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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, 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.
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, 1501-1535 p.Article 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.

• 3.
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, 1-10 p.Conference 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

• 4.
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, 535-550 p.Article 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.

• 5.
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, 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.

• 6.
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, 679-695 p.Article 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

• 7.
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, 1105-1114 p.Article 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.

• 8.
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, 615–627- p.Article 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.

• 9.
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, 739-746 p.Conference 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.

• 10.
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 < ∞

• 11.
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, 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.

• 12. Abylayeva, A.M.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Additive weighted Lp estimates of some classes of integralIn: Mathematical Inequalities & Applications, ISSN 1331-4343, E-ISSN 1848-9966, jmi-2360Article in journal (Refereed)
• 13. 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)
• 14.
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, 623-658 p.Article 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.

• 16.
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.

• 17.
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, 751-764 p.Article 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.

• 19.
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.

• 20.
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.

• 21.
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.

• 22.
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.

• 23.
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)
• 24. 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, 167-180 p.Article in journal (Refereed)
• 25. Aiki, T.
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, 1345-1365 p.Article in journal (Refereed)
• 26. 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, 119-129 p.Article in journal (Refereed)
• 27.
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, 15-28 p.Article in journal (Refereed)
• 28. Aiki, Toyohiko
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, 1117-1129 p.Article in journal (Refereed)
• 29. 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, 1451-1464 p.Article in journal (Refereed)
• 30.
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, 3-14 p.Article 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.

• 31.
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.

• 32.
Department of Pure Mathematics, Eurasian National University.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. 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 4, 419-434 p.Article 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

• 33.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Analys av reporäntans påverkan på prissättningen av bostäder: Slår reporänteförändringar lika mycket på bostäder av olika storlek?2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

The aim of this study is to investigate whether changes of the repo rate has diverse effects on apartments of different sizes, targeting specific areas in Stockholm. A conclusion, that the effect of the repo rate differs for apartments of different sizes, was made based on regression analysis and hypothesis testing. The housing market is characterized by vast shifts and the repo rate has reached a historical low-point of -0.25 per cent. It is reflected upon how the central bank’s steering interest rate actually impacts the prices on the housing market and whether it has distinct effects on apartments of different sizes. Apartments sold between years 2005-2015 have been analyzed where the gravity of the repo rate has been taken into consideration and if its significance varies amongst apartments of different sizes. Important parameters concerning apartment prices have been utilized in the constructed model.

• 34. Albeverioa, S.
Linnaeus University, Faculty of Science and Engineering, School of Computer Science, Physics and Mathematics.
The Cauchy problems for evolutionary pseudo-differential equations over p-adic field and the wavelet theory2011In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 375, no 1, 82-98 p.Article in journal (Refereed)
• 35. Aleksanyan, H.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.). KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).
L2-estimates for singular oscillatory integral operators2016In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 441, no 2, 529-548 p.Article in journal (Refereed)

In this note we study singular oscillatory integrals with linear phase function over hypersurfaces which may oscillate, and prove estimates of L2L2 type for the operator, as well as for the corresponding maximal function. If the hypersurface is flat, we consider a particular class of a nonlinear phase functions, and apply our analysis to the eigenvalue problem associated with the Helmholtz equation in R3.

• 36.
Stockholm University, Faculty of Science, Department of Mathematics.
On eigenvalues of the Schrödinger operator with a complex-valued polynomial potential2010Licentiate thesis, comprehensive summary (Other academic)

In this thesis, we generalize a recent result of A. Eremenko and A. Gabrielov on irreducibility of the spectral discriminant for the Schroedinger equation with quartic potentials.

In the first paper, we consider the eigenvalue problem with a complex-valued polynomial potential of arbitrary degree d and show that the spectral determinant of this problem is connected and irreducible. In other words, every eigenvalue can be reached from any other by analytic continuation. We also prove connectedness of the parameter spaces of the potentials that admit eigenfunctions satisfying k > 2 boundary conditions, except for the case d is even and k = d/2. In the latter case, connected components of the parameter space are distinguished by the number of zeros of the eigenfunctions.

In the second paper, we only consider even polynomial potentials, and show that the spectral determinant for the eigenvalue problem consists of two irreducible components. A similar result to that of paper I is proved for k boundary conditions.

• 37.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimering av antal flygplanssäten: Modellering med avseende på yta, intäkt och efterfrågan 2014Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

When managing the number of seats in a plane it is important to take into account the passenger intensity, i.e. how tightly the seats are located. The critical variable for these decisions is the distance between a point on one seat and the same point on the next seat. Critical variables that have small values , i.e. short distance, means more rows of seats and thus higher profits. Any unused space is an expensive waste due to the fact that the difference between profit and loss for a given flight can be as little as less than a cost of a seat.

The purpose of this thesis is to develop a mathematical model to find the optimal seat allocation between classes in an airplane. The modeling shall be performed so that the revenues for the airlines and usage of the surface of the cabin are maximized and yet meet demand. This thesis also aims to investigate which different market strategies of airlines there are and how these affect the seat allocation.

The report shows that the revenue and demand are not the only factors that affect the optimal number of seats for a class, but that there are also external factors that may play a role. The model's ranking in reality is difficult to assess because of the lack of realistic and reliable data that can be used for a basis for decisions

• 38.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Valuing Patents with Linear Regression: Identifying value indicators and using a linear regression model to value  patents2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This thesis consist of two parts. The first part of the thesis will conduct a multiple regression on a data-set obtained from the Ocean Tomo’s auction results between 2006 to 2008 with the purpose to identify key value indicators and investigate to what extent it is possible to predict the value of a patent. The final regression model consist of the following covariates Average number of citings per year, share of active family members, age of the patent, average invested USD per year, and nine CPC’s as dummy variables. The second part of the thesis will investigate why it is difficult to value a patent and the different factors and changes that have contributed to a growing importance of patent valuation by applying theories from knowledge-based economy and industrial change. This is done by conducting a literature review and interviews.

The results of this thesis states that it is only possible to construct a model that has an explanation degree of 50.21%. The complexity of a patents value derives from uncertainties about future context of the patent and non-quantifiable parameters of the patent. Furthermore we find evidence of a shift from tangible assets to intangible assets in industrial nations which motivates the growing importance of patent valuation.

• 39.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
A new approach for studying cavitation in lubrication2014In: Journal of tribology, ISSN 0742-4787, E-ISSN 1528-8897, Vol. 136, no 1, 11706Article in journal (Refereed)

The underlying theory, in this paper, is based on clear physical arguments related to conservation of mass flow and considers both incompressible and compressible fluids. The result of the mathematical modeling is a system of equations with two unknowns, which are related to the hydrodynamic pressure and the degree of saturation of the fluid. Discretization of the system leads to a linear complementarity problem (LCP), which easily can be solved numerically with readily available standard methods and an implementation of a model problem in matlab code is made available for the reader of the paper. The model and the associated numerical solution method have significant advantages over today's most frequently used cavitation algorithms, which are based on Elrod-Adams pioneering work

• 40.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Fluid and Experimental Mechanics. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Flow in thin domains with a microstructure: Lubrication and thin porous media2017In: AIP Conference Proceedings, ISSN 0094-243X, E-ISSN 1551-7616, Vol. 1798, 020172Article in journal (Refereed)

This paper is devoted to homogenization of different models of flow in thin domains with a microstructure. The focus is on applications connected to the effect of surface roughness in full film lubrication, but a parallel to flow in thin porous media is also discussed. Mathematical models of such flows naturally include two small parameters. One is connected to the fluid film thickness and the other to the microstructure. The corresponding asymptotic analysis is a delicate problem, since the result depends on how fast the two small parameters tend to zero relative to each other. We give a review of the current status in this area and point out some future challenges.

• 41.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science. Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Homogenization of a Reynolds equation describing compressible flow2012In: Journal of Mathematical Analysis and Applications, ISSN 0022-247X, E-ISSN 1096-0813, Vol. 390, no 2, 456-471 p.Article in journal (Refereed)

We homogenize a Reynolds equation with rapidly oscillating film thickness function hε, assuming a constant compressiblity factor in the pressure-density relation. The oscillations are due to roughness on the bounding surfaces of the fluid film. As shown by previous studies, homogenization is an effective approach for analyzing the effects of surface roughness in hydrodynamic lubrication. By two-scale convergence theory we obtain the limit problem (homogenized equation) and strong convergence in L2 for the unknown density ρε. By adding a small corrector term we also obtain strong convergence in the Sobolev norm.

• 42.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Homogenization of the Reynolds equation2013In: Encyclopedia of Tribology, Berlin: Springer-Verlag New York Inc. , 2013, 1685-1690 p.Chapter in book (Refereed)
• 43.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Machine Elements.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
A new concept in cavitation modelling2013In: Tribo Lyon 2013: book of abstracts : a joint event of WTC 2013, Lyon, 2013, 170- p.Conference paper (Refereed)
• 44.
Linköping University, Department of Electrical Engineering. Linköping University, Faculty of Science & Engineering.
Linköping University, Department of Electrical Engineering, Information Coding. Linköping University, Faculty of Science & Engineering. Linköping University, Department of Electrical Engineering, Integrated Circuits and Systems. Linköping University, Faculty of Science & Engineering.
Transfer Characteristics and Bandwidth Limitation in a Linear-Drift Memristor Model2015In: 2015 EUROPEAN CONFERENCE ON CIRCUIT THEORY AND DESIGN (ECCTD), IEEE , 2015, 332-335 p.Conference paper (Refereed)

The linear-drift memristor model, suggested by HP Labs a few years ago, is used in this work together with two window functions. From the equations describing the memristor model, the transfer characteristics of a memristor is formulated and analyzed. A first-order estimation of the cut-off frequency is shown, that illustrates the bandwidth limitation of the memristor and how it varies with some of its physical parameters. The design space is elaborated upon and it is shown that the state speed, the variation of the doped and undoped regions of the memristor, is inversely proportional to the physical length, and depth of the device. The transfer characteristics is simulated for Joglekar-Wolf, and Biolek window functions and the results are analyzed. The Joglekar-Wolf window function causes a distinct behavior in the tranfer characteristics at cut-off frequency. The Biolek window function on the other hand gives a smooth state transfer function, at the cost of loosing the one-to-one mapping between charge and state. We also elaborate on the design constraints derived from the transfer characteristics.

• 45.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Optimization and Systems Theory.
Optimization of Production Scheduling in the Dairy Industry2015Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

This thesis presents a case study of mathematical production scheduling optimization applied on Arla Foods AB’s production of dairy products. The scheduling was performed as a possible remedy for problems caused by overcrowded finished goods warehouse. Based on the scheduling, conclusions were made on whether the existing two-shift production is sufficient or if an additional night shift should be introduced. In parallel, an empirical and theoretical analysis on the perceived effects of night shift work on employees was conducted.

For the optimization, mixed integer programming was used to model the production context through a discrete time scheduling lot-sizing model developed in this thesis. The model developed and implemented on Arla Foods AB contributes to the research field through its feature of relatively low complexity enabling scheduling of extensive production systems when applied in industrial contexts where products may be categorized.

The thesis concludes that mathematical production scheduling can solve Arla Foods AB’s production problematics and suggests reallocation of the existing shifts for the purpose of reduced costs and acceptable warehouse levels. This reallocation would incur production during inconvenient hours whereas management remedies reducing negative effects of night shift work are identified.

• 46.
Luleå University of Technology, Department of Engineering Sciences and Mathematics, Mathematical Science.
Near-boundary asymptotics for correlation kernels2013In: Journal of Geometric Analysis, ISSN 1050-6926, E-ISSN 1559-002X, Vol. 23, no 1, 73-95 p.Article in journal (Refereed)

We discuss asymptotic formulas for the correlation kernel corresponding to a (more or less) general potential Q in the plane. If Kn is such a kernel, there is a known asymptotic formula Kn(z, z)=nΔQ(z)+B1(z)+n-1B2(z)+⋯ valid for z in the interior of a certain compact set known as the "droplet" corresponding to Q (on which ΔQ>0). On the other hand, if z is in the exterior of the droplet, Kn(z, z) converges to zero exponentially in n. Results of this type are useful in random matrix theory and conformal field theory; they have recently been used to prove the Gaussian field convergence in the interior of the droplet for fluctuations of eigenvalues of random normal matrices. To be able to extend such results beyond the interior, it becomes necessary to have a certain uniformity of estimates as z approaches the boundary either from the interior or from the exterior. Such estimates have to our knowledge hitherto not been known on a rigorous level. This note intends to fill this gap. We will consider applications in later publications. Our treatment of the (interior) asymptotics relies in an essential way on previous work due to Berman, Berndtsson, and Sjöstrand (Ark. Mat. 46, 2008), and Berman (Indiana Univ. Math. J. 58, 2009). We hope that this note can to some extent be regarded as a contribution to that work.

• 47.
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematical Statistics.
Approximate Bayesian Learning of Partition Directed Acyclic Graphs2016Independent thesis Advanced level (degree of Master (Two Years)), 20 credits / 30 HE creditsStudent thesis

Partition directed acyclic graphs (PDAGs) is a model whereby the conditional probability tables (CPTs) are partitioned into parts with equal probability. In this way, the number of parameters that need to be learned can be significantly reduced so that some problems become more computationally feasible. PDAGs have been shown to be connected to labeled DAGs (LDAGs) and the connection is summarized here. Furthermore, a clustering algorithm is compared to an exact algorithm for determining a PDAG. To evaluate the algorithm, we use it on simulated data where the expected result is known.

• 48. Anderson, D.
University of Borås, School of Engineering. University of Borås, School of Engineering.
The optimal journey from A to B2008In: American Journal of Physics, ISSN 0002-9505, E-ISSN 1943-2909, Vol. 76, no 9, 863-866 p.Article in journal (Refereed)
• 49.
Jönköping University, School of Engineering, JTH, Mathematics.
On the curvature of an inner curve in a Schwarz--Christoffel mapping2009In: Further Progress in Analysis: Proceedings of the 6th International ISAAC Congress, Ankara, Turkey, 2007, World Scientific , 2009, 281-290 p.Conference paper (Refereed)

In the so called outer polygon method, an approximative conformal mapping for a given simply connected region Ω is constructed using a Schwarz–Christoffel mapping for an outer polygon, a polygonal region of which Ω is a subset. The resulting region is then bounded by a C-curve, which among other things means that its curvature is bounded.In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz–Christoffel mapping from R, the unit disk or upper half–plane, to a polygonal region P of a curve inside R. From the Schwarz–Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.

• 50.
Växjö University, Faculty of Mathematics/Science/Technology, School of Mathematics and Systems Engineering.
On the curvature of an inner curve in a Schwarz-Christoffel mapping2007Report (Other academic)

In the so called outer polygon method, an approximative conformal mapping for a given simply connected region \Omega is constructed using a Schwarz-­Christoffel mapping for an outer polygon, a polygonal region of which \Omega is a subset. The resulting region is then bounded by a C^\infty -curve, which among other things means that its curvature is bounded.

In this work, we study the curvature of an inner curve in a polygon, i.e., the image under the Schwarz-­Christoffel mapping from R, the unit disk or upper half­plane, to a polygonal region P of a curve inside R. From the Schwarz-­Christoffel formula, explicit expressions for the curvature are derived, and for boundary curves, appearing in the outer polygon method, estimations of boundaries for the curvature are given.

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