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• 1.
University Pretoria, South Africa.
University of the Basque Country, Spain. Mälardalens högskola, Akademin för utbildning, kultur och kommunikation, Utbildningsvetenskap och Matematik.
Common Fixed Points of Generalized Rational Type Cocyclic Mappings in Multiplicative Metric Spaces2015Ingår i: Discrete dynamics in nature and society, ISSN 1026-0226, E-ISSN 1607-887X, Vol. 2015, 532725Artikel i tidskrift (Refereegranskat)

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. Abdikalikova, Zamira
Compactness of embedding between Sobolev type spaces with multiweighted derivatives2009Ingår i: AIHT : Analysis, Inequalities and Homogenization Theory: Midnight sun conference in honor of Lars-Erik Persson, 2009Konferensbidrag (Övrigt vetenskapligt)

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. Abdikalikova, Zamira
Embedding theorems for spaces with multiweighted derivatives2007Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)

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. Abdikalikova, Zamira
Some new results concerning boundedness and compactness for embeddings between spaces with multiweighted derivatives2009Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

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 ≤ q2009Rapport (Övrigt vetenskapligt)
• 6. Abdikalikova, Zamira
Summability of a Tchebysheff system of functions2007Rapport (Övrigt vetenskapligt)
• 7.
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 12011Ingår i: Czechoslovak Mathematical Journal, ISSN 0011-4642, E-ISSN 1572-9141, Vol. 61, nr 1, 7-26 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Boundedness and compactness of the embedding between spaces with multiweighted derivatives when 1≤ q2009Rapport (Övrigt vetenskapligt)
• 9.
Högskolan i Jönköping, Tekniska Högskolan, JTH, Matematik.
Strong L1 convergence to equilibrium without entropy conditions for the Boltzmann equation1999Ingår i: Communications in Partial Differential Equations, ISSN 0360-5302, E-ISSN 1532-4133, Vol. 24, nr 7-8, 1501-1535 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. University of Tromsø ; The Arctic University of Norway, Narvik.
Fejer and Hermite–Hadamard Type Inequalitiesfor N-Quasiconvex Functions2017Ingår i: Mathematical notes of the Academy of Sciences of the USSR, ISSN 0001-4346, E-ISSN 1573-8876, Vol. 102, nr 5-6, 599-609 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some New Refined Hardy Type Inequalities with Breaking Points p = 2 or p = 32014Ingår i: Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation: 22nd International Workshop in Operator Theory and its Applications, Sevilla, July 2011 / [ed] Manuel Cepedello Boiso; Håkan Hedenmalm; Marinus A. Kaashoek; Alfonso Montes Rodríguez; Sergei Treil, Basel: Encyclopedia of Global Archaeology/Springer Verlag, 2014, 1-10 s.Konferensbidrag (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new refined Hardy type inequalities with general kernels and measures2010Ingår i: Aequationes Mathematicae, ISSN 0001-9054, E-ISSN 1420-8903, Vol. 79, nr 1-2, 157-172 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Inequalities for averages of quasiconvex and superquadratic functions2016Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 19, nr 2, 535-550 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new estimates of the ‘Jensen gap’2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2016, 39Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Some new scales of refined Hardy type inequalities via functions related to superquadracity2013Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 16, nr 3, 679-695 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. University of Zagreb. University of Zagreb.
General inequalities via isotonic subadditive functionals2007Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 10, nr 1, 15-28 s.Artikel i tidskrift (Refereegranskat)

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 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 inequalities2012Ingår i: 9th International Conference on Mathematical Problems in Engineering, Aerospace and Sciences: ICNPAA 2012 / [ed] Seenith Sivasundaram, Melville, NY: American Institute of Physics (AIP), 2012, 739-746 s.Konferensbidrag (Refereegranskat)

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 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 inequalities2015Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 18, nr 2, 615-627 s.Artikel i tidskrift (Refereegranskat)

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 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 inequalities2014Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 17, nr 3, 1105-1114 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik.
Inequalities for some classes of Hardy type operators and compactness in weighted Lebesgue spaces2016Doktorsavhandling, sammanläggning (Övrigt vetenskapligt)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Boundedness and compactness of a class of Hardy type operators2016Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, nr 1, 324Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. UiT, Tromso.
Hardy type inequalities and compactness of a class of integral operators with logarithmic singularities2018Ingår i: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, Vol. 21, nr 1, 201-215 s.Artikel i tidskrift (Refereegranskat)

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 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 Kernels2017Ingår i: Journal of Mathematical Inequalities, ISSN 1846-579X, E-ISSN 1848-9575, Vol. 11, nr 3, 683-694 s.Artikel i tidskrift (Refereegranskat)

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"2015Ingår i: Mathematical Biosciences and Engineering, ISSN 1547-1063, E-ISSN 1551-0018, Vol. 12, nr 2Artikel i tidskrift (Refereegranskat)
• 25.
Institute of Mathematics of the Polish Academy of Sciences, Warsaw, Poland.
Umeå universitet, Teknisk-naturvetenskapliga fakulteten, Institutionen för matematik och matematisk statistik.
The boundary Harnack inequality for variable exponent p-Laplacian, Carleson estimates, barrier functions and p(⋅)-harmonic measures2016Ingår i: Annali di Matematica Pura ed Applicata, ISSN 0373-3114, E-ISSN 1618-1891, Vol. 195, nr 2, 623-658 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
On a new class of Hardy-type inequalities2012Ingår i: Journal of inequalities and applications (Print), ISSN 1025-5834, E-ISSN 1029-242X, Vol. 2012, nr 259Artikel i tidskrift (Refereegranskat)

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, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
In times of regional geopolitical turmoil – Why do some equity funds performbetter than others?2014Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)

I tider av geopolitiskt tumult – hur kommer det sig att vissa investeringsportföljer, aktiefonder, presterar bättre än andra? Är det ren tur, effekten av systematisk risk eller spelar faktorer så som investeringsstilar och förvaltningsförmåga en signifikant roll i en fonds avkastning?

Eftersom finansiella marknader ofta reflekterar makromiljön, kan man urskilja att mycket av de föränderligheter östeuropeiska aktier upplevde förra året tycks härstamma från ett antal geopolitiska händelser; så som förra sommarens sammandrabbningar mellan turkisk polis och demonstranter till den aktuella krisen gällande Ryssland och Ukraina. Det säger sig självt att händelserna har påverkat avkastningen på bland annat aktieinvesteringar i regionen och således skapat en orolig miljö för investerare och fondförvaltare som investerar i Östeuropa.

Denna uppsats ämnar utforska dessa makroekonomiska händelsers påverkan på marknaden och således fondförvaltarnas investeringsportföljer – fonder. Uppsatsen ämnar även bidra med aspekter för eventuella investeringsstrategier som är att föredra över andra under geopolitiskt oroliga omständigheter i syfte att minimera efterföljande risker.

• 28.
Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
Statistical Modelling and the Fokker-Planck Equation2008Självständigt arbete på avancerad nivå (magisterexamen)Studentuppsats (Examensarbete)

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 Domanis1992Ingår i: SIAM Journal on Mathematical Analysis, Vol. 5, nr 23, 751-764 s.Artikel i tidskrift (Refereegranskat)

Galerkinmetoden studeras för att lösa ingegralekvationer med randvärden för Laplacepoperatorn för non-smooth områden. Konvergens visas med ett villkor på nätstorleken., vilket består av den lokala krökningen för approximerande områden. Feluppskattningar är härledda, och resultaten generaliserar för system av ekvationer.

• 30.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Optimeringslära och systemteori.
ESG-investerande och portföljresultat: En studie av ESG-investerande utifrån metoden bäst-i-klassen2015Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)

Till följd av en mer globaliserad och industriell omvärld har hållbarhetsfrågor sett till miljö och samhälle blivit en vardaglig rubrik i finansvärlden. Att företag ska ha aktivt arbete mot hållbarhet och ansvarstagande är på så när en självklarhet om inte ett måste. Denna studies syfte är att undersöka ansvarsfullt investerande och portföljresultat. För att analysera detta förhållande fokuserar arbetet på ESG där dess dimensioner inkluderas gemensamt genom optimering, diskussion och slutsats. Arbetet berör hur ESG kan integreras i investeringsprocessen men tyngden av studien och den övergripande frågan angriper diskussionen kring en portföljs resultat vid inkluderande av ESG. Metoder som används är Modern portföljteori kombinerat med implementering av ESG enligt ”bäst-i-klassen”. Studiens resultat leder till slutsatsen att ESG utöver dess positiva effekter, förutsatt en korrekt bedömning, på hållbarhet även är finansiellt argumenterbart för investerare.

• 31.
Blekinge Tekniska Högskola, Sektionen för teknik, Avdelningen för telekommunikationssystem.
Security Issues in Wireless Systems2009Självständigt arbete på avancerad nivå (magisterexamen)Studentuppsats (Examensarbete)

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 Tekniska Högskola, Sektionen för ingenjörsvetenskap.
Blekinge Tekniska Högskola, Sektionen för ingenjörsvetenskap.
Optimal Solutions Of Fuzzy Relation Equations2010Självständigt arbete på avancerad nivå (masterexamen)Studentuppsats (Examensarbete)

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 Tekniska Högskola, Sektionen för ingenjörsvetenskap.
Modeling and Simulation of Urea Dosing System2013Självständigt arbete på avancerad nivå (masterexamen)Studentuppsats (Examensarbete)

Conclusions In the theory section, we have shown two fundamental principles of fluid flow, conservation of mass (continuity equation) and conservation of momentum (the Cauchy equation) of fluid motion. To get to Euler equations we employed the Navier-Stokes equations for incompressible flow, by neglecting fluid viscosity making μ=0 [21], with this assumption Navier-Stokes equations take the form of Euler equations, detailed discussions and derivations might be found at Atil’s lecture notes[21][23] The second last step is derivation of exact solutions to the Navier-Stokes quations, the Hagen–Poiseuille eqautions, by applying basic physics with the assumptions of laminar flow, constant viscosity and straight pipe with circular cross-section, we derived Hagen–Poiseuille eqautions, this led to a relationship between pressure changes over a length L of pipe, and a friction factor associated with viscous effects We then applied Euler equations to derive well known Bernoulli equation, which signifies that when the velocity increases in a fluid stream, the pressure decreases and when velocity decreases the pressure increases [31] [15] We must highlight that all of these equations have their roots in the Navier– Stokes equations, once again underscoring the universality of these equations in the context of describing the motion of fluids [10] Why did we have to derive all these equations? It is important when applying any equation that we are aware of the restrictions on its use, the restrictions are normally seen in the derivation of the equation when certain simplifying assumptions about the nature of the problem are made. If we ignore the restrictions, we may get inaccurate results from the equation. e.g. an equation was derived while assuming that the flow was incompressible, which means that the speed of the flow is much less than the speed of sound. If you use this form for a supersonic flow, the answer will be wrong [32] In the Modeling and simulations section, the following steps have been completed as given on the goal statement: To broaden our level of understanding and interactions of different components we shown simplified model of the UDS To ensure model meets requirements and fulfills its intended use we have verified (e.g. Right flow, pressure, and mass flow rate) To gain confidence in the model we have validated by comparing model with the real system data and found acceptable agreement We have also shown Effects of various parameters of the system, such as Volumetric Efficiency of the pump, return restriction diameter variations, relationship between flow rate and speed Finally we have demonstrated Adblue density as function of pressure and temperature, and effects of the temperature on Dynamic and Kinematic viscosity of the Adblue, more Adblue fluid properties is also given on Appendix B

• 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 sciences2014Ingår i: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 7, nr 1Artikel i tidskrift (Refereegranskat)
• 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 propagation2013Ingår i: Interfaces and free boundaries (Print), ISSN 1463-9963, E-ISSN 1463-9971, Vol. 15, nr 2, 167-180 s.Artikel i tidskrift (Refereegranskat)
• 36. Aiki, T.
Karlstads universitet, Fakulteten för hälsa, natur- och teknikvetenskap (from 2013), Institutionen för matematik och datavetenskap.
Existence and uniqueness of solutions to a mathematical model predicting service life of concrete structures2009Ingår i: Advances in Mathematical Sciences and Applications, ISSN 1343-4373, Vol. 19, 119-129 s.Artikel i tidskrift (Refereegranskat)
• 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 limit2012Ingår i: Discrete and Continuous Dynamical Systems. Series S, ISSN 1937-1632, E-ISSN 1937-1179, Vol. 5, nr 1, 15-28 s.Artikel i tidskrift (Refereegranskat)
• 38.
Gifu University, Japan.
Eindhoven University of Technology.
Large time behavior of solutions to a moving-interface problem modeling concrete carbonation2010Ingår i: Communications on Pure and Applied Analysis, ISSN 1534-0392, E-ISSN 1553-5258, Vol. 9, nr 5, 1117-1129 s.Artikel i tidskrift (Refereegranskat)
• 39.
Tokyo Womens University.
Netherlands.
Large-time asymptotics of moving-reaction interfaces involving nonlinear Henry’s law and time-dependent Dirichlet data2013Ingår i: Nonlinear Analysis, ISSN 0362-546X, E-ISSN 1873-5215, Vol. 93, 3-14 s.Artikel i tidskrift (Refereegranskat)

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 sulfatation2014Ingår i: Mathematical methods in the applied sciences, ISSN 0170-4214, E-ISSN 1099-1476, Vol. 38, nr 7, 1451-1464 s.Artikel i tidskrift (Refereegranskat)
• 41.
Gifu University, Japan.
Eindhoven University of Technology.
On uniqueness of a weak solution of one-dimensional concrete carbonation problem2011Ingår i: Discrete and Continuous Dynamical Systems, ISSN 1078-0947, E-ISSN 1553-5231, Vol. 29, nr 4, 1345-1365 s.Artikel i tidskrift (Refereegranskat)

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 tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Coercive estimates for the solutions of some singular differential equations and their applications2013Licentiatavhandling, sammanläggning (Övrigt vetenskapligt)

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.
Department of Pure Mathematics, Eurasian National University.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper. 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 equations2015Ingår i: Applicable Analysis, ISSN 0003-6811, E-ISSN 1563-504X, Vol. 94, nr 4, 419-434 s.Artikel i tidskrift (Refereegranskat)

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

• 44.
Department of Mathematics, Claremont McKenna College.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Real interpolation and measure of weak noncompactness1995Ingår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, Vol. 175, nr 1, 5-12 s.Artikel i tidskrift (Refereegranskat)

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.

• 45.
Department of Mathematics, Claremont McKenna College.
Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
Lipschitz-Orlicz spaces and the Laplace equation1996Ingår i: Mathematische Nachrichten, ISSN 0025-584X, E-ISSN 1522-2616, nr 178, 81-101 s.Artikel i tidskrift (Refereegranskat)
• 46.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
KTH, Skolan för teknikvetenskap (SCI), Matematik (Inst.), Matematisk statistik.
Analys av reporäntans påverkan på prissättningen av bostäder: Slår reporänteförändringar lika mycket på bostäder av olika storlek?2015Självständigt arbete på grundnivå (kandidatexamen), 10 poäng / 15 hpStudentuppsats (Examensarbete)

Syftet med denna studie är att undersöka huruvida reporänteförändringar har diverse påverkan på bostäder av olika storlek, med fokus på ett antal områden i Stockholm. Efter utförda regressionsanalyser samt hypotesprövningar har det kunnat konstateras att reporäntans påverkan på bostadspriser skiljer sig åt för olika bostadsstorlekar. Bostadsmarknaden präglas idag av stora förändringar och reporäntan är på en historisk lågpunkt, -0.25%. Det spekuleras kring hur Riksbankens styrränta faktiskt påverkar priserna på bostadsmarknaden och om denna påverkar olika stora bostäder i olika stor grad. Sålda lägenheter mellan åren 2005-2015 har analyserats där hänsyn har tagits till reporäntan. Analysens fokus har varit på reporäntans betydelse samt om denna betydelse varierar för olika stora bostäder. Viktiga parametrar kring pris av bostadsrätter har använts i modellen som konstruerats.

• 47.
Institute of Mathematics, Ruhr-Universität, D-44780 Bochum.
SISSA. Luleå tekniska universitet.
Symmetries of Schrödinger operator with point interactions1998Ingår i: Letters in Mathematical Physics, ISSN 0377-9017, E-ISSN 1573-0530, Vol. 45, nr 1, 33-47 s.Artikel i tidskrift (Refereegranskat)

The transformations of all the Schrödinger operators with point interactions in dimension one under space reflection P, time reversal T and (Weyl) scaling Wλ are presented. In particular, those operators which are invariant (possibly up to a scale) are selected. Some recent papers on related topics are commented upon

• 48.
Institut für Angewandte Mathematik, Universität Bonn.
Institut für Angewandte Mathematik, Universität Bonn. Luleå tekniska universitet.
Many body problems with "spin"-related contact interactions2001Ingår i: Reports on mathematical physics, ISSN 0034-4877, E-ISSN 1879-0674, Vol. 47, nr 2, 157-166 s.Artikel i tidskrift (Refereegranskat)

We study quantum mechanical systems with "spin"-related contact interactions in one dimension. The boundary conditions describing the contact interactions are dependent on the spin states of the particles. In particular we investigate the integrability of N-body systems with δ-interactions and point spin couplings. Bethe ansatz solutions, bound states and scattering matrices are explicitly given. The cases of generalized separated boundary condition and some Hamiltonian operators corresponding to special spin related boundary conditions are also discussed.

• 49.
BiBoS Research Center.
Fachbereich Physik, Universität-GH Essen. Luleå tekniska universitet. Fachbereich Physik, Universität-GH Essen. Nuclear Physics Institute, Czech Academy of Sciences.
S-matrix, resonances, and wave functions for transport through billiards with leads1996Ingår i: Journal of Mathematical Physics, ISSN 0022-2488, E-ISSN 1089-7658, Vol. 37, nr 10, 4888-4903 s.Artikel i tidskrift (Refereegranskat)

For a simple model describing the S-matrices of open resonators the statistical properties of the resonances are investigated, as well as the wave functions inside the resonator

• 50.
Department of Mathematics, Ruhr-University, Bochum.
Luleå tekniska universitet.
Finite rank perturbations and distribution theory1999Ingår i: Proceedings of the American Mathematical Society, ISSN 0002-9939, E-ISSN 1088-6826, Vol. 127, nr 4, 1151-1161 s.Artikel i tidskrift (Refereegranskat)
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