| 1. |
- Melin, Jan, et al.
(författare)
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Two types of limit cycles of a resonant converter modelled by a three-dimensional system
- 2008
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Ingår i: Nonlinear Analysis. - : Elsevier. - 1751-570X .- 1878-7460. ; 2:4, s. 1275-1286
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Tidskriftsartikel (refereegranskat)abstract
- In this paper, the long-run dynamics of a controlled resonant converter, modelled as a piecewise system, is studied. The modelling of the resonant converter can be done using various approximations and the long-run dynamics of the two dimensional cases were earlier analysed. In this paper, we discuss results that can be extended to the three dimensional case. It seems that limit cycles describe the longrun dynamics in important situations in the three dimensional case, too. Our objective is to relate the limit cycles found previously in the two-dimensional case to those found now in the three dimensional approximation.
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| 2. |
- Toft, Joachim, 1964-
(författare)
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Continuity properties for non-commutative convolution algebras with applications in pseudo-differential calculus
- 2002
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Ingår i: Bulletin des Sciences Mathématiques. - PARIS : Elsevier. - 0007-4497 .- 1952-4773. ; 126:2, s. 115-142
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Tidskriftsartikel (refereegranskat)abstract
- We study continuity properties for a family {sp}p1 of increasing Banach algebras under the twisted convolution, which also satisfies that asp, if and only if the Weyl operator aw(x,D) is a Schatten–von Neumann operator of order p on L2. We discuss inclusion relations between the sp-spaces, Besov spaces and Sobolev spaces. We prove also a Young type result on sp for dilated convolution. As an application we prove that f(a)s1, when as1 and f is an entire odd function. We finally apply the results on Toeplitz operators and prove that we may extend the definition for such operators.
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| 3. |
- Meleshko, Sergey, et al.
(författare)
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Symmetries of Integro-Differential Equations : with applications in mechanics and plasma physics
- 2010
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- This book aims to coherently present applications of group analysis to integro-differential equations in an accessible way. The book will be useful to both physicists and mathematicians interested in general methods to investigate nonlinear problems using symmetries. Differential and integro-differential equations, especially nonlinear, present the most effective way for describing complex processes. Therefore, methods to obtain exact solutions of differential equations play an important role in physics, applied mathematics and mechanics. This book provides an easy to follow, but comprehensive, description of the application of group analysis to integro-differential equations. The book is primarily designed to present both fundamental theoretical and algorithmic aspects of these methods. It introduces new applications and extensions of the group analysis method. The authors have designed a flexible text for postgraduate courses spanning a variety of topics.
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| 4. |
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| 5. |
- Svensson, Per-Anders, 1967-, et al.
(författare)
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On the Number of Equivalence Classes of Attracting Dynamical Systems
- 2009
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Ingår i: P-Adic Numbers, Ultrametric Analysis, and Applications. - Moskva : Pleiades Publishing, Inc.. - 2070-0466 .- 2070-0474. ; 1:3, s. 264-270
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Tidskriftsartikel (refereegranskat)abstract
- We study discrete dynamical systems of the kind h(x) = x + g(x), where g(x) is a monic irreducible polynomial with coefficients in the ring of integers of a p-adic field K. The dynamical systems of this kind, having attracting fixed points, can in a natural way be divided into equivalence classes, and we investigate whether something can be said about the number of those equivalence classes, for a certain degree of the polynomial g(x).
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| 6. |
- Khamitova, Raisa
(författare)
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Symmetries and conservation laws
- 2009
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Conservation laws play an important role in science. The aim of this thesis is to provide an overview and develop new methods for constructing conservation laws using Lie group theory. The derivation of conservation laws for invariant variational problems is based on Noether’s theorem. It is shown that the use of Lie-Bäcklund transformation groups allows one to reduce the number of basic conserved quantities for differential equations obtained by Noether’s theorem and construct a basis of conservation laws. Several examples on constructing a basis for some well-known equations are provided.Moreover, this approach allows one to obtain new conservation laws even for equations without Lagrangians. A formal Lagrangian can be introduced and used for computing nonlocal conservation laws. For self-adjoint or quasi-self-adjoint equations nonlocal conservation laws can be transformed into local conservation laws.One of the fields of applications of this approach is electromagnetic theory, namely, nonlocal conservation laws are obtained for the generalized Maxwell-Dirac equations. The theory is also applied to the nonlinear magma equation and its nonlocal conservation laws are computed.
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| 7. |
- Nyqvist, Robert
(författare)
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Algebraic Dynamical Systems, Analytical Results and Numerical Simulations
- 2007
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Doktorsavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis we study discrete dynamical system, given by a polynomial, over both finite extension of the fields of p-adic numbers and over finite fields. Especially in the p-adic case, we study fixed points of dynamical systems, and which elements that are attracted to them. We show with different examples how complex these dynamics are.For certain polynomial dynamical systems over finite fields we prove that the normalized average of the numbers of linear factors modulo prime numbers exists. We also show how to calculate the average, by using Chebotarev's Density Theorem. The non-normalized version of the average of the number of linear factors of linearized polynomials modulo prime numbers, tends to infinity, so in that case we find an asymptotic formula instead.We have also used a computer to study different behaviors, such as iterations of polynomials over the p-adic fields and the asymptotic relation mention above. In the last chapter we present the computer programs used in different part of the thesis.
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| 8. |
- Ibragimov, Nail H.
(författare)
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Selected works. Volume 3
- 2008
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Bok (övrigt vetenskapligt/konstnärligt)abstract
- Volume III contains Dr.Sci thesis (1972) and papers written during 1987-2004. The main topics in this volume include Lie groups in mathematical physics and mathematical modelling, fluid dynamics, Huygens’ principle and approximate symmetries of equations with small parameter.
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| 9. |
- Ibragimov, Nail H., et al.
(författare)
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Utilization of photon orbital angular momentum in the low-frequency radio domain
- 2007
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Ingår i: Physical Review Letters. - : American Physical Society. - 0031-9007 .- 1079-7114. ; 99:8
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Tidskriftsartikel (refereegranskat)abstract
- We show numerically that vector antenna arrays can generate radio beams that exhibit spin and orbital angular momentum characteristics similar to those of helical Laguerre-Gauss laser beams in paraxial optics. For low frequencies (1 GHz), digital techniques can be used to coherently measure the instantaneous, local field vectors and to manipulate them in software. This enables new types of experiments that go beyond what is possible in optics. It allows information-rich radio astronomy and paves the way for novel wireless communication concepts.
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| 10. |
- Mbiydzenyuy, Gideon
(författare)
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Assessment of Telematic Systems for Road Freight Transport
- 2010
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- The focus of this thesis is the assessment of telematic systems for road freight transport from a planning perspective. The aim is to support strategic decisions related to architectural choices for such systems, with the possibility to achieve synergies by supporting multiple telematic services. The past decade has witnessed enormous growth in cargo volumes resulting in increasing demand for transport capacity. To match this increasing demand only with expansion of infrastructure, e.g. road and vehicles, does not seem to be a sustainable strategy. One of the few approaches with the potential to improve the use of current transport capacity is the integrated use of modern information and communication technology, otherwise known as telematic systems for road transport, an important component within Intelligent Transport Systems (ITS). This type of systems can deliver multiple services that can be used to improve the efficiency and safety of road freight transport. However, attempts to unleash the potential of telematic systems and make maximum possible use of the available transport capacity have been hindered by several challenges ranging from planning and design to development and deployment. Considering the large scope of possible telematic services that can potentially be deployed in road freight transport, this thesis suggests a framework in order to enable structured assessment of telematic systems. Based on the suggested framework, a set of potential transport telematic services are identified and a method for quantifying the value of the services to society is developed. The suggested method takes into account the expected impact on different transportation challenges, such as accidents, fuel consumption, and infrastructure maintenance. Quantitative methods are provided for studying the value of services sharing a common infrastructure. Using quantified benefits of services and costs of various functionalities required by telematic services, the concept of a multi-service architecture is investigated using optimization methods, which handles the multi-dimensional relations between different services that are otherwise difficult to analyze with traditional cost-benefit analysis. The analyses show which telematic services can be achieved with different approaches, such as vehicle-to-vehicle communication, vehicle-to-infrastructure communication, etc. Although multi-service architectures are promising, several challenges need to be overcome, including security, service quality, privacy, and business models. The knowledge gained from the work presented in this thesis can be valuable for different stakeholders, such as governments, service providers, and transport service users, in fostering the planning, design, development, and deployment of telematic systems in transport.
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