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Titlebook: Analysis of Dirac Systems and Computational Algebra; Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa Textbook 2004 Springer Science+Bus

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发表于 2025-3-21 19:39:34 | 显示全部楼层 |阅读模式
期刊全称Analysis of Dirac Systems and Computational Algebra
影响因子2023Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa
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发行地址The main treatment is devoted to the analysis of systems of linear partial differential equations (PDEs) with constant coefficients, focusing attention on null solutions of Dirac systems.All the neces
学科分类Progress in Mathematical Physics
图书封面Titlebook: Analysis of Dirac Systems and Computational Algebra;  Fabrizio Colombo,Irene Sabadini,Daniele C. Struppa Textbook 2004 Springer Science+Bus
影响因子.The subject of Clifford algebras has become an increasingly rich area of research with a significant number of important applications not only to mathematical physics but to numerical analysis, harmonic analysis, and computer science....The main treatment is devoted to the analysis of systems of linear partial differential equations with constant coefficients, focusing attention on null solutions of Dirac systems. In addition to their usual significance in physics, such solutions are important mathematically as an extension of the function theory of several complex variables. The term "computational" in the title emphasizes two main features of the book, namely, the heuristic use of computers to discover results in some particular cases, and the application of Gröbner bases as a primary theoretical tool....Knowledge from different fields of mathematics such as commutative algebra, Gröbner bases, sheaf theory, cohomology, topological vector spaces, and generalized functions (distributions and hyperfunctions) is required of the reader. However, all the necessary classical material is initially presented....The book may be used by graduate students and researchers interested in (hype
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发表于 2025-3-21 23:45:53 | 显示全部楼层
Background Material, generalized function An appendix containing the basic definitions of category theory completes the chapter. Because of the purely instrumental nature of this chapter, we have made no pretense of completeness, and the reader might want to skip this material and refer to it only as the need occurs.
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Analysis of Dirac Systems and Computational Algebra
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Mirva Salminen,Gerald Zojer,Kamrul HossainIn this section we recall the fundamental notions about Clifford algebras. The reader interested in a more thorough treatment can consult [40], [55], [78], [118].
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The Cauchy-Fueter System and Its Variations,ded as background to develop the theory of quaternionic hyperfunctions in one variable. Therefore we give an overview of the theory without proofs, for which we give references pointing out the main differences and the similarities with the theory of holomorphic functions in one complex variable.
发表于 2025-3-23 01:41:58 | 显示全部楼层
Mirva Salminen,Gerald Zojer,Kamrul Hossain book accessible to readers who are not experts in either the algebraic or analytic aspects, we have given the minimum of exposition of the various needed tools which are usually spread over several books. The chapter is divided into three parts: algebraic tools, analytical tools and elements of hyp
发表于 2025-3-23 06:17:29 | 显示全部楼层
Digitalisation and Human Securityeve that Euler was the first major mathematician to use the term “algebraic analysis” in connection with his important work on general solutions to linear ordinary differential equations with constant coefficients, [71]. Currently, the term “algebraic analysis” refers to the work of the Japanese sch
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