• East Asian mathematical journal
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• 제33권3호
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• pp.309-315
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• 2017

In this paper, we investigate the regularities of the hyper-complex valued functions of the split quaternion variables. We define several differential operators for the split qunaternionic function. We research several left split regular functions for each differential operators. We also investigate split harmonic functions. And we find the corresponding Cauchy-Riemann system and the corresponding Cauchy theorem for each regular functions on the split quaternion field.

• 대한수학회보
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• 제30권1호
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• pp.29-34
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• 1993

J. Leray [7] proposed a sufficient condition ofr the solvability of the Cauchy problem on the initial hyperplane x$_{1}$=0 with Cauchy data which are holomorphic with respect to the variables parallel to some analytic subvariety S of the initial hyperplane. Limiting the problem to the case of operators with constant coefficients, A. Kaneko [2] proposed a new sharper sufficient condition. Later we generalized this condition and showed that it is necessary and sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data and the distribution Cauchy data which contain variables parallel to S as holomorphic parameters in [5, 6]. In this paper, we extend the results in [6] to the case of operators with variable coefficients and show that it is sufficient for the solvability of the Cauchy problem for the hyperfunction Cauchy data. Our main theorem can be considered as an example of a deep theorem on micro-hyperbolic systems by Kashiwara-Schapira [4] and we give a direct proof based on an elementary sweeping out procedure developed in Kaneko [3].

• Communications for Statistical Applications and Methods
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• 제21권2호
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• pp.183-191
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• 2014

We define a multivariate Cauchy distribution using a probability density function; subsequently, a Ferguson's definition of a multivariate Cauchy distribution can be viewed as a characterization theorem using the characteristic function approach. To clarify this characterization theorem, we construct two dependent Cauchy random variables, but their sum is not Cauchy distributed. In doing so the proofs depend on the characteristic function, but we use the cumulative distribution function to obtain the exact density of their sum. The derivation methods are relatively straightforward and appropriate for graduate level statistics theory courses.

• 호남수학학술지
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• 제37권1호
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• pp.99-112
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• 2015

In this paper we consider the periodic Cauchy problem for the generalized two-component Hunter-Saxton system with analytic initial data and we prove a Cauchy-Kowalevski type theorem for the generalized two-component Hunter-Saxton system, that establishes the existence and uniqueness of real analytic solutions.

• East Asian mathematical journal
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• 제32권5호
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• pp.641-649
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• 2016

In this paper, using three types of conjugations in a bicomplex number filed $\mathcal{T}$, we provide some basic definitions of bicomplex number and definitions of regular functions for each differential operators. And we investigate the corresponding Cauchy-Riemann systems and the corresponding Cauchy theorems in $\mathcal{T}$ in Clifford analysis.

• Journal of applied mathematics & informatics
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• 제8권2호
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• pp.581-590
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• 2001

In this paper we prove a local stability of Gavruta’s theorem for the generalized Hyers-Ulam-Rassias Stability of Cauchy functional equation.

• 대한수학회지
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• 제40권4호
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• pp.747-756
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• 2003

We establish a vanishing theorem on the square-integrable cohomology associated to the Cauchy-Riemann complex on some complete Kaehler manifolds. The hypothesis needed for this result is a growth condition on a primitive of the Kaehler form.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.345-357
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• 2009

We prove a related fixed point theorem for two pairs of mappings on two intuitionistic fuzzy metric spaces. Our result is maiden in this line.

• Kyungpook Mathematical Journal
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• 제32권3_spc호
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• pp.553-559
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• 1992

• Structural Engineering and Mechanics
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• 제66권3호
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• pp.387-397
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• 2018

In this paper, a general closed-form solution for evaluating the dynamic behavior of a Timoshenko beam on elastic foundation under a moving harmonic line load is formulated in the frequency-wavenumber domain and in a moving coordinate system. It is found that the characteristic equation is quartic with real coefficients only, and its poles can be presented explicitly. This enables the substitution of these poles into Cauchy's residue theorem, leading to the general closed-form solution. The solution can be reduced to seven existing closed-form solutions to different sub-problems and a new closed-form solution to the subproblem of a Timoshenko beam on an elastic foundation subjected to a moving quasi-static line load. Two examples are included to verify the solution.