• Journal of the Korean Statistical Society
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• 제8권1호
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• pp.23-36
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• 1979

In the multiple linear regression model a class of weighted least absolute error estimaters, which minimize the sum of weighted absolute residuals, is proposed. It is shown that the weighted least absolute error estimators with Wilcoxon scores are equivalent to the Koul's Wilcoxon type estimator. Therefore, the asymptotic efficiency of the proposed estimator with Wilcoxon scores relative to the least squares estimator is the same as the Pitman efficiency of the Wilcoxon test relative to the Student's t-test. To find the estimates the iterative weighted least squares method suggested by Schlossmacher is applicable.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.773-785
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• 2012

In this paper, we establish sufficient conditions for the existence and uniqueness of solutions to a general class of three-point boundary value problems for a coupled system of nonlinear fractional differential equations. The differential operator is taken in the Caputo fractional derivatives. By using Green's function, we transform the derivative systems into equivalent integral systems. The existence is based on Schauder fixed point theorem and contraction mapping principle. Finally, some examples are given to show the applicability of our results.

• 대한수학회논문집
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• 제22권2호
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• pp.219-225
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• 2007

Since the time of Euler, the dilogarithm and polylogarithm functions have been studied by many mathematicians who used various notations for the dilogarithm function $Li_2(z)$. These functions are related to many other mathematical functions and have a variety of application. The main objective of this paper is to present corrected versions of two equivalent factorization formulas involving the Legendre's Chi-function $\chi_2$ and an evaluation of a class of integrals which is useful to evaluate some integrals associated with the dilogarithm function.

• 대한수학회보
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• 제44권4호
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• pp.861-870
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• 2007

In this paper, under suitable conditions, we show that the new class of iterative process with errors introduced by Li et al converges strongly to the unique solution of the equation involving strongly accretive operators in real Banach spaces. Furthermore, we prove that it is equivalent to the classical Ishikawa iterative sequence with errors.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.207-220
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• 2004

Necessary and sufficient conditions are given for the regularity of block triangular fuzzy matrices. This leads to characterization of idem-potency of a class of triangular Toeplitz matrices. As an application, the existence of group inverse of a block triangular fuzzy matrix is discussed. Equivalent conditions for a regular block triangular fuzzy matrix to be expressed as a sum of regular block fuzzy matrices is derived. Further, fuzzy relational equations consistency is studied.

• 충청수학회지
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• 제21권4호
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• pp.519-525
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• 2008

Let f be a diffeomorphisms of a compact $C^{\infty}$ manifold, and let p be a hyperbolic periodic point of f. In this paper, we prove that if generically, f is tame diffeomorphims then the following conditions are equivalent: (i) f is ${\Omega}$-stable, (ii) f has the $C^1$-stable shadowing property (iii) f has the $C^1$-stable inverse shadowing property.

• 충청수학회지
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• 제14권1호
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• pp.61-71
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• 2001

We introduce a new class of ${\sigma}$-coherent frames and show that HA is a ${\sigma}$-coherent frame if A is a ${\sigma}$-frame. Based on this, it is shown that a frame is ${\sigma}$-coherent iff it is isomorphic to the frame of ${\sigma}$-ideals of a ${\sigma}$-frame. Finally we show that ${\sigma}$-COhFrm and ${\sigma}$Frm are equivalent.

• 전자공학회논문지B
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• 제29B권1호
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• pp.26-33
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• 1992

This paper presents lattice structure of bilinear filter and the conversion equations from lattice parameters to direct-form parameters. Billnear models are attractive for adaptive filtering applications because they can approximate a large class of nonlinear systems adequately, and usually with considerable parsimony in the number of coefficients required. The lattice filter formulation transforms the nonlinear filtering problem into an equivalent multichannel linear filtering problem and then uses multichannel lattice filtering algorithms to solve the nonlinear filtering problem. The lattice filters perform a Gram-Schmidt orthogonalization of the input data and have very good easily extended to more general nonlinear output feedback structures.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제12권3호
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• pp.229-235
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• 2005

The notions of spherically concave functions defined on a subregion of the Riemann sphere P are introduced in different ways in Kim & Minda [The hyperbolic metric and spherically convex regions. J. Math. Kyoto Univ. 41 (2001), 297-314] and Kim & Sugawa [Charaterizations of hyperbolically convex regions. J. Math. Anal. Appl. 309 (2005), 37-51]. We show continuity of the concave function defined in the latter and show that the two notions of the concavity are equivalent for a function of class $C^2$. Moreover, we find more characterizations for spherically concave functions.

• 대한수학회논문집
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• 제15권2호
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• pp.357-370
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• 2000

In [6], Cheng-Ye You gave a condition equivalent to the Nielsen number product formula for fiber maps. And Jerzy Jezierski also gave a similar condition for coincidences of fiber maps. The main purpose of this paper is to find the condition for which holds the product formula for Nielsen root numbers N(f;a) = N(f;a) N(fb;a).