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| 2. |
- Carlsson, Linus, 1972-, et al.
(författare)
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A note on B-envelope of holomorphy and B-extendable domains
- 2008
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Ingår i: Complex Variables and Elliptic Equations. - Abingdon, Oxon, UK : Taylor & Francis. - 1747-6933 .- 1747-6941. ; 53:4, s. 307-309
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Tidskriftsartikel (refereegranskat)abstract
- Let B subset of H(infinity)(X) be a Banach Algebra on a Riemann domain X over C(n). We show that under certain conditions on B and X, all functions in B can be extended to functions in B(E(B, X)) where E(B, X) is the B-envelope of holomorphy.
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| 3. |
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| 4. |
- Carlsson, Linus, 1972-
(författare)
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Nebenhülle and the Gleason problem
- 2010
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Ingår i: Proceedings of the American Mathematical Society. - : American Mathematical Society (AMS). - 0002-9939 .- 1088-6826. ; 138:1, s. 267-273
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Tidskriftsartikel (refereegranskat)
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| 5. |
- Lundengård, Karl, 1987-
(författare)
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Generalized Vandermonde matrices and determinants in electromagnetic compatibility
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- Matrices whose rows (or columns) consists of monomials of sequential powers are called Vandermonde matrices and can be used to describe several useful concepts and have properties that can be helpful for solving many kinds of problems. In this thesis we will discuss this matrix and some of its properties as well as a generalization of it and how it can be applied to curve fitting discharge current for the purpose of ensuring electromagnetic compatibility.In the first chapter the basic theory for later chapters is introduced. This includes the Vandermonde matrix and some of its properties, history, applications and generalizations, interpolation and regression problems, optimal experiment design and modelling of electrostatic discharge currents with the purpose to ensure electromagnetic compatibility.The second chapter focuses on finding the extreme points for the determinant for the Vandermonde matrix on various surfaces including spheres, ellipsoids, cylinders and tori. The extreme points are analysed in three dimensions or more.The third chapter discusses fitting a particular model called the p-peaked Analytically Extended Function (AEF) to data taken either from a standard for electromagnetic compatibility or experimental measurements. More specifically the AEF will be fitted to discharge currents from the IEC 62305-1 and IEC 61000-4-2 standards for lightning protection and electrostatic discharge immunity as well as some experimentally measured data of similar phenomena.
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| 6. |
- Arnlind, Joakim, et al.
(författare)
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Construction of n-Lie algebras and n-ary Hom-Nambu-Lie algebras
- 2011
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Ingår i: Journal of Mathematical Physics. - : AIP Publishing. - 0022-2488 .- 1089-7658. ; 52:12, s. 123502-
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Tidskriftsartikel (refereegranskat)abstract
- As n-ary operations, generalizing Lie and Poisson algebras, arise in many different physical contexts, it is interesting to study general ways of constructing explicit realizations of such multilinear structures. Generically, they describe the dynamics of a physical system, and there is a need of understanding their quantization. Hom-Nambu-Lie algebras provide a framework that might be an appropriate setting in which n-Lie algebras (n-ary Nambu-Lie algebras) can be deformed, and their quantization studied. We present a procedure to construct (n + 1)-ary Hom-Nambu-Lie algebras from n-ary Hom-Nambu-Lie algebras equipped with a generalized trace function. It turns out that the implications of the compatibility conditions, that are necessary for this construction, can be understood in terms of the kernel of the trace function and the range of the twisting maps. Furthermore, we investigate the possibility of defining (n + k)-Lie algebras from n-Lie algebras and a k-form satisfying certain conditions. (C) 2011 American Institute of Physics. [doi:10.1063/1.3653197]
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| 7. |
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| 8. |
- Silvestrov, Sergei
(författare)
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Interpolation of Normed Abelian Groups and Non-Commutative Integration
- 2012
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Ingår i: Analysis for Science, Engineering and Beyond. - Berlin : Springer Berlin/Heidelberg. - 9783642202353 ; , s. 325-341
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Bokkapitel (refereegranskat)abstract
- This is a concise review concerned first of all with the two pioneering far reaching and in many ways yet to be fully explored important papers by Gunnar Sparr and Jaak Peetre on interpolation of normed abelian groups and on non-commutative integration. These papers introduced a general framework unifying many previously known interpolation results and methods in the ways applicable for non-commutative integration and non-commutative extensions of the function spaces, the directions of importance for example in non-commutative geometry and applications in quantum physics. Whence some notions and methods from these papers have been applied in various contexts, many other methods and ideas are yet to be discovered and developed further. In addition to the concise review of these important works by Jaak Peetre and Gunnar Sparr, a brief review is presented also of some related works on non-commutative spaces and non-commutative integration in the contexts of the theory of operator algebras and non-commutative geometry
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| 9. |
- Carlsson, Linus, 1972-
(författare)
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An equivalence to the Gleason problem
- 2010
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Ingår i: Journal of Mathematical Analysis and Applications. - : Elsevier BV. - 0022-247X .- 1096-0813. ; 370:2, s. 373-378
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Tidskriftsartikel (refereegranskat)abstract
- In this article we study the Gleason problem locally. A new method for solving the Gleason A problem is presented. This is done by showing an equivalent statement to the Gleason A problem. In order to prove this statement, necessary and a sufficient conditions for a bounded domain to have the Gleason A property are found. Also an example of a bounded but not smoothly-bounded domain in C(n) is given, which satisfies the sufficient condition at the origin, and hence has the Gleason A property there.
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| 10. |
- Wang, Siyang, et al.
(författare)
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CONVERGENCE OF FINITE DIFFERENCE METHODS FOR THE WAVE EQUATION IN TWO SPACE DIMENSIONS
- 2018
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Ingår i: Mathematics of Computation. - : American Mathematical Society (AMS). - 0025-5718 .- 1088-6842. ; 87:314, s. 2737-2763
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Tidskriftsartikel (refereegranskat)abstract
- When using a finite difference method to solve an initial-boundary-value problem, the truncation error is often of lower order at a few grid points near boundaries than in the interior. Normal mode analysis is a powerful tool to analyze the effect of the large truncation error near boundaries on the overall convergence rate, and has been used in many research works for different equations. However, existing work only concerns problems in one space dimension. In this paper, we extend the analysis to problems in two space dimensions. The two dimensional analysis is based on a diagonalization procedure that decomposes a two dimensional problem to many one dimensional problems of the same type. We present a general framework of analyzing convergence for such one dimensional problems, and explain how to obtain the result for the corresponding two dimensional problem. In particular, we consider two kinds of truncation errors in two space dimensions: the truncation error along an entire boundary, and the truncation error localized at a few grid points close to a corner of the computational domain. The accuracy analysis is in a general framework, here applied to the second order wave equation. Numerical experiments corroborate our accuracy analysis.
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