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• 1.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Embedding theorems for spaces with multiweighted derivatives2007Licentiatavhandling, med artikler (Annet vitenskapelig)

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.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives2009Doktoravhandling, med artikler (Annet vitenskapelig)

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.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Summability of a Tchebysheff system of functions2007Rapport (Annet vitenskapelig)
• 5.
L.N. Gumilyov Eurasian National University.
L.N. Gumilyov Eurasian National University. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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

• 6.
L.N. Gumilyov Eurasian National University.
L.N. Gumilyov Eurasian National University. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1≤ q2009Rapport (Annet vitenskapelig)
• 7.
University of Haifa.
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 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—Some new extensions and refinements of Hermite–Hadamard and Fejer type inequali-ties for functions which are N-quasiconvex are derived and discussed.

• 8.
Department of Mathematics, University of Haifa, Haifa, Israel.
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 Inequalities2018Inngår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 3, s. 759-772Artikkel i tidsskrift (Fagfellevurdert)

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] .

• 9.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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

• 10.
Department of Mathematics, University of Haifa.
Faculty of Textile Technology, University of Zagreb. Faculty of Textile Technology, University of Zagreb. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.

• 11.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.

• 12.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new estimates of the ‘Jensen gap’2016Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, artikkel-id 39Artikkel i tidsskrift (Fagfellevurdert)

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.

• 13.
University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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

• 14.
University of Haifa, Department of Mathematics.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. University of Zagreb. University of Zagreb.
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)

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.

• 15.
University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.

• 16.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.

• 17.
Department of Mathematics, University of Haifa.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.

• 18.
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Boundedness and compactness of a class of Hardy type operators2016Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, artikkel-id 324Artikkel i tidsskrift (Fagfellevurdert)

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.

• 19.
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana, Kazakhstan .
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 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)

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

• 20.
L. N.Gumilev Eurasian National University, Khazakstan.
L. N.Gumilev Eurasian National University, Khazakstan. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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. 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

• 21.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
On permutations and equity among generationsInngår i: Artikkel i tidsskrift (Annet vitenskapelig)

In the literature on intergenerational justice, there is a widely held view that in order to live up to the utilitarian ideal of equal regard for all individuals, including those who have not yet been born, we must impose infinite permutation invariance conditions known as axioms of extended anonymity. I argue that such conditions do not bear relevance to the utilitarian ideal. I do so by showing that all examples that have been used to motivate extended anonymity axioms can be accounted for with an alternative principle that is supported independently.

Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
On a new class of Hardy-type inequalities2012Inngår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, nr 259Artikkel i tidsskrift (Fagfellevurdert)

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.

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)]2004Inngår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 93, nr 16, s. 169904-Artikkel i tidsskrift (Annet vitenskapelig)
• 24.
School of Physics, University of Exeter.
School of Physics, University of Exeter. School of Physics, University of Exeter. School of Natural Science, University of Newcastle upon Tyne. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Degradation of boron-doped Czochralski-grown silicon solar cells2004Inngår i: Physical Review Letters, ISSN 0031-9007, E-ISSN 1079-7114, Vol. 93, nr 5, s. 055504-1Artikkel i tidsskrift (Fagfellevurdert)

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.

• 25.
School of Physics, University of Exeter.
School of Physics, University of Exeter. School of Natural Science, University of Newcastle upon Tyne. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Theory of boron-vacancy complexes in silicon2005Inngår i: Physical Review B. Condensed Matter and Materials Physics, ISSN 1098-0121, E-ISSN 1550-235X, Vol. 71, nr 16, s. 165211-Artikkel i tidsskrift (Fagfellevurdert)

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.

• 26.
Department of Chemistry, University of Sussex, Falmer, Brighton.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Materialvetenskap. Electrical, Electronic and Computer Engineering, University of Newcastle upon Tyne. Department of Chemistry, University of Sussex, Falmer, Brighton.
DFT study of the chemistry of sulfur in graphite, including interactions with defects, edges and folds2013Inngår i: Carbon, ISSN 0008-6223, E-ISSN 1873-3891, Vol. 62, s. 256-262Artikkel i tidsskrift (Fagfellevurdert)

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.

• 27.
Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Drift, underhåll och akustik.
Luleå tekniska universitet, Institutionen för samhällsbyggnad och naturresurser, Drift, underhåll och akustik. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Multivariate process parameter change identification by neural network2013Inngår i: The International Journal of Advanced Manufacturing Technology, ISSN 0268-3768, E-ISSN 1433-3015, Vol. 69, nr 9-12, s. 2261-2268Artikkel i tidsskrift (Fagfellevurdert)

Whenever there is an out-of-control signal in process parameter control charts, maintenance engineers try to diagnose the cause near the time of the signal which is not always lead to prompt identification of the source(s) of the out-of-control condition and this in some cases yields to extremely high monetary loses for manufacture owner. This paper applies multivariate exponentially weighted moving average (MEWMA) control charts and neural networks to make the signal identification more effective. The simulation of this procedure shows that this new control chart can be very effective in detecting the actual change point for all process dimension and all shift magnitudes considered. This methodology can be used in manufacturing and process industries to predict change points and expedite the search for failure causing parameters, resulting in improved quality at reduced overall cost. This research shows development of MEWMA by usage of neural network for identifying the step change point and the variable responsible for the change in the process mean vector.

• 28.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Coercive estimates for the solutions of some singular differential equations and their applications2013Licentiatavhandling, med artikler (Annet vitenskapelig)

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.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Maximal regularity of the solutions for some degenerate differential equations and their applications2018Doktoravhandling, med artikler (Annet vitenskapelig)

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

$ly=-y''+r(x)y'+s(x)\bar{y}'$

in the Hilbert space $L_2:= L_2 (\mathbb{R}),\ \mathbb{R}=(-\infty, +\infty),$(here $\bar y$ 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 operator $l$ 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 $l$ in $L_2$ 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

$Ly = -\rho(x)(\rho(x)y')'+ r(x)y' + q(x)y$

in $L_2(\mathbb{R})$, where $\rho=\rho (x), r=r(x)$ are continuously differentiable functions, and $q=q(x)$ is a continuous function. In this paper we show that the operator $L$ is continuously invertible when these coefficients satisfy some suitable conditions and obtain the following estimate for $y \in D(L)$:

$\||-\rho(\rho y')'\||_2+\||r y'\||_2+\||q y\||_2\leq c \||L y\||_2$,

where $D(L)$ is the domain of $L$.

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

$-m_1(x)\left(m_2(x)\left(m_3(x)y'\right)'\right)'+[q(x)+ir(x)+\lambda]y=f(x) \ (0.1)$

are studied in the space $L_p(\mathbb{R})$.

In paper D we investigate the case when $m_1=m_3=m$ and $m_2=1$.

Moreover, in paper E the equation (0.1) is studied when $m_3=1$. Finally, in paper F the equation (0.1) is investigated under certain additional conditions on $m_j(x) (j=1,2,3)$.

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

$\left\|m_1(x)(m_2(x)\left(m_3(x)y')'\right)'\right\|^p_p+\left\|(q(x)+ir(x)+\lambda)y\right\|^p_p \leq c \left\|f(x)\right\|^p_p$

for the solution $y$ of equation (0.1).

• 30.
Department of Pure Mathematics, Eurasian National University.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Department of Mathematics, Narvik University College. Department of Pure Mathematics, Eurasian National University. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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

• 31.
Department of Mathematics, Claremont McKenna College.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.

• 32.
Department of Mathematics, Claremont McKenna College.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Lipschitz-Orlicz spaces and the Laplace equation1996Inngår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, nr 178, s. 81-101Artikkel i tidsskrift (Fagfellevurdert)
• 33.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Contributions to process capability indices and plots2008Doktoravhandling, med artikler (Annet vitenskapelig)

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.

• 34.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Process capability analysis with focus on indices for one-sided specification limits2006Licentiatavhandling, med artikler (Annet vitenskapelig)

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.

• 35.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Process capability indices for Weibull distributions and upper specification limits2008Rapport (Annet vitenskapelig)
• 36.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Process capability indices for Weibull distributions and upper specification limits2009Inngår i: Quality and Reliability Engineering International, ISSN 0748-8017, E-ISSN 1099-1638, Vol. 25, nr 3, s. 317-334Artikkel i tidsskrift (Fagfellevurdert)

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.

• 37. Albing, Malin
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Elliptical safety region plots for Cpk2011Inngår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 38, nr 6, s. 1169-1187Artikkel i tidsskrift (Fagfellevurdert)

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

• 38. Albing, Malin
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Elliptical Safety Region Plots for Cpk, Cpu and Cpl2008Rapport (Annet vitenskapelig)
• 39. Albing, Malin
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Process capability indices for one-sided specifications and skew zero-bound distributions2006Rapport (Annet vitenskapelig)
• 40. Albing, Malin
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Skewed zero-bound distributions and process capability indices for upper specifications2009Inngår i: Journal of Applied Statistics, ISSN 0266-4763, E-ISSN 1360-0532, Vol. 36, nr 2, s. 205-221Artikkel i tidsskrift (Fagfellevurdert)

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.

• 41.
School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne.
School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne. School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne. School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne. School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne. School of Electrical and Electronic Engineering, Newcastle University, Newcastle upon Tyne. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Oxygen vacancy migration in compressively strained SrTiO32013Inngår i: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 113, nr 2Artikkel i tidsskrift (Fagfellevurdert)

The intrinsic properties of strontium titanate render it promising in applications such as gate dielectrics and capacitors. However, there is growing evidence that oxygen vacancies significantly impact upon its use, with the diffusion and deep donor level of the oxygen vacancy leading to electrical leakage. Where grown epitaxially on a lattice mismatched substrate, SrTiO 3 undergoes bi-axial strain, altering its crystal structure and electronic properties. In this paper, we present the results of first-principles simulations to evaluate the impact of strain in a (001) plane upon the migration of oxygen vacancies. We show that in the range of strains consistent with common substrate materials, diffusion energies in different directions are significantly affected, and for high values of strain may be altered by as much as a factor of two. The resulting diffusion anisotropy is expected to impact upon the rate at which oxygen vacancies are injected into the films under bias, a critical factor in the leakage and resistive switching seen in this material

• 42.
Newcastle University.
Newcastle University. Newcastle University. Newcastle University. Newcastle University. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Impact of tensile strain on the oxygen vacancy migration in SrTiO3: Density functional theory calculations2013Inngår i: Journal of Applied Physics, ISSN 0021-8979, E-ISSN 1089-7550, Vol. 113, nr 22Artikkel i tidsskrift (Fagfellevurdert)

Strontium titanate is a promising dielectric material for device applications including capacitors and gate dielectrics. However, oxygen vacancies, which are inevitable donor defects mobile under bias at room temperature, lead to undesirable leakage current in SrTiO3 thin films. Epitaxially grown SrTiO3 on lattice mismatched substrates leads to strained SrTiO3, inducing structural phase transitions from a cubosymmetric non-ferroelectric geometry to tetragonal and orthorhombic structures, depending upon the sign of the strain. In this study, density functional calculations have been performed to determine the impact of isotropic biaxial tensile strain in a (001) plane upon the phase of SrTiO3 and the activation energy for the migration of oxygen vacancies in such strained SrTiO3. The phase transition of the host material yields anisotropy in oxygen vacancy diffusion for diffusion within and between planes parallel to the strain. We found a general reduction in the barrier for diffusion within and normal to the plane of tensile strain. The inter-plane diffusion barrier reduces up to 25% at high values of strain. The variation in the barrier corresponding to in-plane diffusion is smaller in comparison to inter-plane diffusion. Finally, we reflect upon how the interplay between lattice strain with native defects plays a crucial role in the conduction mechanism of thin film, strained SrTiO3

• 43.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.

• 44.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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

• 45.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Homogenization of the Reynolds equation2005Rapport (Annet vitenskapelig)
• 46.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
Department of Mathematics and Statistics, University of Cape Coast. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
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)

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.

• 47.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Reiterated homogenization applied in hydrodynamic lubrication2008Inngår i: Proceedings of the Institution of mechanical engineers. Part J, journal of engineering tribology, ISSN 1350-6501, E-ISSN 2041-305X, Vol. 222, nr 7, s. 827-841Artikkel i tidsskrift (Fagfellevurdert)

This work is devoted to studying the combined effect that arises due to surface texture and surface roughness in hydrodynamic lubrication. An effective approach in tackling this problem is by using the theory of reiterated homogenization with three scales. In the numerical analysis of such problems, a very fine mesh is needed, suggesting some type of averaging. To this end, a general class of problems is studied that, e.g. includes the incompressible Reynolds problem in both artesian and cylindrical coordinate forms. To demonstrate the effectiveness of the method several numerical results are presented that clearly show the convergence of the deterministic solutions towards the homogenized solution.Moreover, the convergence of the friction force and the load carrying capacity of the lubricant film is also addressed in this paper. In conclusion, reiterated homogenization is a feasible mathematical tool that facilitates the analysis of this type of problem.

• 48.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Reiterated homogenization of a nonlinear Reynolds-type equation2008Rapport (Annet vitenskapelig)
• 49.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
Department of Mathematics and Statistics, University of Cape Coast. Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Variational bounds applied to unstationary hydrodynamic lubrication2008Inngår i: International Journal of Engineering Science, ISSN 0020-7225, E-ISSN 1879-2197, Vol. 46, nr 9, s. 891-906Artikkel i tidsskrift (Fagfellevurdert)

This paper is devoted to the effects of surface roughness in hydrodynamic lubrication. The numerical analysis of such problems requires a very fine mesh to resolve the surface roughness, hence it is often necessary to do some type of averaging. Previously, homogenization (a rigorous form of averaging) has been successfully applied to Reynolds type differential equations. More recently, the idea of finding upper and lower bounds on the effective behavior, obtained by homogenization, was applied for the first time in tribology. In these pioneering works, it has been assumed that only one surface is rough. In this paper we develop these results to include the unstationary case where both surfaces may be rough. More precisely, we first use multiple-scale expansion to obtain a homogenization result for a class of variational problems including the variational formulation associated with the unstationary Reynolds equation. Thereafter, we derive lower and upper bounds corresponding to the homogenized (averaged) variational problem. The bounds reduce the numerical analysis, in that one only needs to solve two smooth problems, i.e. no local scale has to be considered. Finally, we present several examples, where it is shown that the bounds can be used to estimate the effects of surface roughness with very high accuracy.

• 50.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Maskinelement.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Homogenization of the unstationary incompressible Reynolds equation2007Inngår i: Tribology International, ISSN 0301-679X, E-ISSN 1879-2464, Vol. 40, nr 9, s. 1344-1350Artikkel i tidsskrift (Fagfellevurdert)

This paper is devoted to the effects of surface roughness during hydrodynamic lubrication. In the numerical analysis a very fine mesh is needed to resolve the surface roughness, suggesting some type of averaging. A rigorous way to do this is to use the general theory of homogenization. In most works about the influence of surface roughness, it is assumed that only the stationary surface is rough. This means that the governing Reynolds type equation does not involve time. However, recently, homogenization was successfully applied to analyze a situation where both surfaces are rough and the lubricant is assumed to have constant bulk modulus. In this paper we will consider a case where both surfaces are assumed to be rough, but the lubricant is incompressible. It is also clearly demonstrated, in this case that homogenization is an efficient approach. Moreover, several numerical results are presented and compared with those corresponding to where a constant bulk modulus is assumed to govern the lubricant compressibility. In particular, the result shows a significant difference in the asymptotic behavior between the incompressible case and that with constant bulk modulus.

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