• East Asian mathematical journal
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• v.25 no.4
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• pp.481-486
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• 2009

The first object of this note is to show that a summation formula due to Padmanabham for three-variables hypergeometric function $X_8$ introduced by Exton can be proved in a different (from Padmanabham's and his observation) yet, in a sense, conventional method, which has been employed in obtaining a variety of identities associated with hypergeometric series. The second purpose is to point out that one of two seemingly new hypergeometric identities due to Exton was already recorded and the other one is easily derivable from the first one. A corrected and a little more compact form of a general transform involving hypergeometric functions due to Exton is also given.

• Journal of KIISE:Software and Applications
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• v.37 no.9
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• pp.694-705
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• 2010

The mutation operation is the main operation in the evolutionary programming which has been widely used for the optimization of real valued function. In general, the mutation operation utilizes both a probability distribution and its parameter to change values of variables, and the parameter itself is subject to its own mutation operation which requires other parameters. However, since the optimal values of the parameters entirely depend on a given problem, it is rather hard to find an optimal combination of values of parameters when there are many parameters in a problem. To solve this shortcoming at least partly, if not entirely, in this paper, we propose a new mutation operation in which the parameter for the variable mutation is theoretically estimated from the self-adaptive perspective. Since the proposed algorithm estimates the scale parameter of the Cauchy probability distribution for the mutation operation, it has an advantage in that it does not require another mutation operation for the scale parameter. The proposed algorithm was tested against the benchmarking problems. It turned out that, although the relative superiority of the proposed algorithm from the optimal value perspective depended on benchmarking problems, the proposed algorithm outperformed for all benchmarking problems from the perspective of the computational time.

• Journal of applied mathematics & informatics
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• v.8 no.3
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• pp.899-907
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• 2001

Complex variable methods are used to solve the first and the second fundamental problems for infinite plate with two holes having arbitrary shapes which are conformally mapped on the domain outside of the unit circle by means of rational mapping function. Some applications are investigated and some special cases are derived.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.183-198
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• 2003

We highlight the alternative presentation of the Cauchy-Riemann conditions for the analyticity of a complex variable function and consider plane equilibrium problem for an elastic transversely isotropic layer, in finite deformation. We state the fundamental problems and consider traction boundary value problem, as an example of fundamental problem-one. A simple solution of“Lame's problem”for an infinite layer is obtained. The profile of the deformed contour is given; and this depends on the order of the term used in the power series specification for the complex potential and on the material constants of the medium.

• Communications of the Korean Mathematical Society
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• v.27 no.2
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• pp.265-277
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• 2012

In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

• The Pure and Applied Mathematics
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• v.19 no.2
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• pp.193-198
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• 2012

We show that every unbounded approximate Pexiderized exponential type function has the exponential type. That is, we obtain the superstability of the Pexiderized exponential type functional equation $$f(x+y)=e(x,y)g(x)h(y)$$. From this result, we have the superstability of the exponential functional equation $$f(x+y)=f(x)f(y)$$.

• East Asian mathematical journal
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• v.29 no.3
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• pp.293-302
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• 2013

We research properties of ternary numbers and hyperholomorphic functions with values in $\mathbb{C}$(2). We represent reduced quaternion numbers and obtain some propertries in dual reduced quaternion systems in view of Clifford analysis. Moreover, we obtain Cauchy theorems with respect to dual reduced quaternions.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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• pp.37-52
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• 2000

This paper is concerned with the impulsive Cauchy problem (equation omitted) where u is a possibly discontinuous vector-valued function and f, $g_{i}$ : $IR^{n}$ -> $IR^{n}$ are suitably smooth functions. We show that the input-output map is Lipschitz continuous and investigate compactness of reachable sets.

• The Pure and Applied Mathematics
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• v.20 no.2
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• pp.129-136
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• 2013

We research properties of ternary numbers with values in ${\Lambda}(2)$. Also, we represent dual ternary numbers in the sense of Clifford algebras of real six dimensional spaces. We give generation theorems in dual ternary number systems in view of Clifford analysis, and obtain Cauchy theorems with respect to dual ternary numbers.

• Journal of applied mathematics & informatics
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• v.42 no.2
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• pp.237-243
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• 2024

A similarity transformation of a solution of the Cauchy problem for the linear difference equation in Hilbert space has been studied. In this manuscript, we obtain necessary and sufficient conditions for linear equivalence of the discrete semigroup of operators, generated by the solution of the difference equation utilizing four Canonical semigroups.