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• 1.
University Pretoria, South Africa.
University of the Basque Country, Spain. Mälardalen University, School of Education, Culture and Communication, Educational Sciences and Mathematics.
Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces2015In: Discrete dynamics in nature and society, ISSN 1026-0226, E-ISSN 1607-887X, Vol. 2015, article id 532725Article in journal (Refereed)

The aim of this paper is to present fixed point result of mappings satisfying a generalized rational contractive condition in the setup of multiplicative metric spaces. As an application, we obtain a common fixed point of a pair of weakly compatible mappings. Some common fixed point results of pair of rational contractive types mappings involved in cocyclic representation of a nonempty subset of a multiplicative metric space are also obtained. Some examples are presented to support the results proved herein. Our results generalize and extend various results in the existing literature.

• 2.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Compactness of embedding between Sobolev type spaces with multiweighted derivatives2009In: AIHT : Analysis, Inequalities and Homogenization Theory: Midnight sun conference in honor of Lars-Erik Persson, 2009Conference paper (Other academic)

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.

• 3.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Embedding theorems for spaces with multiweighted derivatives2007Licentiate thesis, comprehensive summary (Other academic)

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.

• 4.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives2009Doctoral thesis, comprehensive summary (Other academic)

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.

• 5. Abdikalikova, Zamira
Compactness of embedding between spaces with multiweighted derivatives: the case 1 ≤ p ≤ q2009Report (Other academic)
• 6.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Summability of a Tchebysheff system of functions2007Report (Other academic)
• 7.
L.N. Gumilyov Eurasian National University.
L.N. Gumilyov Eurasian National University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 12011In: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 61, no 1, p. 7-26Article in journal (Refereed)

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

• 8.
L.N. Gumilyov Eurasian National University.
L.N. Gumilyov Eurasian National University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1≤ q2009Report (Other academic)
• 9.
Jönköping University, School of Engineering, JTH, Mathematics.
Strong L1 convergence to equilibrium without entropy conditions for the Boltzmann equation1999In: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 24, no 7-8, p. 1501-1535Article in journal (Refereed)

The main result of this paper is that for the har dsphere kernel, the solution of the spatially homogenous Boltzmann equation converges strongly in L1 to equilibrium given that the initial data f0 belongs to L1(R3,(1+v^2)dv). This was previously known to be true with the additional assumption that f0logf0 belonged to L1(R3), which corresponds to bounded initial entropy.

• 10.
University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. University of Tromsø ; The Arctic University of Norway, Narvik.
Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions2017In: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 102, no 5-6, p. 599-609Article in journal (Refereed)

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

• 11.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 32014In: 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, p. 1-10Conference paper (Refereed)

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

• 12.
Department of Mathematics, University of Haifa.
Faculty of Textile Technology, University of Zagreb. Faculty of Textile Technology, University of Zagreb. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new refined Hardy type inequalities with general kernels and measures2010In: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 79, no 1-2, p. 157-172Article in journal (Refereed)

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.

• 13.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Inequalities for averages of quasiconvex and superquadratic functions2016In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, no 2, p. 535-550Article in journal (Refereed)

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.

• 14.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new estimates of the ‘Jensen gap’2016In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, article id 39Article in journal (Refereed)

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.

• 15.
University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new scales of refined Hardy type inequalities via functions related to superquadracity2013In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, no 3, p. 679-695Article in journal (Refereed)

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

• 16.
University of Haifa, Department of Mathematics.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. University of Zagreb. University of Zagreb.
General inequalities via isotonic subadditive functionals2007In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, no 1, p. 15-28Article in journal (Refereed)

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.

• 17.
University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On some new developments of Hardy-type inequalities2012In: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2012, p. 739-746Conference paper (Refereed)

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.

• 18.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On γ-quasiconvexity, superquadracity and two-sided reversed Jensen type inequalities2015In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 18, no 2, p. 615-627Article in journal (Refereed)

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.

• 19.
Department of Mathematics, University of Haifa.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new scales of refined Jensen and Hardy type inequalities2014In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, no 3, p. 1105-1114Article in journal (Refereed)

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.

• 20.
Luleå University of Technology, Department of Engineering Sciences and Mathematics.
Inequalities for some classes of Hardy type operators and compactness in weighted Lebesgue spaces2016Doctoral thesis, comprehensive summary (Other academic)

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 $\alpha$-order fractional integrationoperators are considered including the well-known classical Weyl, Riemann-Liouville, Erdelyi-Kober and Hadamard operators. Here 0 < $\alpha$ < 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 < ∞

• 21.
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 University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Boundedness and compactness of a class of Hardy type operators2016In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, no 1, article id 324Article in journal (Refereed)

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.

• 22.
Department of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Astana .
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. UiT, Tromso.
Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018In: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, no 1, p. 201-215Article in journal (Refereed)

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

• 23.
L. N.Gumilev Eurasian National University, Khazakstan.
L. N.Gumilev Eurasian National University, Khazakstan. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Additive weighted Lp estimates of some classes of integral operators involving generalized Oinarov Kernels2017In: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, no 3, p. 683-694Article in journal (Refereed)

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

• 24. Ackelh, A.S.
Institute for Complex Molecular Systems & Centre for Analysis, Scientific computing and Applications, Eindhoven University of Technology.
Preface to "modeling with measures"2015In: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 12, no 2Article in journal (Refereed)
• 25.
Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland.
Umeå University, Faculty of Science and Technology, Department of Mathematics and Mathematical Statistics.
The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures2016In: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, no 2, p. 623-658Article in journal (Refereed)

We investigate various boundary decay estimates for p(⋅)-harmonic functions. For domains in Rn,n≥2satisfying the ball condition (C1,1-domains), we show the boundary Harnack inequality for p(⋅)-harmonic functions under the assumption that the variable exponent p is a bounded Lipschitz function. The proof involves barrier functions and chaining arguments. Moreover, we prove a Carleson-type estimate for p(⋅)-harmonic functions in NTA domains in Rn and provide lower and upper growth estimates and a doubling property for a p(⋅)-harmonic measure.

Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
On a new class of Hardy-type inequalities2012In: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, no 259Article in journal (Refereed)

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.

• 27.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
In times of regional geopolitical turmoil – Why do some equity funds performbetter than others?2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

In times of regional geopolitical turmoil – why do some investment portfolios, equity funds, perform better than others? Is it simply luck, the effects of systematic risk or do factors such as investment styles and managerial skills play a significant part in the performance of a fund?

As financial markets often reflect the macro environment, much of the previous year’s fluctuations of Eastern European stocks can be seen to derive from a number of geopolitical events; from the 2013 summer clashes between the Turkish police and opposing parties to the current issue concerning Russia and Ukraine. Needless to say, these events have affected return on equity in their regions and created a distressed environment for investors and equity fund managers investing in Eastern Europe.

This thesis aims to explore how the aforementioned macroeconomic events impact the market and thus the portfolios of asset managers. The thesis also intends to provide aspects of eventual investment strategies that are more preferable than others under such circumstances, in order to mitigate the subsequent risks.

• 28.
Blekinge Institute of Technology, School of Engineering.
Statistical Modelling and the Fokker-Planck Equation2008Independent thesis Advanced level (degree of Master (One Year))Student thesis

A stochastic process or sometimes called random process is the counterpart to a deterministic process in theory. A stochastic process is a random field, whose domain is a region of space, in other words, a random function whose arguments are drawn from a range of continuously changing values. In this case, Instead of dealing only with one possible 'reality' of how the process might evolve under time (as is the case, for example, for solutions of an ordinary differential equation), in a stochastic or random process there is some indeterminacy in its future evolution described by probability distributions. This means that even if the initial condition (or starting point) is known, there are many possibilities the process might go to, but some paths are more probable and others less. However, in discrete time, a stochastic process amounts to a sequence of random variables known as a time series. Over the past decades, the problems of synergetic are concerned with the study of macroscopic quantitative changes of systems belonging to various disciplines such as natural science, physical science and electrical engineering. When such transition from one state to another take place, fluctuations i.e. (random process) may play an important role. Fluctuations in its sense are very common in a large number of fields and nearly every system is subjected to complicated external or internal influences that are often termed noise or fluctuations. Fokker-Planck equation has turned out to provide a powerful tool with which the effects of fluctuation or noise close to transition points can be adequately be treated. For this reason, in this thesis work analytical and numerical methods of solving Fokker-Planck equation, its derivation and some of its applications will be carefully treated. Emphasis will be on both for one variable and N- dimensional cases.

Localized Galerkin Estimates for Boundary Integral Equations on Lipschitz Domanis1992In: SIAM Journal on Mathematical Analysis, Vol. 5, no 23, p. 751-764Article in journal (Refereed)

The Galerkin method is studied for solving the boundary integral equations associated with the Laplace operator on nonsmooth domains. Convergence is established with a condition on the meshsize, which involves the local curvature on certain approximating domains. Error estimates are also proved, and the results are generalized to systems of equations.

• 30.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
ESG-investerande och portföljresultat: En studie av ESG-investerande utifrån metoden bäst-i-klassen2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

As a result of a more globalized and industrial world, sustainability issues in terms of the environment and society has become an everyday heading in the financial world. The fact that companies should work actively towards sustainability and accountability is today a necessity rather than a choice. The purpose of this study is to research responsible investment (RI) and portfolio performance. To examine this relationship the study focuses on ESG where its dimensions will be included jointly through optimization, discussion and conclusion. The report outlines how ESG can be integrated into the investment process, but the weight of the study addresses the discussion of a portfolio's performance at the inclusion of ESG. Methods used are Modern Portfolio Theory (MPT) combined with the implementation of ESG according to "best-in-class". The results of the study lead towards the conclusion that ESG in addition to its positive effects, provided an accurate assessment, on sustainability also is financially arguable for investors.

• 31.
Blekinge Institute of Technology, School of Engineering, Department of Telecommunication Systems.
Security Issues in Wireless Systems2009Independent thesis Advanced level (degree of Master (One Year))Student thesis

ireless Communication is one of the fields of Telecommunications which is growing with the tremendous speed. With the passage of time wireless communication devices are becoming more and more common. It is not only the technology of business but now people are using it to perform their daily tasks, be it for calling, shopping, checking their emails or transfer their money. Wireless communication devices include cellular phones, cordless phones and satellite phones, smart phones like Personal Digital Assistants (PDA), two way pagers, and lots of their devices are on their way to improve this wireless world. In order to establish two way communications, a wireless link may be using radio waves or Infrared light. The Wireless communication technologies have become increasingly popular in our everyday life. The hand held devices like Personal Digital Assistants (PDA) allow the users to access calendars, mails, addresses, phone number lists and the internet. Personal digital assistants (PDA) and smart phones can store large amounts of data and connect to a broad spectrum of networks, making them as important and sensitive computing platforms as laptop PCs when it comes to an organization’s security plan. Today’s mobile devices offer many benefits to enterprises. Mobile phones, hand held computers and other wireless systems are becoming a tempting target for virus writers. Mobile devices are the new frontier for viruses, spam and other potential security threats. Most viruses, Trojans and worms have already been created that exploit vulnerabilities. With an increasing amount of information being sent through wireless channels, new threats are opening up. Viruses have been growing fast as handsets increasingly resemble small computers that connect with each other and the internet. Hackers have also discovered that many corporate wireless local area networks (WLAN) in major cities were not properly secured. Mobile phone operators say that it is only a matter of time before the wireless world is hit by the same sorts of viruses and worms that attack computer software.

• 32.
Blekinge Institute of Technology, School of Engineering.
Blekinge Institute of Technology, School of Engineering.
Optimal Solutions Of Fuzzy Relation Equations2010Independent thesis Advanced level (degree of Master (Two Years))Student thesis

Fuzzy relation equations are becoming extremely important in order to investigate the optimal solution of the inverse problem even though there is a restrictive condition for the availability of the solution of such inverse problems. We discussed the methods for finding the optimal (maximum and minimum) solution of inverse problem of fuzzy relation equation of the form \$R \circ Q = T\$ where for both cases R and Q are kept unknown interchangeably using different operators (e.g. alpha, sigma etc.). The aim of this study is to make an in-depth finding of best project among the host of projects, depending upon different factors (e.g. capital cost, risk management etc.) in the field of civil engineering. On the way to accomplish this aim, two linguistic variables are introduced to deal with the uncertainty factor which appears in civil engineering problems. Alpha-composition is used to compute the solution of fuzzy relation equation. Then the evaluation of the projects is orchestrated by defuzzifying the obtained results. The importance of adhering to such synopsis, in the field of civil engineering, is demonstrated by an example.

• 33.
Blekinge Institute of Technology, School of Engineering.
Modeling and Simulation of Urea Dosing System2013Independent thesis Advanced level (degree of Master (Two Years))Student thesis

To protect our health and environment from pollution, among others regulatory agencies in the European Union (EU) and legislation from the U.S. Environmental Protection Agency (EPA) has required that pollutants produced by diesel engines - such as nitrogen oxides (NOx), hydrocarbons (HC) and particulate matter (PM) - be reduced. The key emission reduction and control technologies available for NOx control on Diesel engines are combination of Exhaust Gas Recirculation (EGR) and Selective Catalytic Reduction (SCR). SCR addresses emission reduction through the use of Diesel Exhuast Fluid (DEF), which has a trade-name AdBlue. Which is 32.5% high purity urea and 67.5% deionized water, Adblue in the hot exhaust gas decomposes into ammonia (NH3) which then reacts with surface of the catalyst to produce harmless nitrogen(N2) and water (H20). Highest NOx conversion ratios while avoiding ammonia slip is achieved by Efficient SCR and accurate Urea Dosing System it’s therefore critical we model and simulate the UDS in order to analyze and gain holistic understanding of the UDS dynamic behavior. The process of Modeling and Simulating of Urea Dosing System is a result of a compromise between two opposing trends. Firstly, one needs to use as much mathematical models as it takes to correctly describe the fundamental principles of fluid dynamics such as, (1) mass is conserved (2), Newton’s second law and (3) energy is conserved, secondly the model needs to be as simple as possible, in order to express a simple and useful picture of real systems. Numerical model for the simulation of Urea Dosing System is implemented in GT Suite® environment, it is complete UDS Model (Hydraulic circuit and Dosing Unit) and it stands out for its ease of use and simulation fastness, The UDS model has been developed and validated using as reference Hilite Airless Dosing System at the ATC Lab, results provided by the model allow to analyze the UDS pump operation, as well the complete system, showing the trend of some important parameters which are difficult to measure such as viscosity, density, Reynolds number and giving plenty of useful information to understand the influence of the main design parameters of the pump, such as volumetric efficiency, speed and flow relations.

• 34.
Japan Womens Univ, Fac Sci, Dept Math, Bunkyo Ku, Tokyo.
Vrije Univ Amsterdam, Fac Sci, Dept Math, Amsterdam, Netherlands. Bukkyo Univ, Sch Educ Math, Kita Ku, Kyoto. Eindhoven Univ Technol, Dept Math & Comp Sci,.
Analysis of non-equilibrium evolution problems: Selected topics in material and life sciences2014In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 7, no 1Article in journal (Refereed)
• 35. Aiki, T.
Eindhoven Univ Technol, Dept Math & Comp Sci.
A free-boundary problem for concrete carbonation: Front nucleation and rigorous justification of the root t-law of propagation2013In: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 15, no 2, p. 167-180Article in journal (Refereed)
• 36. Aiki, T.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures2009In: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 19, p. 119-129Article in journal (Refereed)
• 37.
Gifu University, Japan.
Eindhoven University Technology, Netherlands. Eindhoven University Technology, Netherlands.
On a one-dimensional shape-memory alloy model in its fast-temperature- activation limit2012In: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 5, no 1, p. 15-28Article in journal (Refereed)
• 38.
Gifu University, Japan.
Eindhoven University of Technology.
Large time behavior of solutions to a moving-interface problem modeling concrete carbonation2010In: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 9, no 5, p. 1117-1129Article in journal (Refereed)
• 39.
Tokyo Womens University.
Netherlands.
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data2013In: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 93, p. 3-14Article in journal (Refereed)

We study the large-time behavior of the free boundary position capturing the one-dimensional motion of the carbonation reaction front in concrete-based materials. We extend here our rigorous justification of the t-behavior of reaction penetration depths by including nonlinear effects due to deviations from the classical Henry's law and time-dependent Dirichlet data.

• 40. Aiki, Toyohiko
Eindhoven University of Technology.
Large-time behavior of a two-scale semilinear reaction-diffusion system for concrete sulfatation2014In: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 38, no 7, p. 1451-1464Article in journal (Refereed)
• 41.
Gifu University, Japan.
Eindhoven University of Technology.
On uniqueness of a weak solution of one-dimensional concrete carbonation problem2011In: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 29, no 4, p. 1345-1365Article in journal (Refereed)

In our previous works we studied a one-dimensional free-boundary model related to the aggressive penetration of gaseous carbon dioxide in unsaturated concrete. Essentially, global existence and uniqueness of weak solutions to the model were obtained when the initial functions are bounded on the domain. In this paper we investigate the well-posedness of the problem for the case when the initial functions belong to a $\displaystyle{{L}}^{{2}}-$ class. Specifically, the uniqueness of weak solutions is proved by applying the dual equation method.

• 42.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Coercive estimates for the solutions of some singular differential equations and their applications2013Licentiate thesis, comprehensive summary (Other academic)

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.

• 43.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Maximal regularity of the solutions for some degenerate differential equations and their applications2018Doctoral thesis, comprehensive summary (Other academic)

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).

• 44. Akhmetkaliyeva, Raya D.
Coersive solvability of the differential equation of the third order with complex valued coefficients2013In: Vestnik ENU, Vol. 95, no 4, p. 355-361Article in journal (Refereed)
• 45.
L.N. Gumilyov Eurasian National University, Astana, Kazakhstan.
On Solvability of Third-Order Singular Differential Equation2017In: FAIA 2017: Functional Analysis in Interdisciplinary Applications, Springer, 2017, Vol. 216, p. 106-112Conference paper (Refereed)

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.

• 46. Akhmetkaliyeva, Raya D.
On separation of a degenerate differential operator in Hilbert space2011Conference paper (Refereed)

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.

• 47.
Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University.
Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University. Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University.
Compactness of the resolvent of one second order differential operator2014In: 10th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences (ICNPAA 2014) / [ed] Sivasundaram, Seenith, American Institute of Physics (AIP), 2014, Vol. 1637, no 1, p. 13-17, article id 13Conference paper (Refereed)

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.

• 48.
Department of Pure Mathematics, Eurasian National University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Department of Mathematics, Narvik University College. Department of Pure Mathematics, Eurasian National University. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Some new results concerning a class of third-order differential equations2015In: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 94, no 2, p. 419-434Article in journal (Refereed)

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

• 49.
Department of Mathematics, Claremont McKenna College.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Real interpolation and measure of weak noncompactness1995In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 175, no 1, p. 5-12Article in journal (Refereed)

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.

• 50.
Department of Mathematics, Claremont McKenna College.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Lipschitz-Orlicz spaces and the Laplace equation1996In: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, no 178, p. 81-101Article in journal (Refereed)
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