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  • 1.
    Abdikalikova, Zamira
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Compactness of embedding between Sobolev type spaces with multiweighted derivatives2009Ingår i: AIHT : Analysis, Inequalities and Homogenization Theory: Midnight sun conference in honor of Lars-Erik Persson, 2009Konferensbidrag (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 2.
    Abdikalikova, Zamira
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Embedding theorems for spaces with multiweighted derivatives2007Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 3.
    Abdikalikova, Zamira
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives2009Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 4. Abdikalikova, Zamira
    et al.
    Baiarystanov, Askar O.
    Oinarov, Ryskul
    Compactness of embedding between spaces with multiweighted derivatives: the case 1 ≤ p ≤ q2009Rapport (Övrigt vetenskapligt)
  • 5.
    Abdikalikova, Zamira
    et al.
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Kalybay, Aigerim
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Summability of a Tchebysheff system of functions2007Rapport (Övrigt vetenskapligt)
  • 6.
    Abdikalikova, Zamira
    et al.
    L.N. Gumilyov Eurasian National University.
    Oinarov, Ryskul
    L.N. Gumilyov Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 12011Ingår i: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 61, nr 1, s. 7-26Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 7.
    Abdikalikova, Zamira
    et al.
    L.N. Gumilyov Eurasian National University.
    Oinarov, Ryskul
    L.N. Gumilyov Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1≤ q2009Rapport (Övrigt vetenskapligt)
  • 8.
    Abramovic, Shoshana
    et al.
    University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. University of Tromsø ; The Arctic University of Norway, Narvik.
    Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions2017Ingår i: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 102, nr 5-6, s. 599-609Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Abstract—Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.

  • 9.
    Abramovich, S.
    et al.
    Department of Mathematics, University of Haifa, Haifa, Israel.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UIT The Arctic University of Norway, Narvik, Norway.
    Extensions and Refinements of Fejer and Hermite–Hadamard Type Inequalities2018Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 3, s. 759-772Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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] .

  • 10.
    Abramovich, Shosana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 32014Ingår 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. 1-10Konferensbidrag (Refereegranskat)
    Abstract [en]

    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

  • 11.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Krulić, Kristina
    Faculty of Textile Technology, University of Zagreb.
    Pečarić, Josip
    Faculty of Textile Technology, University of Zagreb.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new refined Hardy type inequalities with general kernels and measures2010Ingår i: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 79, nr 1-2, s. 157-172Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 12.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Inequalities for averages of quasiconvex and superquadratic functions2016Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, nr 2, s. 535-550Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 13.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new estimates of the ‘Jensen gap’2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, artikel-id 39Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 14.
    Abramovich, Shoshana
    et al.
    University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new scales of refined Hardy type inequalities via functions related to superquadracity2013Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, nr 3, s. 679-695Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 15.
    Abramovich, Shoshana
    et al.
    University of Haifa, Department of Mathematics.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Pecaric, Josip
    University of Zagreb.
    Varosanec, Sanja
    University of Zagreb.
    General inequalities via isotonic subadditive functionals2007Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, nr 1, s. 15-28Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 16.
    Abramovich, Shoshana
    et al.
    University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On some new developments of Hardy-type inequalities2012Ingår 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. 739-746Konferensbidrag (Refereegranskat)
    Abstract [en]

    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.

  • 17.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities2015Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 18, nr 2, s. 615-627Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 18.
    Abramovich, Shoshana
    et al.
    Department of Mathematics, University of Haifa.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Samko, Natasha
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new scales of refined Jensen and Hardy type inequalities2014Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, nr 3, s. 1105-1114Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 19.
    Abylayeva, Akbota
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik.
    Inequalities for some classes of Hardy type operators and compactness in weighted Lebesgue spaces2016Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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 by

    K+ 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 < ∞

  • 20.
    Abylayeva, Akbota M.
    et al.
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .
    Oinarov, Ryskul
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Boundedness and compactness of a class of Hardy type operators2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikel-id 324Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 21.
    Abylayeva, Akbota M.
    et al.
    Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan .
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, Tromso, Norway. RUDN University, Moscow, Russia.
    Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 1, s. 201-215, artikel-id 21-16Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 22.
    Abylayeva, A.M.
    et al.
    L. N.Gumilev Eurasian National University, Khazakstan.
    Baiarystanov, A.O.
    L. N.Gumilev Eurasian National University, Khazakstan.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels2017Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, nr 3, s. 683-694Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Abstract. 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

  • 23. Adeleke, E.
    et al.
    Cizmesija, A.
    Oguntuase, James
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Pokaz, D.
    On a new class of Hardy-type inequalities2012Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, nr 259Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 24. Adey, J
    et al.
    Jones, R
    Palmer, D W
    Briddon, P R
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Erratum: Degradation of Boron-Doped Czochralski-Grown Silicon Solar Cells [Phys. Rev. Lett., 93, 055504 (2004)]2004Ingår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 93, nr 16, s. 169904-Artikel i tidskrift (Övrigt vetenskapligt)
  • 25.
    Adey, J.
    et al.
    School of Physics, University of Exeter.
    Jones, R.
    School of Physics, University of Exeter.
    Palmer, D.W.
    School of Physics, University of Exeter.
    Briddon, P.R.
    School of Natural Science, University of Newcastle upon Tyne.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Degradation of boron-doped Czochralski-grown silicon solar cells2004Ingår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 93, nr 5, s. 055504-1Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The formation mechanism and properties of the boron-oxygen center responsible for the degradation of Czochralski-grown Si(B) solar cells during operation is investigated using density functional calculations. We find that boron traps an oxygen dimer to form a bistable defect with a donor level in the upper half of the band gap. The activation energy for its dissociation is found to be 1.2 eV. The formation of the defect from mobile oxygen dimers, which are shown to migrate by a Bourgoin mechanism under minority carrier injection, has a calculated activation energy of 0.3 eV. These energies and the dependence of the generation rate of the recombination center on boron concentration are in good agreement with observations.

  • 26.
    Adey, J.
    et al.
    School of Physics, University of Exeter.
    Palmer, D.W,
    School of Physics, University of Exeter.
    Briddon, P.R.
    School of Natural Science, University of Newcastle upon Tyne.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Theory of boron-vacancy complexes in silicon2005Ingår i: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 71, nr 16, s. 165211-Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The substitutional boron-vacancy BsV complex in silicon is investigated using the local density functional theory. These theoretical results give an explanation of the experimentally reported, well established metastability of the boron-related defect observed in p-type silicon irradiated at low temperature and of the two hole transitions that are observed to be associated with one of the configurations of the metastable defect. BsV is found to have several stable configurations, depending on charge state. In the positive charge state the second nearest neighbor configuration with C1 symmetry is almost degenerate with the second nearest neighbor configuration that has C1h symmetry since the bond reconstruction is weakened by the removal of electrons from the center. A third nearest neighbor configuration of BsV has the lowest energy in the negative charge state. An assignment of the three energy levels associated with BsV is made. The experimentally observed Ev+0.31 eV and Ev+0.37 eV levels are related to the donor levels of second nearest neighbor BsV with C1 and C1h symmetry respectively. The observed Ev+0.11 eV level is assigned to the vertical donor level of the third nearest neighbor configuration. The boron-divacancy complex BsV2 is also studied and is found to be stable with a binding energy between V2 and Bs of around 0.2 eV. Its energy levels lie close to those of the V2. However, the defect is likely to be an important defect only in heavily doped material.

  • 27.
    Adjizian, J.J.
    et al.
    Department of Chemistry, University of Sussex, Falmer, Brighton.
    Latham, Chris
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Öberg, Sven
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap.
    Briddon, P.R.
    Electrical, Electronic and Computer Engineering, University of Newcastle upon Tyne.
    Heggie, M.I.
    Department of Chemistry, University of Sussex, Falmer, Brighton.
    DFT study of the chemistry of sulfur in graphite, including interactions with defects, edges and folds2013Ingår i: Carbon, ISSN 0008-6223, E-ISSN 1873-3891, Vol. 62, s. 256-262Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Sulfur has several roles, desirable and undesirable, in graphitization. We perform density functional theory calculations within the local density approximation to define the structures and energetics of sulphur in graphite, including its interactions with point defects and edges, in order to understand its role in the later stages of graphitization. We find sulphur does not cross-link layers, except where there are defects. It reacts very strongly with vacancies in neighbouring layers to form a six coordinate split vacancy structure, analogous to that found in diamond. It is also highly stable at basal edge sites, where, as might be expected, the size and valency of sulfur can be easily accommodated. This suggests a role for sulphur in stabilizing graphene edges, and following from this, we show that sulfur dimers can open, i.e. unzip, folds in graphite rapidly and exothermically.

  • 28.
    Akhmetkaliyeva, Raya
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Coercive estimates for the solutions of some singular differential equations and their applications2013Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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.

  • 29.
    Akhmetkaliyeva, Raya
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Maximal regularity of the solutions for some degenerate differential equations and their applications2018Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    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).

                             

                           

                                 

  • 30. Akhmetkaliyeva, Raya D.
    Coersive solvability of the differential equation of the third order with complex valued coefficients2013Ingår i: Vestnik ENU, Vol. 95, nr 4, s. 355-361Artikel i tidskrift (Refereegranskat)
  • 31.
    Akhmetkaliyeva, Raya D.
    L.N. Gumilyov Eurasian National University, Astana, Kazakhstan.
    On Solvability of Third-Order Singular Differential Equation2017Ingår i: FAIA 2017: Functional Analysis in Interdisciplinary Applications, Springer, 2017, Vol. 216, s. 106-112Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this paper some new existence and uniqueness results are proved and maximal regularity estimates of solutions of third-order differential equation with unbounded coefficients are given.

  • 32. Akhmetkaliyeva, Raya D.
    et al.
    Ospanov, K. N.
    On separation of a degenerate differential operator in Hilbert space2011Konferensbidrag (Refereegranskat)
    Abstract [en]

    A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

  • 33.
    Akhmetkaliyeva, Raya D.
    et al.
    Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University.
    Ospanov, K. N.
    Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University.
    Zulkhazhav, A.
    Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University.
    Compactness of the resolvent of one second order differential operator2014Ingår 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, artikel-id 13Konferensbidrag (Refereegranskat)
    Abstract [en]

    In this work a necessary and sufficient condition for the compactness of the resolvent of one second order degenerate differential operator in L-2 is obtained. We also discuss the two-sided estimates for the radius of fredholmness of this operator.

  • 34.
    Akhmetkaliyeva, Raya D.
    et al.
    Department of Pure Mathematics, Eurasian National University.
    Persson, Lars-Erik
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Mathematics, Narvik University College.
    Ospanov, K.N.
    Department of Pure Mathematics, Eurasian National University.
    Wall, Peter
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Some new results concerning a class of third-order differential equations2015Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 94, nr 2, s. 419-434Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 35.
    Aksoy, A. G.
    et al.
    Department of Mathematics, Claremont McKenna College.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Real interpolation and measure of weak noncompactness1995Ingår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 175, nr 1, s. 5-12Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 36.
    Aksoy, A.G.
    et al.
    Department of Mathematics, Claremont McKenna College.
    Maligranda, Lech
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Lipschitz-Orlicz spaces and the Laplace equation1996Ingår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, nr 178, s. 81-101Artikel i tidskrift (Refereegranskat)
  • 37.
    Albeverio, S.
    et al.
    Institute of Mathematics, Ruhr-Universität, D-44780 Bochum.
    Dabrowski, L.
    SISSA.
    Kurasov, Pavel
    Luleå tekniska universitet.
    Symmetries of Schrödinger operator with point interactions1998Ingår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 45, nr 1, s. 33-47Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 38.
    Albeverio, S.
    et al.
    Institut für Angewandte Mathematik, Universität Bonn.
    Fei, S-M
    Institut für Angewandte Mathematik, Universität Bonn.
    Kurasov, Pavel
    Luleå tekniska universitet.
    Many body problems with "spin"-related contact interactions2001Ingår i: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 47, nr 2, s. 157-166Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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.

  • 39.
    Albeverio, S.
    et al.
    BiBoS Research Center.
    Haake, F.
    Fachbereich Physik, Universität-GH Essen.
    Kurasov, Pavel
    Luleå tekniska universitet.
    Kus, M.
    Fachbereich Physik, Universität-GH Essen.
    Šeba, P.
    Nuclear Physics Institute, Czech Academy of Sciences.
    S-matrix, resonances, and wave functions for transport through billiards with leads1996Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 37, nr 10, s. 4888-4903Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 40.
    Albeverio, S.
    et al.
    Department of Mathematics, Ruhr-University, Bochum.
    Kurasov, Pavel
    Luleå tekniska universitet.
    Finite rank perturbations and distribution theory1999Ingår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 127, nr 4, s. 1151-1161Artikel i tidskrift (Refereegranskat)
  • 41.
    Albeverio, S.
    et al.
    Department of Mathematics, Ruhr-University, Bochum.
    Kurasov, Pavel
    Luleå tekniska universitet.
    Rank one perturbations of not semibounded operators1997Ingår i: Integral equations and operator theory, ISSN 0378-620X, E-ISSN 1420-8989, Vol. 27, nr 4, s. 379-400Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    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

  • 42. Albeverio, Sergio
    et al.
    Hilbert, Astrid
    Luleå tekniska universitet.
    Kolokoltsov, Vassily
    Sur le comportement asymptotique du noyau associé à une diffusion dégénérée2000Ingår i: Comptes Rendus Mathematiques de l'Academie des Sciences = Mathematical reports of the academy of science, ISSN 0706-1994, Vol. 22, nr 4, s. 151-159Artikel i tidskrift (Refereegranskat)
  • 43.
    Albing, Malin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Contributions to process capability indices and plots2008Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    This thesis presents contributions within the field of process capability analysis. Process capability analysis deals with how to assess the capability of processes. Based on process capability analysis one can determine how the process performs relative to its product requirements or specifications. An important part within process capability analysis is the use of process capability indices. This thesis focuses on process capability indices and process capability plots. The thesis consists of six papers and a summary. The summary gives a background to the research area, a short overview of the six papers, and some suggestions for future research. The thesis summary also consists of some new results, not presented in any of the appended papers. In paper I, the frequency and use of process capability analysis, together with statistical process control and design of experiments, within Swedish companies hiring alumni students are investigated. We also investigate what motivates organisations to implement or not implement these statistical methods, and what is needed to increase the use. In papers II-III we generalize the ideas with process capability plots and propose two graphical methods, for deeming a process capable at a given significance level, when the studied quality characteristic is assumed to be normally distributed. In paper II we derive estimated process capability plots for the case when the specification interval is one-sided. In paper III we derive elliptical safety region plots for the process capability index Cpk and its one-sided correspondences. The proposed graphical methods are helpful to determine if it is the variability, the deviation from target, or both that need to be reduced to improve the capability. In papers IV-VI we propose a new class of process capability indices designed for the situation with an upper specification limit, a target value zero, and where the studied quality characteristic has a skewed, zero- bound distribution with a long tail towards large values. The proposed class of indices is simple and possesses properties desirable for process capability indices. The results in papers IV-VI are also valid for the situation with a target value, not equal to zero but equal to a natural lower limit of the quality characteristic. Three estimators of the proposed class of indices are studied and the asymptotic distributions of these estimators are derived. We also consider decision procedures, based on the estimated indices, suitable for deeming the process capability at a given significance level. The new results in the summary combines the ideas from paper II with the results in papers IV-VI and a graphical method for the class of indices proposed in IV-VI are derived.

  • 44.
    Albing, Malin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Process capability analysis with focus on indices for one-sided specification limits2006Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)
    Abstract [en]

    In this thesis some aspects of process capability analysis are considered. Process capability analysis deals with how to assess the capability of manufacturing processes. Based on the process capability analysis one can determine how the process performs relative to its product requirements or specifications. An important part within process capability analysis is the use of process capability indices. This thesis focuses on process capability indices in the situation when the specification limits are one- sided. The thesis consists of a summary and three papers, of which one is already published in an international journal. The summary gives a background to the research area, a short overview of the three papers, and some suggestions for future research. In Paper I, the frequency and use of process capability analysis together with statistical process control and design of experiments, within Swedish companies hiring alumni students are investigated. We also investigate what motivates organisations to implement or not implement these statistical methods, if there are differences in use that can be related to organisational types and what will be needed to increase the use. One conclusion drawn from the results is that the students employed in the Swedish industrial sector witness a modest use of these statistical methods and use in other sectors hiring the alumni is uncommon. In Paper II we present a graphical method useful when doing capability analysis having one-sided specification limits. This is an extension of the process capability plots previously developed for two-sided specification intervals. Under the assumption of normality we suggest estimated process capability plots to be used to assess process capability at a given significance level. The presented graphical approach is helpful to determine if it is the variability, the deviation from target, or both that need to be reduced to improve the capability. In Paper III the situation with non-negative process data having a skew distribution with a long tail towards large values are considered, when an upper specification limit only exists and the target value is 0. No proper indices exist for this specific situation, which is common in practice. We contribute to this area by proposing a new class of indices designed for skew, zero-bound distributions when an upper specification only exists and the target value is 0. This new class of indices is simple and possesses properties desirable for process capability indices. Two estimators of the proposed index are studied and the asymptotic distributions of these estimators are derived. Furthermore, we consider decision procedures, based on the estimated indices, suitable for deeming the process capability or not.

  • 45.
    Albing, Malin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Process capability indices for Weibull distributions and upper specification limits2008Rapport (Övrigt vetenskapligt)
  • 46.
    Albing, Malin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Process capability indices for Weibull distributions and upper specification limits2009Ingår i: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 25, nr 3, s. 317-334Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    We consider a previously proposed class of capability indices that are useful when the quality characteristic of interest has a skewed, zero-bound distribution with a long tail towards large values and there is an upper specification with a pre-specified target value, T = 0. We investigate this class of process capability indices when the underlying distribution is a Weibull distribution and focus on the situation when the Weibull distribution is highly skewed. We propose an estimator of the index in the studied class, based on the maximum likelihood estimators of the parameters in the Weibull distribution, and derive the asymptotic distribution for this estimator. Furthermore, we suggest a decision rule based on the estimated index and its asymptotic distribution, and presents a power comparison between the proposed estimator and a previously studied estimator. A simulation study is also performed to investigate the true significance level when the sample size is small or moderate. An example from a Swedish industry is presented.

  • 47. Albing, Malin
    et al.
    Vännman, Kerstin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Elliptical safety region plots for Cpk2011Ingår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 38, nr 6, s. 1169-1187Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The process capability index Cpk is widely used when measuring the capability of a manufacturing process. A process is defined to be capable if the capability index exceeds a stated threshold value, e.g. Cpk4/3. This inequality can be expressed graphically using a process capability plot, which is a plot in the plane defined by the process mean and the process standard deviation, showing the region for a capable process. In the process capability plot, a safety region can be plotted to obtain a simple graphical decision rule to assess process capability at a given significance level. We consider safety regions to be used for the index Cpk. Under the assumption of normality, we derive elliptical safety regions so that, using a random sample, conclusions about the process capability can be drawn at a given significance level. This simple graphical tool is helpful when trying to understand whether it is the variability, the deviation from target, or both that need to be reduced to improve the capability. Furthermore, using safety regions, several characteristics with different specification limits and different sample sizes can be monitored in the same plot. The proposed graphical decision rule is also investigated with respect to power

  • 48. Albing, Malin
    et al.
    Vännman, Kerstin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Elliptical Safety Region Plots for Cpk, Cpu and Cpl2008Rapport (Övrigt vetenskapligt)
  • 49. Albing, Malin
    et al.
    Vännman, Kerstin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Process capability indices for one-sided specifications and skew zero-bound distributions2006Rapport (Övrigt vetenskapligt)
  • 50. Albing, Malin
    et al.
    Vännman, Kerstin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Skewed zero-bound distributions and process capability indices for upper specifications2009Ingår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 36, nr 2, s. 205-221Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    A common practical situation in process capability analysis, which is not well developed theoretically, is when the quality characteristic of interest has a skewed distribution with a long tail towards relatively large values and an upper specification limit only exists. In such situations it is not uncommon that the smallest possible value of the characteristic is 0 and this also is the best value to obtain. Hence a target value 0 is assumed to exist. We investigate a new class of process capability indices for this situation. Two estimators of the proposed index are studied and the asymptotic distributions of these estimators are derived. Furthermore we suggest a decision procedure useful when drawing conclusions about the capability at a given significance level, based on the estimated indices and their asymptotic distributions. A simulation study is also performed, assuming that the quality characteristic is Weibull distributed, to investigate the true significance level when the sample size is finite.

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