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European Physical Journal C: Particles and Fields, 2021 In a soliton sector of a quantum field theory, it is often convenient to expand the quantum fields in terms of normal modes. Normal mode creation and annihilation operators can be normal ordered, and their normal ordered products have vanishing ...
Jarah Evslin
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Normal ordering of degenerate integral powers of number operator and its applications
Applied Mathematics in Science and Engineering, 2022 The normal ordering of an integral power of the number operator in terms of boson operators is expressed with the help of the Stirling numbers of the second kind. As a ‘degenerate version’ of this, we consider the normal ordering of a degenerate integral
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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Some stochastic orderings of multivariate skew-normal random vectors
AIMS Mathematics, 2023 In this paper, we investigate some multivariate integral stochastic orderings of skew-normal random vectors. We derive the results of the sufficient and/or necessary conditions by applying an identity for $ Ef({\mathbf Y})-Ef({\mathbf X}) $, where ...
Xueyan Li, Chuancun Yin
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Normal ordering associated with λ-Stirling numbers in λ-shift algebra
Demonstratio Mathematica, 2023 It is known that the Stirling numbers of the second kind are related to normal ordering in the Weyl algebra, while the unsigned Stirling numbers of the first kind are related to normal ordering in the shift algebra.
Kim Taekyun, Kim Dae San, Kim Hye Kyung
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Some identities involving degenerate Stirling numbers arising from normal ordering
AIMS Mathematics, 2022 In this paper, we derive some identities and recurrence relations for the degenerate Stirling numbers of the first kind and of the second kind, which are degenerate versions of the ordinary Stirling numbers of the first kind and of the second kind.
Taekyun Kim, Dae San Kim , Hye Kyung Kim
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Degenerate r-Bell Polynomials Arising from Degenerate Normal Ordering
Journal of Mathematics, 2022 Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via boson operators ...
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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Generalized degenerate Stirling numbers arising from degenerate Boson normal ordering
Applied Mathematics in Science and Engineering, 2023 It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results.
Taekyun Kim, Dae San Kim, Hye Kyung Kim
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Exploring the flavor structure of quarks and leptons with reinforcement learning
Journal of High Energy Physics, 2023 We propose a method to explore the flavor structure of quarks and leptons with reinforcement learning. As a concrete model, we utilize a basic value-based algorithm for models with U(1) flavor symmetry.
Satsuki Nishimura +2 more
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Entropy, 2023 The geometric first-order integer-valued autoregressive process (GINAR(1)) can be particularly useful to model relevant discrete-valued time series, namely in statistical process control.
Manuel Cabral Morais
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Complete normal ordering 1: Foundations
Nuclear Physics B, 2016 We introduce a new prescription for quantising scalar field theories (in generic spacetime dimension and background) perturbatively around a true minimum of the full quantum effective action, which is to ‘complete normal order’ the bare action of ...
John Ellis +2 more
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