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:17:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_17_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Some scales of refined Jensen and Hardy type inequalities are derived and discussed. The key object in our technique is ? -quasiconvex functions K(x) defined by K(x)x-? =? (x) , where Φ is convex on [0,b) , 0 < b > ∞ and γ > 0.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:17:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 19. Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels Abylayeva, A. M. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt606",{id:"formSmash:items:resultList:18:j_idt606",widgetVar:"widget_formSmash_items_resultList_18_j_idt606",onLabel:"Abylayeva, A. M. ",offLabel:"Abylayeva, A. M. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt609",{id:"formSmash:items:resultList:18:j_idt609",widgetVar:"widget_formSmash_items_resultList_18_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); L. N.Gumilev Eurasian National University, Khazakstan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Baiarystanov, A. O.L. N.Gumilev Eurasian National University, Khazakstan.Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT The Artic University of Norway, Norway.Wall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:18:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels2017Inngår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, nr 3, s. 683-694Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_18_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:18:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_18_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Inequalities of the formkuK f kq 6C(kr f kp +kvH f kp) , f > 0,are considered, where K is an integral operator of Volterra type and H is the Hardy operator.Under some assumptions on the kernel K we give necessary and sufficient conditions for suchan inequality to hold.1

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:18:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_18_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:18:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_18_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:18:j_idt869:0:fullText"});}); 20. Inequalities for some classes of Hardy type operators and compactness in weighted Lebesgue spaces Abylayeva, Akbota PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt606",{id:"formSmash:items:resultList:19:j_idt606",widgetVar:"widget_formSmash_items_resultList_19_j_idt606",onLabel:"Abylayeva, Akbota ",offLabel:"Abylayeva, Akbota ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:19:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Inequalities for some classes of Hardy type operators and compactness in weighted Lebesgue spaces2016Doktoravhandling, med artikler (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_19_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:19:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_19_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This PhD thesis is devoted to investigate weighted differential Hardy inequalities and Hardy-type inequalities with the kernel when the kernel has an integrable singularity, and also the additivity of the estimate of a Hardy type operator with a kernel.The thesis consists of seven papers (Papers 1, 2, 3, 4, 5, 6, 7) and an introduction where a review on the subject of the thesis is given. In Paper 1 weighted differential Hardy type inequalities are investigated on the set of compactly supported smooth functions, where necessary and sufficient conditions on the weight functions are established for which this inequality and two-sided estimates for the best constant hold. In Papers 2, 3, 4 a more general class of -order fractional integrationoperators are considered including the well-known classical Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard operators. Here 0 < < 1. In Papers 2 and 3 the boundedness and compactness of two classes of such operators are investigated namely of Weyl and Riemann-Liouville type, respectively, in weighted Lebesgue spaces for 1 < p ≤ q < 1 and 0 < q < p < ∞. As applications some new results for the fractional integration operators of Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard are given and discussed.In Paper 4 the Riemann-Liouville type operator with variable upper limit is considered. The main results are proved by using a localization method equipped with the upper limit function and the kernel of the operator. In Papers 5 and 6 the Hardy operator with kernel is considered, where the kernel has a logarithmic singularity. The criteria of the boundedness and compactness of the operator in weighted Lebesgue spaces are given for 1 < p ≤ q < ∞ and 0 < q < p < ∞, respectively. In Paper 7 we investigated the weighted additive estimates for integral operators K

^{+}and K¯ defined byK

^{+}ƒ(x) := ∫ k(x,s) ƒ(s)ds, K¯ ƒ(x) := ∫ k(x,s)ƒ(s)ds.It is assumed that the kernel k of the operators K

^{+}and K^{- }belongs to the general Oinarov class. We derived the criteria for the validity of these addittive estimates when 1 ≤ p≤ q < ∞PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:19:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_19_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:19:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_19_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:19:j_idt869:0:fullText"});}); 21. Boundedness and compactness of a class of Hardy type operators Abylayeva, Akbota M. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt606",{id:"formSmash:items:resultList:20:j_idt606",widgetVar:"widget_formSmash_items_resultList_20_j_idt606",onLabel:"Abylayeva, Akbota M. ",offLabel:"Abylayeva, Akbota M. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt609",{id:"formSmash:items:resultList:20:j_idt609",widgetVar:"widget_formSmash_items_resultList_20_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Oinarov, RyskulDepartment of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana.Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:20:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Boundedness and compactness of a class of Hardy type operators2016Inngår i: Journal of inequalities and applications, ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikkel-id 324Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_20_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:20:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_20_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We establish characterizations of both boundedness and of compactness of a general class of fractional integral operators involving the Riemann-Liouville, Hadamard, and Erdelyi-Kober operators. In particular, these results imply new results in the theory of Hardy type inequalities. As applications both new and well-known results are pointed out.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:20:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 22. Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities Abylayeva, Akbota M. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt606",{id:"formSmash:items:resultList:21:j_idt606",widgetVar:"widget_formSmash_items_resultList_21_j_idt606",onLabel:"Abylayeva, Akbota M. ",offLabel:"Abylayeva, Akbota M. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt609",{id:"formSmash:items:resultList:21:j_idt609",widgetVar:"widget_formSmash_items_resultList_21_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan .PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, Tromso, Norway. RUDN University, Moscow, Russia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:21:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 1, s. 201-215, artikkel-id 21-16Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_21_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:21:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_21_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We establish criteria for both boundedness and compactness for some classes of integraloperators with logarithmic singularities in weighted Lebesgue spaces for cases 1 < p 6 q <¥ and 1 < q < p < ¥. As corollaries some corresponding new Hardy inequalities are pointedout.1

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:21:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 23. On a new class of Hardy-type inequalities Adeleke, E.O. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt606",{id:"formSmash:items:resultList:22:j_idt606",widgetVar:"widget_formSmash_items_resultList_22_j_idt606",onLabel:"Adeleke, E.O. ",offLabel:"Adeleke, E.O. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt609",{id:"formSmash:items:resultList:22:j_idt609",widgetVar:"widget_formSmash_items_resultList_22_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, University of Agriculture, Abeokuta, Ogun State P. M. B. 2240, Nigeria.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Čižmešija, A.Department of Mathematics, University of Zagreb, Bijenička cesta 30, Zagreb, 10000, Croatia.Oguntuase, James A.Department of Mathematics, University of Agriculture, Abeokuta, Ogun State P. M. B. 2240, Nigeria.Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Narvik University College, P.O. Box 385, Narvik, N-8505, Norway.Pokaz, D.Faculty of Civil Engineering, University of Zagreb, Kačićeva 26, Zagreb, 10000, Croatia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:22:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On a new class of Hardy-type inequalities2012Inngår i: Journal of inequalities and applications, ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, nr 259Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_22_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:22:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_22_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); In this paper, we generalize a Hardy-type inequality to the class of arbitrary non-negative functions bounded from below and above with a convex function multiplied with positive real constants. This enables us to obtain new generalizations of the classical integral Hardy's, Hardy-Hilbert's, Hardy-Littlewood-P\'{o}lya's and P\'{o}lya-Knopp's inequalities as well as of Godunova's and of some recently obtained inequalities in multidimensional settings. Finally, we apply a similar idea to functions bounded from below and above with a superquadratic function.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:22:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 24. Selected papers of the international workshop on difference and differential inequalities, Gebze, Kocaeli, Turkey, July 3--7, 1996 Agarwal, R.P.et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_23_j_idt609",{id:"formSmash:items:resultList:23:j_idt609",widgetVar:"widget_formSmash_items_resultList_23_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Zafer, A.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:23:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Selected papers of the international workshop on difference and differential inequalities, Gebze, Kocaeli, Turkey, July 3--7, 19961998Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 1, nr 3, s. 347-461Artikkel i tidsskrift (Fagfellevurdert)25. Coercive estimates for the solutions of some singular differential equations and their applications Akhmetkaliyeva, Raya PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt606",{id:"formSmash:items:resultList:24:j_idt606",widgetVar:"widget_formSmash_items_resultList_24_j_idt606",onLabel:"Akhmetkaliyeva, Raya ",offLabel:"Akhmetkaliyeva, Raya ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Fundamental and Applied Mathematics, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:24:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Coercive estimates for the solutions of some singular differential equations and their applications2013Licentiatavhandling, med artikler (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_24_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:24:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_24_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This Licentiate thesis deals with the study of existence and uniqueness together with coercive estimates for solutions of certain differential equations. The thesis consists of four papers (papers A, B, C and D) and an introduction, which put these papers into a more general frame and which also serves as an overview of this interesting field of mathematics. In the text below the functions r(x), q(x), m(x) etc. are functions on (-∞,+∞), which are different but well defined in each paper. In paper A we study the separation and approximation properties for the differential operator ly=-y″+r(x)y′+q(x)y in the Hilbert space L2 :=L2(R), R=(-∞,+∞), as well as the existence problem for a second order nonlinear differential equation in L2 . Paper B deals with the study of separation and approximation properties for the differential operator ly=-y″+r(x)y′+s(x)‾y′ in the Hilbert spaceL2:=L2(R), R=(-∞,+∞), (here ¯y is the complex conjugate of y). A coercive estimate for the solution of the second order differential equation ly =f is obtained and its applications to spectral problems for the corresponding differential operatorlis demonstrated. Some sufficient conditions for the existence of the solutions of a class of nonlinear second order differential equations on the real axis are obtained. In paper C we study questions of the existence and uniqueness of solutions of the third order differential equation (L+λE)y:=-m(x)(m(x)y′)″+[q(x)+ir(x)+λ]y=f(x), (0.1) and conditions, which provide the following estimate: ||m(x)(m(x)y′)″||pp+||(q(x)+ir(x)+λ)y||pp≤ c||f(x)||pp for a solution y of (0.1). Paper D is devoted to the study of the existence and uniqueness for the solutions of the following more general third order differential equation with unbounded coefficients: -μ1(x)(μ2(x)(μ1(x)y′)′)′+(q(x)+ir(x)+λ)y=f(x). Some new existence and uniqueness results are proved and some normestimates of the solutions are given.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:24:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_24_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:24:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_24_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:24:j_idt869:0:fullText"});}); 26. Maximal regularity of the solutions for some degenerate differential equations and their applications Akhmetkaliyeva, Raya PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt606",{id:"formSmash:items:resultList:25:j_idt606",widgetVar:"widget_formSmash_items_resultList_25_j_idt606",onLabel:"Akhmetkaliyeva, Raya ",offLabel:"Akhmetkaliyeva, Raya ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Fundamental and Applied Mathematics, Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana 010000, Kazakhstan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:25:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Maximal regularity of the solutions for some degenerate differential equations and their applications2018Doktoravhandling, med artikler (Annet vitenskapelig)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_25_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:25:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_25_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This PhD thesis deals with the study of existence and uniqueness together with coercive estimates for solutions of certain differential equations.

The thesis consists of six papers (papers A, B, C, D, E and F), two appendices and an introduction, which put these papers and appendices into a more general frame and which also serves as an overview of this interesting field of mathematics.

In the text below the functionsr = r(x), q = q(x), m = m(x) etc. are functions on (−∞,+∞), which are different but well defined in each paper. Paper A deals with the study of separation and approximation properties for the differential operator

in the Hilbert space (here is the complex conjugate of ). A coercive estimate for the solution of the second order differential equation is obtained and its applications to spectral problems for the corresponding differential operator is demonstrated. Some sufficient conditions for the existence of the solutions of a class of nonlinear second order differential equations on the real axis are obtained.

In paper B necessary and sufficient conditions for the compactness of the resolvent of the second order degenerate differential operator in is obtained. We also discuss the two-sided estimates for the radius of fredholmness of this operator.

In paper C we consider the minimal closed differential operator

in , where are continuously differentiable functions, and is a continuous function. In this paper we show that the operator is continuously invertible when these coefficients satisfy some suitable conditions and obtain the following estimate for :

,

where is the domain of .

In papers D, E, and F various differential equations of the third order of the form

are studied in the space .

In paper D we investigate the case when and .

Moreover, in paper E the equation (0.1) is studied when . Finally, in paper F the equation (0.1) is investigated under certain additional conditions on .

For these equations we establish sufficient conditions for the existence and uniqueness of the solution, and also prove an estimate of the form

for the solution of equation (0.1).

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:25:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_25_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:25:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_25_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:25:j_idt869:0:fullText"});}); 27. Coersive solvability of the differential equation of the third order with complex valued coefficients Akhmetkaliyeva, Raya D.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:26:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Coersive solvability of the differential equation of the third order with complex valued coefficients2013Inngår i: Vestnik ENU, Vol. 95, nr 4, s. 355-361Artikkel i tidsskrift (Fagfellevurdert)28. On Solvability of Third-Order Singular Differential Equation Akhmetkaliyeva, Raya D. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_27_j_idt606",{id:"formSmash:items:resultList:27:j_idt606",widgetVar:"widget_formSmash_items_resultList_27_j_idt606",onLabel:"Akhmetkaliyeva, Raya D. ",offLabel:"Akhmetkaliyeva, Raya D. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); L.N. Gumilyov Eurasian National University, 2 Satpayev Str., Astana, 010008, Kazakhstan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:27:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On Solvability of Third-Order Singular Differential Equation2017Inngår i: Functional Analysis in Interdisciplinary Applications: Astana, Kazakhstan, October 2017 / [ed] Tynysbek Sh. Kalmenov; Erlan D. Nursultanov; Michael V. Ruzhansky; Makhmud A. Sadybekov, Springer, 2017, s. 106-112Konferansepaper (Fagfellevurdert)29. Compactness of the Resolvent of One Second Order Differential Operator Akhmetkaliyeva, Raya D. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt606",{id:"formSmash:items:resultList:28:j_idt606",widgetVar:"widget_formSmash_items_resultList_28_j_idt606",onLabel:"Akhmetkaliyeva, Raya D. ",offLabel:"Akhmetkaliyeva, Raya D. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_28_j_idt609",{id:"formSmash:items:resultList:28:j_idt609",widgetVar:"widget_formSmash_items_resultList_28_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Ospanov, K. N.Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan.Zulkhazhav, A.Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, 010008, Kazakhstan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:28:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Compactness of the Resolvent of One Second Order Differential Operator2014Inngår i: 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (ICNPAA 2014) / [ed] Sivasundaram, Seenith, American Institute of Physics (AIP), 2014, Vol. 1637, nr 1, s. 13-17, artikkel-id 13Konferansepaper (Fagfellevurdert)30. Some new results concerning a class of third-order differential equations Akhmetkaliyeva, Raya D. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt606",{id:"formSmash:items:resultList:29:j_idt606",widgetVar:"widget_formSmash_items_resultList_29_j_idt606",onLabel:"Akhmetkaliyeva, Raya D. ",offLabel:"Akhmetkaliyeva, Raya D. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt609",{id:"formSmash:items:resultList:29:j_idt609",widgetVar:"widget_formSmash_items_resultList_29_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Pure Mathematics, Eurasian National University, Munaytpassov k., 13, Astana,010008, Kazakhstan.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Mathematics, Narvik University College,Postboks 385, Narvik 8505, Norway.Ospanov, K.N.Department of Pure Mathematics, Eurasian National University, Munaytpassov k., 13, Astana,010008, Kazakhstan.Wall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:29:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Some new results concerning a class of third-order differential equations2015Inngår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 94, nr 2, s. 419-434Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_29_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:29:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_29_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We consider the following third-order differential equation with unbounded coefficients:Some new existence and uniqueness results are proved, and precise estimates of the norms of the solutions are given. The obtained results may be regarded as a unification and extension of all other results of this type

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:29:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 31. Real interpolation and measure of weak noncompactness Aksoy, A. G. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt606",{id:"formSmash:items:resultList:30:j_idt606",widgetVar:"widget_formSmash_items_resultList_30_j_idt606",onLabel:"Aksoy, A. G. ",offLabel:"Aksoy, A. G. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt609",{id:"formSmash:items:resultList:30:j_idt609",widgetVar:"widget_formSmash_items_resultList_30_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, Claremont McKenna College.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Maligranda, LechLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:30:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Real interpolation and measure of weak noncompactness1995Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 175, nr 1, s. 5-12Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_30_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:30:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_30_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Behavior of weak measures of noncompactness under real interpolation is investigated. It is shown that "convexity type" theorems hold true for weak measures of noncompactness.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:30:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)FULLTEXT01$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_30_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:30:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_30_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:30:j_idt869:0:fullText"});}); 32. Lipschitz-Orlicz Spaces and the Laplace Equation Aksoy, A.G. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt606",{id:"formSmash:items:resultList:31:j_idt606",widgetVar:"widget_formSmash_items_resultList_31_j_idt606",onLabel:"Aksoy, A.G. ",offLabel:"Aksoy, A.G. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt609",{id:"formSmash:items:resultList:31:j_idt609",widgetVar:"widget_formSmash_items_resultList_31_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics Claremont McKenna College Claremont, CA 91711 USA.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Maligranda, LechLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:31:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Lipschitz-Orlicz Spaces and the Laplace Equation1996Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 178, nr 1, s. 81-101Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_31_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:31:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_31_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Stein and Taibleson gave a characterization for f ϵ L

_{p}(ℝ^{n}) to be in the spaces Lip (α, L_{p}) and Zyg(α, L_{p}) in terms of their Poisson integrals. In this paper we extend their results to Lipschitz-Orlicz spaces Lip (α, L_{m}) and Zygmund-Orlicz spaces Zyg (φ, L_{m}) and to the general function φ ϵ P instead of the power function φ(t)= t^{α}. Such results describe the behavior of the Laplace equation in terms of the smoothness property of differences of f in Orlicz spaces L_{m}(IR^{n}). More general spaces δ^{k}(φ,X, q) are also considered.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:31:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_31_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:31:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_31_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:31:j_idt869:0:fullText"});}); 33. Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space Alaee, Aghil PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt606",{id:"formSmash:items:resultList:32:j_idt606",widgetVar:"widget_formSmash_items_resultList_32_j_idt606",onLabel:"Alaee, Aghil ",offLabel:"Alaee, Aghil ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt609",{id:"formSmash:items:resultList:32:j_idt609",widgetVar:"widget_formSmash_items_resultList_32_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics and Computer Science, Clark University, Worcester, Massachusetts; Center of Mathematical Sciences and Applications, Harvard University, Cambridge, Massachusetts.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Cabrera Pacheco, ArmandoDepartment of Mathematics, Universität Tübingen, 72076 Tübingen, Germany.McCormick, StephenMatematiska institutionen, Uppsala universitet, 751 06 Uppsala, Sweden.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:32:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space2021Inngår i: Transactions of the American Mathematical Society, ISSN 0002-9947, E-ISSN 1088-6850, Vol. 374, nr 5, s. 3535-3555Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_32_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:32:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_32_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We present a quasi-local version of the stability of the positive mass theorem. We work with the Brown–York quasi-local mass as it possesses positivity and rigidity properties, and therefore the stability of this rigidity statement can be studied. Specifically, we ask if the Brown–York mass of the boundary of some compact manifold is close to zero, must the manifold be close to a Euclidean domain in some sense?

Here we consider a class of compact -manifolds with boundary that can be realized as graphs in , and establish the following. If the Brown–York mass of the boundary of such a compact manifold is small, then the manifold is close to a Euclidean hyperplane with respect to the Federer–Fleming flat distance.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:32:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 34. Pseudo-Differential Operators with Point Interactions Albeverino, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt606",{id:"formSmash:items:resultList:33:j_idt606",widgetVar:"widget_formSmash_items_resultList_33_j_idt606",onLabel:"Albeverino, S. ",offLabel:"Albeverino, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt609",{id:"formSmash:items:resultList:33:j_idt609",widgetVar:"widget_formSmash_items_resultList_33_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, Ruhr University Bochum, D 44780, Bochum, Germany; SFB 237 Essen-Bochum-Düsseldorf, Germany; BiBoS Research Center, D 33615, Bielefeld, Germany; CERFIM, Locarno, Switzerland.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kurasov, PavelLuleå tekniska universitet. Department of Mathematics, Ruhr University Bochum, D 44780, Bochum, Germany; Mathematical Institute, Stockholm University, 10691, Stockholm, Sweden; Department of Physics, St. Petersburg University, 198904, St. Petersburg, Russia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:33:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Pseudo-Differential Operators with Point Interactions1997Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 41, nr 1, s. 79-92Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_33_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:33:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_33_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Point interactions for pseudo-differential operators are studied. Necessary and sufficient conditions for a pseudo-differential operator to have nontrivial point perturbations are given. The results are applied to the construction of relativistic spin zero Hamiltonians with point interactions.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:33:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 35. Symmetries of Schrödinger operator with point interactions Albeverio, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt606",{id:"formSmash:items:resultList:34:j_idt606",widgetVar:"widget_formSmash_items_resultList_34_j_idt606",onLabel:"Albeverio, S. ",offLabel:"Albeverio, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt609",{id:"formSmash:items:resultList:34:j_idt609",widgetVar:"widget_formSmash_items_resultList_34_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Institute of Mathematics, Ruhr-Universität, D-44780 Bochum.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Dabrowski, L.SISSA.Kurasov, PavelLuleå tekniska universitet.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:34:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Symmetries of Schrödinger operator with point interactions1998Inngår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 45, nr 1, s. 33-47Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_34_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:34:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_34_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The transformations of all the Schrödinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling Wλ are presented. In particular, those operators which are invariant (possibly up to a scale) are selected. Some recent papers on related topics are commented upon

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:34:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 36. Many body problems with "spin"-related contact interactions Albeverio, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt606",{id:"formSmash:items:resultList:35:j_idt606",widgetVar:"widget_formSmash_items_resultList_35_j_idt606",onLabel:"Albeverio, S. ",offLabel:"Albeverio, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt609",{id:"formSmash:items:resultList:35:j_idt609",widgetVar:"widget_formSmash_items_resultList_35_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Institut für Angewandte Mathematik, Universität Bonn.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fei, S-MInstitut für Angewandte Mathematik, Universität Bonn.Kurasov, PavelLuleå tekniska universitet.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:35:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Many body problems with "spin"-related contact interactions2001Inngår i: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 47, nr 2, s. 157-166Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_35_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:35:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_35_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the integrability of N-body systems with δ-interactions and point spin couplings. Bethe ansatz solutions, bound states and scattering matrices are explicitly given. The cases of generalized separated boundary condition and some Hamiltonian operators corresponding to special spin related boundary conditions are also discussed.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:35:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 37. S-matrix, resonances, and wave functions for transport through billiards with leads Albeverio, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt606",{id:"formSmash:items:resultList:36:j_idt606",widgetVar:"widget_formSmash_items_resultList_36_j_idt606",onLabel:"Albeverio, S. ",offLabel:"Albeverio, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt609",{id:"formSmash:items:resultList:36:j_idt609",widgetVar:"widget_formSmash_items_resultList_36_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); BiBoS Research Center.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Haake, F.Fachbereich Physik, Universität-GH Essen.Kurasov, PavelLuleå tekniska universitet.Kus, M.Fachbereich Physik, Universität-GH Essen.Šeba, P.Nuclear Physics Institute, Czech Academy of Sciences.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:36:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); S-matrix, resonances, and wave functions for transport through billiards with leads1996Inngår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 37, nr 10, s. 4888-4903Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_36_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:36:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_36_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:36:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 38. Rank one perturbations, approximations, and selfadjoint extensions Albeverio, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt606",{id:"formSmash:items:resultList:37:j_idt606",widgetVar:"widget_formSmash_items_resultList_37_j_idt606",onLabel:"Albeverio, S. ",offLabel:"Albeverio, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_37_j_idt609",{id:"formSmash:items:resultList:37:j_idt609",widgetVar:"widget_formSmash_items_resultList_37_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, Ruhr-University Bochum, Germany; SFB 237, Germany; BIBoS Research Center, Germany; CERFIM, Switzerland.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kurasov, P.Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Mathematics, Ruhr-University Bochum, Germany; Department of Mathematical and Computational Physics, St. Petersburg University, 198904, St. Petersburg, Russia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:37:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Rank one perturbations, approximations, and selfadjoint extensions1997Inngår i: Journal of Functional Analysis, ISSN 0022-1236, E-ISSN 1096-0783, Vol. 148, nr 1, s. 152-169Artikkel i tidsskrift (Fagfellevurdert)39. Finite rank perturbations and distribution theory Albeverio, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt606",{id:"formSmash:items:resultList:38:j_idt606",widgetVar:"widget_formSmash_items_resultList_38_j_idt606",onLabel:"Albeverio, S. ",offLabel:"Albeverio, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt609",{id:"formSmash:items:resultList:38:j_idt609",widgetVar:"widget_formSmash_items_resultList_38_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, Ruhr-University Bochum, Bochum, Germany; SFB 237 Essen-Bochum-Düsseldorf, Germany; BiBoS Research Center, Bielefeld, Germany; CERFIM, Locarno, Switzerland.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kurasov, PavelLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Mathematics, Stockholm University, Stockholm, Sweden; Department of Mathematics, Ruhr-University Bochum, Bochum, Germany; Department of Mathematical and Computational Physics, St.Petersburg University, St.Petersburg, Russia.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:38:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Finite rank perturbations and distribution theory1999Inngår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 127, nr 4, s. 1151-1161Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_38_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:38:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_38_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Perturbations A

_{T}of a selfadjoint operator A by symmetric finite rank operators T from H_{2}A) to H_{-2}(A) are studied. The finite dimensional family of selfadjoint extensions determined by A_{T}is given explicitly.PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:38:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 40. Rank one perturbations of not semibounded operators Albeverio, S. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt606",{id:"formSmash:items:resultList:39:j_idt606",widgetVar:"widget_formSmash_items_resultList_39_j_idt606",onLabel:"Albeverio, S. ",offLabel:"Albeverio, S. ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt609",{id:"formSmash:items:resultList:39:j_idt609",widgetVar:"widget_formSmash_items_resultList_39_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Department of Mathematics, Ruhr-University, Bochum.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Kurasov, PavelLuleå tekniska universitet.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:39:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Rank one perturbations of not semibounded operators1997Inngår i: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 27, nr 4, s. 379-400Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_39_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:39:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_39_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Rank one perturbations of selfadjoint operators which are not necessarily semibounded are studied in the present paper. It is proven that such perturbations are uniquely defined, if they are bounded in the sense of forms. We also show that form unbounded rank one perturbations can be uniquely defined if the original operator and the perturbation are homogeneous with respect to a certain one parameter semigroup. The perturbed operator is defined using the extension theory for symmetric operators. The resolvent of the perturbed operator is calculated using Krein's formula. It is proven that every rank one perturbation can be approximated in the operator norm. We prove that some form unbounded perturbations can be approximated in the strong resolvent sense without renormalization of the coupling constant only if the original operator is not semibounded. The present approach is applied to study first derivative and Dirac operators with point interaction, in one dimension

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:39:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 41. Sur le comportement asymptotique du noyau associé à une diffusion dégénérée Albeverio, Sergioet al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_40_j_idt609",{id:"formSmash:items:resultList:40:j_idt609",widgetVar:"widget_formSmash_items_resultList_40_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Hilbert, AstridLuleå tekniska universitet.Kolokoltsov, VassilyPrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:40:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Sur le comportement asymptotique du noyau associé à une diffusion dégénérée2000Inngår i: Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science, ISSN 0706-1994, Vol. 22, nr 4, s. 151-159Artikkel i tidsskrift (Fagfellevurdert)42. Co-creation and critical factors for the development of an efficient public e-tourism system Alharmoodi, Ahmed Abdulla PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt606",{id:"formSmash:items:resultList:41:j_idt606",widgetVar:"widget_formSmash_items_resultList_41_j_idt606",onLabel:"Alharmoodi, Ahmed Abdulla ",offLabel:"Alharmoodi, Ahmed Abdulla ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt609",{id:"formSmash:items:resultList:41:j_idt609",widgetVar:"widget_formSmash_items_resultList_41_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); College of Business, Abu Dhabi University, Abu Dhabi, United Arab Emirates.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Khan, MehmoodCollege of Business, University of Sharjah, Sharjah, United Arab Emirates.Mertzanis, CharilaosCollege of Business, Abu Dhabi University, Abu Dhabi, United Arab Emirates.Gupta, ShivamDepartment of Information Systems, Supply Chain Management & Decision Support, NEOMA Business School, Reims, France.Mikalef, PatrickDepartment of Computer Science, Faculty of Information Technology and Electrical Engineering, Norwegian University of Science and Technology, Norway; Department of Technology Management, SINTEF Digital, Trondheim, Norway; School of Economics and Business, University of Ljubljana, Ljubljana, Slovenia.Parida, VinitLuleå tekniska universitet, Institutionen för ekonomi, teknik, konst och samhälle, Industriell ekonomi. Department of Management, University of Vaasa, Vaasa, Finland.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:41:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Co-creation and critical factors for the development of an efficient public e-tourism system2024Inngår i: Journal of Business Research, ISSN 0148-2963, E-ISSN 1873-7978, Vol. 174, artikkel-id 114519Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_41_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:41:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_41_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This study identifies the factors that guide the adoption of a public e-tourism system resulting in value co-creation in the UAE. Integrating and comparing factors drawn from the third version of the Technology Acceptance Model (TAM3), the Technology-Task-Fit (TTF) theory, and push-to-use, an Analytic Hierarch Process (AHP) model was implemented with data collected using a structured questionnaire from purposively selected UAE e-tourism experts (N = 15) and analyzed using Microsoft Excel. The findings revealed that usefulness, convenience of use, and push-to-use were the most critical aspects for achieving an efficient public e-tourism system that allows for value co-creation in that order of ranking. The findings also suggest that computer self-efficiency is the most critical factor in effectively establishing an e-tourism system followed by government push-to-use. In conclusion, the findings demonstrate that usefulness and ease-of-use backed by computer self-efficiency, result demonstrability, and output quality are vital for the efficient adoption of a public e-tourism system resulting in value co-creation in the UAE.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:41:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_41_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:41:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_41_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:41:j_idt869:0:fullText"});}); 43. On lower-dimensional models in lubrication, Part B Almqvist, Andreas PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt606",{id:"formSmash:items:resultList:42:j_idt606",widgetVar:"widget_formSmash_items_resultList_42_j_idt606",onLabel:"Almqvist, Andreas ",offLabel:"Almqvist, Andreas ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt609",{id:"formSmash:items:resultList:42:j_idt609",widgetVar:"widget_formSmash_items_resultList_42_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Burtseva, EvgeniyaLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Rajagopal, K.Department of Mechanical Engineering, Texas AM University, Texas, United States.Wall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:42:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On lower-dimensional models in lubrication, Part B: Derivation of a Reynolds type of equation for incompressible piezo-viscous fluids2021Inngår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 235, nr 8, s. 1703-1718Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_42_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:42:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_42_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The Reynolds equation is a lower-dimensional model for the pressure in a fluid confined between two adjacent surfaces that move relative to each other. It was originally derived under the assumption that the fluid is incompressible and has constant viscosity. In the existing literature, the lower-dimensional Reynolds equation is often employed as a model for the thin films, which lubricates interfaces in various machine components. For example, in the modelling of elastohydrodynamic lubrication (EHL) in gears and bearings, the pressure dependence of the viscosity is often considered by just replacing the constant viscosity in the Reynolds equation with a given viscosity-pressure relation. The arguments to justify this are heuristic, and in many cases, it is taken for granted that you can do so. This motivated us to make an attempt to formulate and present a rigorous derivation of a lower-dimensional model for the pressure when the fluid has pressure-dependent viscosity. The results of our study are presented in two parts. In Part A, we showed that for incompressible and piezo-viscous fluids it is not possible to obtain a lower-dimensional model for the pressure by just assuming that the film thickness is thin, as it is for incompressible fluids with constant viscosity. Here, in Part B, we present a method for deriving lower-dimensional models of thin-film flow, where the fluid has a pressure-dependent viscosity. The main idea is to rescale the generalised Navier-Stokes equation, which we obtained in Part A based on theory for implicit constitutive relations, so that we can pass to the limit as the film thickness goes to zero. If the scaling is correct, then the limit problem can be used as the dimensionally reduced model for the flow and it is possible to derive a type of Reynolds equation for the pressure.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:42:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 44. On flow of power-law fluids between adjacent surfaces Almqvist, Andreas PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt606",{id:"formSmash:items:resultList:43:j_idt606",widgetVar:"widget_formSmash_items_resultList_43_j_idt606",onLabel:"Almqvist, Andreas ",offLabel:"Almqvist, Andreas ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt609",{id:"formSmash:items:resultList:43:j_idt609",widgetVar:"widget_formSmash_items_resultList_43_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Burtseva, EvgeniyaLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Rajagopal, KumbakonamJ. Mike Walker’66 Department of Mechanical Engineering, Texas A&M University, 100 Mechanical Engineering, Office Building, 3123 TAMU, College Station, TX 77843-3123, TX, USA.Wall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:43:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On flow of power-law fluids between adjacent surfaces: Why is it possible to derive a Reynolds-type equation for pressure-driven flow, but not for shear-driven flow?2023Inngår i: Applications in Engineering Science, ISSN 2666-4968, Vol. 15, artikkel-id 100145Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_43_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:43:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_43_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Flows of incompressible NavierâStokes (Newtonian) fluids between adjacent surfaces are encountered in numerous practical applications, such as seal leakage and bearing lubrication. In seals, the flow is primarily pressure-driven, whereas, in bearings, the dominating driving force is due to shear. The governing NavierâStokes system of equations can be significantly simplified due to the small distance between the surfaces compared to their size. From the simplified system, it is possible to derive a single lower-dimensional equation, known as the Reynolds equation, which describes the pressure field. Once the pressure field is computed, it can be used to determine the velocity field. This computational algorithm is much simpler to implement than a direct numerical solution of the NavierâStokes equations and is therefore widely employed by engineers. The primary objective of this article is to investigate the possibility of deriving a type of Reynolds equation also for non-Newtonian fluids, using the balance of linear momentum. By considering power-law fluids we demonstrate that it is not possible for shear-driven flows, whereas it is feasible for pressure-driven flows. Additionally, we demonstrate that in the full 3D model, a normal stress boundary condition at the inlet/outlet implies a Dirichlet condition for the pressure in the Reynolds equation associated with pressure-driven flow. Furthermore, we establish that a Dirichlet condition for the velocity at the inlet/outlet in the 3D model results in a Neumann condition for the pressure in the Reynolds equation.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:43:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_43_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:43:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_43_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:43:j_idt869:0:fullText"});}); 45. On lower-dimensional models in lubrication, Part A Almqvist, Andreas PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt606",{id:"formSmash:items:resultList:44:j_idt606",widgetVar:"widget_formSmash_items_resultList_44_j_idt606",onLabel:"Almqvist, Andreas ",offLabel:"Almqvist, Andreas ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt609",{id:"formSmash:items:resultList:44:j_idt609",widgetVar:"widget_formSmash_items_resultList_44_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Burtseva, EvgeniyaLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Rajagopal, KumbakonamDepartment of Mechanical Engineering, Texas A&M University, Texas, USA.Wall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:44:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On lower-dimensional models in lubrication, Part A: Common misinterpretations and incorrect usage of the Reynolds equation2021Inngår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 235, nr 8, s. 1692-1702Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_44_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:44:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_44_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Most of the problems in lubrication are studied within the context of Reynolds’ equation, which can be derived by writing the incompressible Navier-Stokes equation in a dimensionless form and neglecting terms which are small under the assumption that the lubricant film is very thin. Unfortunately, the Reynolds equation is often used even though the basic assumptions under which it is derived are not satisfied. One example is in the mathematical modelling of elastohydrodynamic lubrication (EHL). In the EHL regime, the pressure is so high that the viscosity changes by several orders of magnitude. This is taken into account by just replacing the constant viscosity in either the incompressible Navier-Stokes equation or the Reynolds equation by a viscosity-pressure relation. However, there are no available rigorous arguments which justify such an assumption. The main purpose of this two-part work is to investigate if such arguments exist or not. In Part A, we formulate a generalised form of the Navier-Stokes equation for piezo-viscous incompressible fluids. By dimensional analysis of this equation we, thereafter, show that it is not possible to obtain the Reynolds equation, where the constant viscosity is replaced with a viscosity-pressure relation, by just neglecting terms which are small under the assumption that the lubricant film is very thin. The reason is that the lone assumption that the fluid film is very thin is not enough to neglect the terms, in the generalised Navier-Stokes equation, which are related to the body forces and the inertia. However, we analysed the coefficients in front of these (remaining) terms and provided arguments for when they may be neglected. In Part B, we present an alternative method to derive a lower-dimensional model, which is based on asymptotic analysis of the generalised Navier-Stokes equation as the film thickness goes to zero.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:44:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 46. On lower-dimensional models of thin film flow, Part C: Derivation of a Reynolds type of equation for fluids with temperature and pressure dependent viscosity Almqvist, Andreas PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt606",{id:"formSmash:items:resultList:45:j_idt606",widgetVar:"widget_formSmash_items_resultList_45_j_idt606",onLabel:"Almqvist, Andreas ",offLabel:"Almqvist, Andreas ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt609",{id:"formSmash:items:resultList:45:j_idt609",widgetVar:"widget_formSmash_items_resultList_45_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Burtseva, EvgeniyaLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Rajagopal, KumbakonamDepartment of Mechanical Engineering, Texas A&M University, College Station, TX, USA.Wall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:45:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); On lower-dimensional models of thin film flow, Part C: Derivation of a Reynolds type of equation for fluids with temperature and pressure dependent viscosity2023Inngår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 237, nr 3, s. 514-526Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_45_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:45:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_45_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper constitutes the third part of a series of works on lower-dimensional models in lubrication. In Part A, it was shown that implicit constitutive theory must be used in the modelling of incompressible fluids with pressure-dependent viscosity and that it is not possible to obtain a lower-dimensional model for the pressure just by letting the film thickness go to zero, as in the proof of the classical Reynolds equation. In Part B, a new method for deriving lower-dimensional models of thin-film flow of fluids with pressure-dependent viscosity was presented. Here, in Part C, we also incorporate the energy equation so as to include fluids with both temperature and pressure dependent viscosity. By asymptotic analysis of this system, as the film thickness goes to zero, we derive a simplified model of the flow. We also carry out an asymptotic analysis of the boundary condition, in the case where the normal stress is specified on one part of the boundary and the velocity on the remaining part.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:45:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Fulltekst (pdf)fulltext$(function(){PrimeFaces.cw("Tooltip","widget_formSmash_items_resultList_45_j_idt869_0_j_idt872",{id:"formSmash:items:resultList:45:j_idt869:0:j_idt872",widgetVar:"widget_formSmash_items_resultList_45_j_idt869_0_j_idt872",showEffect:"fade",hideEffect:"fade",target:"formSmash:items:resultList:45:j_idt869:0:fullText"});}); 47. New insights on lubrication theory for compressible fluids Almqvist, Andreas PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt606",{id:"formSmash:items:resultList:46:j_idt606",widgetVar:"widget_formSmash_items_resultList_46_j_idt606",onLabel:"Almqvist, Andreas ",offLabel:"Almqvist, Andreas ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt609",{id:"formSmash:items:resultList:46:j_idt609",widgetVar:"widget_formSmash_items_resultList_46_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Burtseva, EvgeniyaLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Ràfols, Francesc PérezLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.Wall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:46:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); New insights on lubrication theory for compressible fluids2019Inngår i: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 145, artikkel-id 103170Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_46_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:46:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_46_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); The fact that the film is thin is in lubrication theory utilised to simplify the full Navier–Stokes system of equations. For incompressible and iso-viscous fluids, it turns out that the inertial terms are small enough to be neglected. However, for a compressible fluid, we show that the influence of inertia depends on the (constitutive) density-pressure relationship and may not always be neglected. We consider a class of iso-viscous fluids obeying a power-law type of compressibility, which in particular includes both incompressible fluids and ideal gases. We show by scaling and asymptotic analysis, that the degree of compressibility determines whether the terms governing inertia may or may not be neglected. For instance, for an ideal gas, the inertial terms remain regardless of the film height-to-length ratio. However, by means of a specific modified Reynolds number that we define we show that the magnitudes of the inertial terms rarely are large enough to be influential. In addition, we consider fluids obeying the well-known Dowson and Higginson density-pressure relationship and show that the inertial terms can be neglected, which allows for obtaining a Reynolds type of equation. Finally, some numerical examples are presented in order to illustrate our theoretical results.

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:46:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 48. The homogenization process of the Reynolds equation describing compressible liquid flow Almqvist, Andreas PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt606",{id:"formSmash:items:resultList:47:j_idt606",widgetVar:"widget_formSmash_items_resultList_47_j_idt606",onLabel:"Almqvist, Andreas ",offLabel:"Almqvist, Andreas ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt609",{id:"formSmash:items:resultList:47:j_idt609",widgetVar:"widget_formSmash_items_resultList_47_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Dasht, JohanLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:47:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); The homogenization process of the Reynolds equation describing compressible liquid flow2006Inngår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 39, nr 9, s. 994-1002Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_47_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:47:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_47_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); This paper summarizes the homogenization process of rough, hydrodynamic lubrication problems governed by the Reynolds equation used to describe compressible liquid flow. Here, the homogenized equation describes the limiting result when the wavelength of a modeled surface roughness goes to zero. The lubricant film thickness is modeled by one part describing the geometry/shape of the bearing and a periodic part describing the surface topography/roughness. By varying the periodic part as well as its wavelength, we can try to systematically investigate the applicability of homogenization on this type of problem. The load carrying capacity is the target parameter; deterministic solutions are compared to homogenized by this measure. We show that the load carrying capacity rapidly converges to the homogenized results as the wavelength decreases, proving that the homogenized solution gives a very accurate representation of the problem when real surface topographies are considered

PrimeFaces.cw("Panel","tryPanel",{id:"formSmash:items:resultList:47:j_idt644:0:abstractPanel",widgetVar:"tryPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); 49. Homogenization of the Reynolds equation Almqvist, Andreas PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt606",{id:"formSmash:items:resultList:48:j_idt606",widgetVar:"widget_formSmash_items_resultList_48_j_idt606",onLabel:"Almqvist, Andreas ",offLabel:"Almqvist, Andreas ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_48_j_idt609",{id:"formSmash:items:resultList:48:j_idt609",widgetVar:"widget_formSmash_items_resultList_48_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Dasht, JohanGlavatskih, SergeiLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.Larsson, RolandLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.Marklund, PärLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.Persson, Lars-ErikLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Sahlin, FredrikWall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:48:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Homogenization of the Reynolds equation2005Rapport (Annet vitenskapelig)50. Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications Almqvist, Andreas PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt606",{id:"formSmash:items:resultList:49:j_idt606",widgetVar:"widget_formSmash_items_resultList_49_j_idt606",onLabel:"Almqvist, Andreas ",offLabel:"Almqvist, Andreas ",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); et al. PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt609",{id:"formSmash:items:resultList:49:j_idt609",widgetVar:"widget_formSmash_items_resultList_49_j_idt609",onLabel:"et al.",offLabel:"et al.",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:orgPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Essel, Emmanuel KwameDepartment of Mathematics and Statistics, University of Cape Coast.Fabricius, JohnLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.Wall, PeterLuleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.PrimeFaces.cw("Panel","testPanel",{id:"formSmash:items:resultList:49:etAlPanel",widgetVar:"testPanel",toggleable:true,toggleSpeed:500,collapsed:false,toggleOrientation:"vertical",closable:true,closeSpeed:500}); Multiscale homogenization of a class of nonlinear equations with applications in lubrication theory and applications2011Inngår i: Journal of Function Spaces and Applications, ISSN 0972-6802, E-ISSN 1758-4965, Vol. 9, nr 1, s. 17-40Artikkel i tidsskrift (Fagfellevurdert)Abstract [en] PrimeFaces.cw("SelectBooleanButton","widget_formSmash_items_resultList_49_j_idt644_0_j_idt645",{id:"formSmash:items:resultList:49:j_idt644:0:j_idt645",widgetVar:"widget_formSmash_items_resultList_49_j_idt644_0_j_idt645",onLabel:"Abstract [en]",offLabel:"Abstract [en]",onIcon:"ui-icon-triangle-1-s",offIcon:"ui-icon-triangle-1-e"}); We prove a homogenization result for monotone operators by using the method of multiscale convergence. More precisely, we study the asymptotic behavior as epsilon -> 0 of the solutions u(epsilon) of the nonlinear equation div a(epsilon)(x, del u(epsilon)) = div b(epsilon), where both a(epsilon) and b(epsilon) oscillate rapidly on several microscopic scales and a(epsilon) satisfies certain continuity, monotonicity and boundedness conditions. This kind of problem has applications in hydrodynamic thin film lubrication where the bounding surfaces have roughness on several length scales. The homogenization result is obtained by extending the multiscale convergence method to the setting of Sobolev spaces W-0(1,p)(Omega), where 1 < p < infinity. In particular we give new proofs of some fundamental theorems concerning this convergence that were first obtained by Allaire and Briane for the case p = 2.

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