• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.431-436
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• 2003

Given vectors x and y in a Hilbert space, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equation $Tx_i\;:\;y_i,\;for\;i\;=\;1,\;2,\;{\cdots},\;n$. In this article, we obtained the following : $Let\;x\;=\;\{x_i\}\;and\;y=\{y_\}$ be two vectors in a separable complex Hilbert space H such that $x_i\;\neq\;0$ for all $i\;=\;1,\;2;\cdots$. Let L be a commutative subspace lattice on H. Then the following statements are equivalent. (1) $sup\;\{\frac{\$\mid${\sum_{k=1}}^l\;\alpha_{\kappa}E_{\kappa}y\$\mid$}{\$\mid${\sum_{k=1}}^l\;\alpha_{\kappa}E_{\kappa}x\$\mid$}\;:\;l\;\in\;\mathbb{N},\;\alpha_{\kappa}\;\in\;\mathbb{C}\;and\;E_{\kappa}\;\in\;L\}\;<\;\infty\;and\;$\mid$y_n\$\mid$x_n$\mid$^{-1}\;=\;1\;for\;all\;n\;=\;1,\;2,\;\cdots$. (2) There exists an operator A in AlgL such that Ax = y, A is a unitary operator and every E in L reduces, A, where AlgL is a tridiagonal algebra.

• 한국공간구조학회논문집
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• 제3권4호
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• pp.59-67
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• 2003

Genetic algorithm is one of the best ways to solve a discrete variable optimization problem. Genetic algorithm tends to thrive in an environment in which the search space is uneven and has many hills and valleys. In this study, genetic algorithm is used for solving the design problem of gable structure. The design problem of frame structure has some special features(complicate design space, many nonlinear constrants, integer design variables, termination conditions, special information for frame members, etc.), and these features must be considered in the formulation of optimization problem and the application of genetic algorithm. So, 'FRAME operator', a new genetic operator for solving the frame optimization problem effectively, is developed and applied to the design problem of gable structure. This example shows that the new opreator has the possibility to be an effective frame design operator and genetic algorithm is suitable for the frame optimization problem.

• 충청수학회지
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• 제23권1호
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• pp.37-48
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• 2010

In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

• 대한수학회논문집
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• 제13권3호
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• pp.545-560
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• 1998

Let ø and A be denoted by the structure tensor field of type (1,1) and by the shape operator of a real hypersurface in a complex space form $M_{n}$ (c), c $\neq$ 0 respectively. The main purpose of this paper is to prove that if a real hypersurface in $M_{n}$ (c) satisfies $R_{ξ}$ øA = $AøR_{ξ}$, then the structure vector field ξ is principal, where $R_{ξ}$ / is the Jacobi operator with respect to ξ.

• 한국전산응용수학회:학술대회논문집
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• 한국전산응용수학회 2003년도 KSCAM 학술발표회 프로그램 및 초록집
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• pp.4.1-4
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• 2003

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX= Y. An interpolating operator for n-operators satisfies the equation AXi= Yi, for i = 1,2,...,n, In this article, we showed the following : Let H be a Hilbert space and let L be a subspace lattice on H. Let X and Y be operators acting on H. Assume that rangeX is dense in H. Then the following statements are equivalent : (1) There exists an operator A in AlgL such that AX = Y, A$\^$*/=A and every E in L reduces A. (2) sup｛(equation omitted) : n $\in$ N f$\sub$I/ $\in$ H and E$\sub$I/ $\in$ L｝<$\infty$ and = for all E in L and all f, g in H.

• 대한수학회지
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• 제54권2호
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• pp.563-574
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• 2017

Let $\mathcal{A}$ be a unital real standard Jordan operator algebra acting on a Hilbert space H of dimension at least 2. We show that every bijection ${\phi}$ on $\mathcal{A}$ satisfying ${\phi}(A^2{\circ}B)={\phi}(A)^2{\circ}{\phi}(B)$ is of the form ${\phi}={\varepsilon}{\psi}$ where ${\psi}$ is an automorphism on $\mathcal{A}$ and ${\varepsilon}{\in}\{-1,1\}$. As a consequence if $\mathcal{A}$ is the real algebra of all self-adjoint operators on a Hilbert space H, then there exists a unitary or conjugate unitary operator U on H such that ${\phi}(A)={\varepsilon}UAU^*$ for all $A{\in}\mathcal{A}$.

• 대한수학회보
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• 제52권5호
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• pp.1621-1630
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• 2015

In this paper the notion of Lie derivative of a tensor field T of type (1,1) of real hypersurfaces in complex space forms with respect to the generalized Tanaka-Webster connection is introduced and is called generalized Tanaka-Webster Lie derivative. Furthermore, three dimensional real hypersurfaces in non-flat complex space forms whose generalized Tanaka-Webster Lie derivative of 1) shape operator, 2) structure Jacobi operator coincides with the covariant derivative of them with respect to any vector field X orthogonal to ${\xi}$ are studied.

• 대한수학회논문집
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• 제9권3호
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• pp.593-598
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• 1994

In this note we give some results on the jump (due to Kato [5] and West [7]) of a semi-Fredholm operator. Throughout this note, suppose X is an Banach space and write L(X) for the set of all bounded linear operators on X. A operator $T \in L(x)$ is called upper semi-Fredholm if it has closed range with finite dimensional null space, and lower semi-Fredholm if it has closed range with its range of finite co-dimension. It T is either upper or lower semi-Fredholm we shall call it semi-Fredholm and Fredholm it is both. The index of a (semi-) Fredholm operator T is given by $$ index(T) = n(T) = d(T),$$ where $n(T) = dim T^{-1}(0)$ and d(T) = codim T(X).

• 대한수학회지
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• 제49권2호
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• pp.395-404
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• 2012

Our first aim of this paper is to define maximal operators a-quadratic variation and of a-conditional quadratic variation for vectorvalued tree martingales and to show that these maximal operators and maximal operators of vector-valued tree martingale transforms are all sublinear operators. The second purpose is to prove that maximal operator inequalities of a-quadratic variation and of a-conditional quadratic variation for vector-valued tree martingales hold provided 2 ${\leq}$ a < $\infty$ by means of Marcinkiewicz interpolation theorem. Based on a result of reference [10] and using Marcinkiewicz interpolation theorem, we also propose a simple proof of maximal operator inequalities for vector-valued tree martingale transforms, under which the vector-valued space is a UMD space.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제14권3호
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• pp.161-166
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• 2007

Given operators X and Y acting on a Hilbert space H, an interpolating operator is a bounded operator A such that AX = Y. An interpolating operator for n-operators satisfies the equation $AX_i=Y_i$, for i = 1,2,...,n. In this article, we showed the following: Let L, be a subspace lattice on a Hilbert space H and let X and Y be operators in B(H). Then the following are equivalent: (1) $$sup\{\frac{{\parallel}E^{\bot}Yf{\parallel}}{{\overline}{\parallel}E^{\bot}Xf{\parallel}}\;:\;f{\epsilon}H,\;E{\epsilon}L}\}\;<\;{\infty},\;sup\{\frac{{\parallel}Xf{\parallel}}{{\overline}{\parallel}Yf{\parallel}}\;:\;f{\epsilon}H\}\;<\;{\infty}$$ and $\bar{range\;X}=H=\bar{range\;Y}$. (2) There exists an invertible operator A in AlgL such that AX=Y.