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SELF-ADJOINT INTERPOLATION ON AX = Y IN B(H)
곽승곤,김기숙 호남수학회 2008 호남수학학술지 Vol.30 No.4
Given operators [수식]and [수식] acting on a Hilbert space H, an interpolating operator is a bounded operator A acting on H such that [수식] In this article, if the range of Xk is dense in H for a certain k in f1; 2; ¢ ¢ ¢ ; ng, then the following are equivalent: (1) There exists a self-adjoint operator A in B(H) such that AXi = [수식](2) sup [수식]for all f,g in H
INVERTIBLE INTERPOLATION ON Ax = y IN A TRIDIAGONAL ALGEBRA ALGL
곽승곤,강주호 호남수학회 2011 호남수학학술지 Vol.33 No.1
Given vectors x and y in a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that Ax = y. We show the following : Let AlgL be a tridiagonal algebra on a separable complex Hilbert space H and let x = (x_i) and y = (y_i) be vectors in H. Then the following are equivalent:(1) There exists an invertible operator A = (a_(kj)) in AlgL such that Ax = y. (2) There exist bounded sequences {α_n} and {β_n} in C such that for all k ∈ N,α_(2k-1) ≠ 0, [수식], [수식] and y_1 = α_1x_1 + α_2x_2y_(2k) = α_(4k)-_1x_(2k)y_(2k+1) = α_(4k)x_(2k) + α_(4k)+_1x(2k+1) + α_(4k)+_2x_(2k+2).
SELF-ADJOINT INTERPOLATION ON Ax = y IN ALGL
곽승곤,강주호 한국전산응용수학회 2011 Journal of applied mathematics & informatics Vol.29 No.3
Given vectors x and y in a Hilbert space H, an interpolating operator is a bounded operator T such that Tx = y. An interpolating operator for n vectors satisfies the equations Tx_i = y_i, for i = 1, 2, . . . , n. In this paper the following is proved : Let L be a subspace lattice on a Hilbert space H. Let x and y be vectors in H and let P_x be the projection onto sp(x). If P_xE = EP_x for each E ∈ L, then the following are equivalent. (1) There exists an operator A in AlgL such that Ax = y, Af = 0 for all f in sp(x)^⊥ and A = A^*. (2) sup [수식] < ∞, y∈sp(x) and < x, y >+<y, x>.
제7차 교육과정의 선택과목인 이산수학에 관한 연구 : 그래프 이론을 중심으로 Focusing on graph theory
곽승곤,박수정 대구대학교 기초과학연구소 2003 基礎科學硏究 Vol.19 No.3
In this information-oriented society of the 21st century, computer is considered as an extremely useful tool that is of necessity. Let us think about what is needed in order to manage a computer well. Mathematical ability is mostly needed in managing a computer well. In order to build mathematical ability, one has to follow the flow of the era, deviating from the existing traditional mathematics. The field which has an important role in the current era is "discrete mathematics". With the fact that a computer -the lion of the day in various fields- is a discrete machine, it is only right to prepare so that discrete problems can be learned easily and interestingly. Keeping pace with this, computer utilization in education worldwide, has become an important means of education. Computer utilization in Korea is becoming an important means of education, following the flow of the era. However, there are many inadequacies in educational knowledge that can solve discrete problems. Accordingly, "discrete mathematics" was established as an independent subject, as an in-depth elective subject of the 7th National Curriculum, and was applied to the first-year of high school from this year (2002) and "discrete mathematics" will be taught to second-year and third-year of high school in full-scale, from 2003. As such, the importance of discrete mathematics is emphasized in the education world and discrete mathematics is being selected as an independent subject. However, there are many cases where not only general people, but the teachers themselves are new to discrete mathematics in reality. There could be a burden on the fact that a new method of learning has to be conducted, deviating from the traditional learning method. And, with the characteristic of it being an elective subject, there might be difficulties in teaching it efficiently. Accordingly, after investigating the background and concept of discrete mathematics and the graph theory, which is closely related to actual life in discrete mathematics, examples of how it is applied in actual life and the teaching means of graph theory were presented, to be of help in any way possible, for teachers who teach discrete mathematics at school.