• Kyungpook Mathematical Journal
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• 제33권1호
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• pp.1-11
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• 1993

• 대한수학회보
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• 제47권6호
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• pp.1205-1211
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• 2010

In the present article, we investigate the possibility of a real-valued map on the space of tuples of commuting trace-class self-adjoint operators, which behaves like the usual trace map on the space of trace-class linear operators. It turns out that such maps are related with continuous group homomorphisms from the Milnor's K-group of the real numbers into the additive group of real numbers. Using this connection, it is shown that any such trace map must be trivial, but it is proposed that the target group of a nontrivial trace should be a linearized version of Milnor's K-theory as with the case of universal determinant for commuting tuples of matrices rather than just the field of constants.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.407-414
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• 2008

In this paper, we study the self-adjoint second order boundary value problem with integral boundary conditions: (p(t)x'(t))'+f(t,x(t))=0, t $${\in}$$ (0,1), x'(0)=0, x(1) = $${\int}_0^1$$ x(s)g(s)ds. A new result on the existence of positive solutions is obtained. The interesting points are: the first, we employ a new tool-the recent Leggett-Williams norm-type theorem for coincidences; the second, the boundary value problem is involved in integral condition; the third, the solutions obtained are positive.

• 에너지공학
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• 제15권4호
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• pp.250-255
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• 2006

원자력 분야에서 중성자 수송계산을 위해 개발되어 널리 사용되는 방향차분법을 시간 종속 복사 열전달식의 해를 구하는데 적용하였다. 광자의 방향별 밀도를 자체수반형 2계 편미분방정식으로 나타내어 해의 안정성을 높였고 매질의 온도방정식의 비선형성은 다단계 선형화법을 사용하여 근사하였다. 본 연구에서 개발된 해법을 전형적인 Marshak wave 문제에 적용하였고 계산 결과를 기존의 Monte Carlo의 계산결과와 비교하여 그 우월성을 보였다.

• 호남수학학술지
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• 제45권1호
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• pp.123-129
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• 2023

In this paper, we introduce the reverse of the operator Davis-Choi-Jensen's inequality. Our results are employed to establish a new bound for the Furuta inequality. More precisely, we prove that, if $A,\;B{\in}{\mathcal{B}}({\mathcal{H}})$ are self-adjoint operators with the spectra contained in the interval [m, M] with m < M and A ≤ B, then for any $r{\geq}{\frac{1}{t}}>1,\,t{\in}(0,\,1)$ $A^r{\leq}({\frac{M1_{\mathcal{H}}-A}{M-m}}m^{rt}+{\frac{A-m1_{\mathcal{H}}}{M-m}}M^{rt}){^{\frac{1}{t}}}{\leq}K(m,\;M,\;r)B^r,$ where K (m, M, r) is the generalized Kantorovich constant.

• Korean Journal of Mathematics
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• 제17권2호
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• pp.155-159
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• 2009

In this paper, we consider the operator T satisfying $T^{*k}({\mid}T^2{\mid}-{\mid}T{\mid}^2)T^k{\geq}0$ and prove that if the operator is injective and has the real spectrum, then it is self-adjoint.

• Journal of applied mathematics & informatics
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• 제3권2호
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• pp.117-128
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• 1996

Complementation theory in krein spaces can be extended for any self-adjoint transformation. There is a close relation between Julia operators and linear systems. The theory of Julia operators can be used to construct distinct Krein spaces which are the state spaces of extended canonical linear systems with given transfer function.

• Kyungpook Mathematical Journal
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• 제28권2호
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• pp.221-226
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• 1988

Using the method of eigenfunction expantion of self adjoint operators, we establish the necessary and sufficient conditions for a reflection positive generalized matrix kernel to be represented in an integral form. This integral converges in the cosidered spaces.

• Journal of applied mathematics & informatics
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• 제15권1_2호
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• pp.503-510
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• 2004

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 paper the following is proved: Let H be a Hilbert space and L be a commutative subspace lattice on H. Let H and y be vectors in H. Let $M_x\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_ix\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;and\;M_y\;=\;\{{\sum{n}{i=1}}\;{\alpha}_iE_iy\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}. Then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y, Af = 0 for all f in ${\overline{M_x}}^{\bot}$, AE = EA for all $E\;{\in}\;L\;and\;A^{*}\;=\;A$. (2) $sup\;\{\frac{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}{{\parallel}{{\Sigma}_{i=1}}^{n}\;{\alpha}_iE_iy{\parallel}}\;:\;n\;{\in}\;N,\;{\alpha}_i\;{\in}\;{\mathbb{C}}\;and\;E_i\;{\in}\;L\}\;<\;{\infty},\;{\overline{M_u}}\;{\subset}{\overline{M_x}}$ and < Ex, y >=< Ey, x > for all E in L.

• Journal of applied mathematics & informatics
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• 제14권1_2호
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• pp.387-395
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• 2004

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 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 range(X) 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 ${\frac{$\mid$$\mid${\sum_{i=1}}^n\;E_iYf_i$\mid$$\mid$}{$\mid$$\mid${\sum_{i=1}}^n\;E_iXf_i$\mid$$\mid$}$:n{\epsilon}N,f_i{\epsilon}H\;and\;E_i{\epsilon}L}\;<\;{\infty}$ and = for all E in L and all f, g in H.