• ETRI Journal
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• 제33권3호
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• pp.401-406
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• 2011

This paper presents a fast block-matching algorithm based on the normalized cross-correlation, where the elimination order is determined based on the gradient magnitudes of subblocks in the current macroblock. Multilevel Cauchy-Schwartz inequality is derived to skip unnecessary block-matching calculations in the proposed algorithm. Also, additional complexity reduction is achieved re-using the normalized cross correlation values for the spatially neighboring macroblock because the search areas of adjacent macroblocks are overlapped. Simulation results show that the proposed algorithm can improve the speed-up ratio up to about 3 times in comparison with the existing algorithm.

• 충청수학회지
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• 제21권2호
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• pp.197-208
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• 2008

In this paper, we obtain the Hyers-Ulam-Rassias stability of a Cauchy-Jensen functional equation $$f(x+y,z)-f(x,z)-f(y,z)=0,\\2f(x,\frac{y+z}2)-f(x,y)-f(x,z)=0$$ in the spirit of Th. M. Rassias.

• 호남수학학술지
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• 제22권1호
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• pp.37-46
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• 2000

We prove the stability of a generalized Cauchy functional equation of the form ; $$f(a_1x+a_2y)=b_1f(x)+b_2f(y)+w.$$ That is, we obtain a partial answer for the open problem which was posed by the Th.M Rassias and J. Tabor on the stability for a generalized functional equation.

• 호남수학학술지
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• 제30권3호
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• pp.567-579
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• 2008

We obtain generalized super stability of Cauchy's gamma-beta functional equation B(x, y) f(x + y) = f(x)f(y), where B(x, y) is the beta function and also generalize the stability in the sense of R. Ger of this equation in the following setting: ${\mid}{\frac{B(x,y)f(x+y)}{f(x)f(y)}}-1{\mid}$ < H(x,y), where H(x,y) is a homogeneous function of dgree p(0 ${\leq}$ p < 1).

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.177-183
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• 1988

In this work, two numerical schemes arc proposed for solving a general form of Cauchy problem. Here, the problem, to be defined, consists of a system of Volterra integro-differential equations. Picard's and Seiddl'a methods of successive approximations are ued to obtain the approximate solution. The convergence of these approximations is established and the rate of convergence is estimated in every case.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권2호
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• pp.167-178
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• 2009

In this paper, we obtain the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation f(x+y, z)-f(x, z)-f(y, z)=0, $$2f\;x,\;{\frac{y+z}{2}}-f(x,\;y)-f(x,\;z)=0$$ in the spirit of P. $G{\breve{a}}vruta$.

• East Asian mathematical journal
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• 제35권1호
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• pp.1-7
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• 2019

We consider the initial value problem of the Schrodinger equation for an interesting Cauchy-Euler type operator ${\mathfrak{R}}$ on ${\mathbb{C}}^n$ that is an analogue of the harmonic oscillator in ${\mathbb{R}}^n$. We get an appropriate $L^1-L^{\infty}$ dispersive estimate for the solution of the initial value problem.

• Journal of applied mathematics & informatics
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• 제39권3_4호
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• pp.277-294
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• 2021

In this paper, we introduce the notions of Wijsman regularly invariant convergence types, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$)-convergence, Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-convergence, Wijsman regularly (${\mathcal{I}}_{\sigma}$, ${\mathcal{I}}^{\sigma}_2$) -Cauchy double sequence and Wijsman regularly (${\mathcal{I}}^*_{\sigma}$, ${\mathcal{I}}^{{\sigma}*}_2$)-Cauchy double sequence of sets. Also, we investigate the relationships among this new notions.

• 대한수학회보
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• 제58권2호
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• pp.515-526
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• 2021

Denote by ��+ the set of probability measures supported on ℝ+. Suppose V�� is the variance function of the Cauchy-Stieltjes Kernel (CSK) family ��-(��) generated by a non degenerate probability measure �� ∈ ��+. We determine the formula for variance function under boolean multiplicative convolution power. This formula is used to identify the relation between variance functions under the map ${\nu}{\mapsto}{\mathbb{M}}_t({\nu})=({\nu}^{{\boxtimes}(t+1)})^{{\uplus}{\frac{1}{t+1}}}$ from ��+ onto itself.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.347-355
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• 2023

For numerical evaluation of Cauchy principal value integrals, we present a simple rational function with a parameter satisfying some reasonable conditions. The proposed rational function is employed in coordinate transformation for accelerating the accuracy of the Gauss quadrature rule. The efficiency of the proposed rational transformation method is demonstrated by the numerical result of a selected test example.