• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.627-647
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• 2015

In this paper, we construct the Schr$\ddot{o}$dinger-Weil representation of the Jacobi group associated with a positive definite symmetric real matrix of degree m and find covariant maps for the Schr$\ddot{o}$dinger-Weil representation.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.63-74
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• 2012

Based on the Hilbert $C^*$-module structure we study the reconstruction theorem for stationary monotone quantum Markov processes from quantum dynamical semigroups. We prove that the quantum stochastic monotone process constructed from a covariant quantum dynamical semigroup is again covariant in the strong sense.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.3
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• pp.339-349
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• 2020

Let P ⋊ ℕ^x be a semidirect product of an additive semigroup P = {0, 2, 3, ⋯ } by a multiplicative positive natural numbers semigroup ℕ^x. We consider a covariant semigroup C^∗-algebra 𝓣(P ⋊ ℕ^x) of the semigroup P ⋊ ℕ^x. We obtain the condition that a state on 𝓣(P ⋊ ℕ^x) can be a ground state of the natural C^∗-dynamical system (𝓣(P ⋊ ℕ^x), ℝ, σ).

• Publications of The Korean Astronomical Society
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• v.7 no.1
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• pp.107-148
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• 1992

This paper presents a cosmological perturbation analysis in a Newtonian framework, using the Newtonian multi component version of the relativistic covariant equations. This work considers the fully nonlinear evolution of the perturbations, and is generalized to multicomponent systems and imperfect fluids. Known nonlinear solutions are presented in a general framework. Quasi-nonlinear analysis, considering both the compressible and rotational modes, is presented, including cases already known in the literature. The Fourier space representation of the conservation equations is also derived in a general context, with various decompositions of the velocity field. Commonly accepted cosmogonical frameworks are critically examined in the context of nonlinear evolution. This work may be regarded as the Newtonian counterpart of a recently presented general relativistic covariant formulation.