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Titlebook: Asymptotic Combinatorics with Application to Mathematical Physics; Vadim Malyshev,Anatoly Vershik Book 2002 Kluwer Academic Publishers 200

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Foundations of Intelligent SystemsMathematics as the Planck constant tends to zero taking pure imaginary values. In the framework of Idempotent Mathematics some basic concepts and results of the theory of group representations (including some unexpected theorems of the Engel type) are discussed.
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Ziad Al Bkhetan,Dariusz Plewczynskiystem enjoys certain integrability properties which allows exact analytical calculations of some interesting physical quantities and counting of planar graphs embedded into the one dimensional line or the circle.
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Foundations of Intelligent SystemsMathematics as the Planck constant tends to zero taking pure imaginary values. In the framework of Idempotent Mathematics some basic concepts and results of the theory of group representations (including some unexpected theorems of the Engel type) are discussed.
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Lecture Notes in Computer ScienceWe give an introductory pedagogical review of rigorous mathematical results concerning combinatorial enumeration and probability distributions for maps on compact orientable surfaces, with an emphasize on applications to two-dimensional quantum gravity.
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Stefano Ferilli,Giuseppe FatigusoRiemann zeta function is an important object of number theory. It was also used for description of disordered systems in statistical mechanics. We show that Riemann zeta function is also useful for the description of correlation functions in quantum integrable models.
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Lecture Notes in Computer ScienceNew quantization methods for quantum problems of many-bodies are presented. These methods are used for quantization of thermodynamics of Quantum Statistics. In particular, this leads to an explanation of the superconductivity and superfluidity for nonzero temperatures.
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https://doi.org/10.1007/3-540-48050-1We formulate general principles of building hypergeometric type series from the Jacobi theta functions that generalize the plain and basic hypergeometric series. Single and multivariable elliptic hypergeometric series are considered in detail. A characterization theorem for a single variable totally elliptic hypergeometric series is proved.
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