• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.705-718
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• 2022

In this paper, for bounded linear operators A, B, C satisfying [AB, B] = [BC, B] = [AB, BC] = 0 we study the Drazin invertibility of the sum of products formed by the three operators A, B and C. In particular, we give an explicit representation of the anti-commutator {A, B} = AB + BA. Also we give some conditions for which the sum A + C is Drazin invertible.

• Proceedings of the KIEE Conference
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• 1987.07b
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• pp.859-863
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• 1987

In this paper, a relationship between difference triangular sets and sum triangular sets is developed to evaluate the weighted number of the third-order intermodulation products. In addition, a lower bound of the intermodulation products falling into the worst signal channel has been derived using the relationship between difference triangular sets and sum triangular sets. The formulas of the lower bound are useful for estimating the intermodulation impairment level in satellite communication systems.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.385-388
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• 2000

The computation of a terminal-pair reliability is started with a Boolean sum of products expression corresponding to simple paths of the pair of nodes. This expression is then transformed into another equivalent expression to be a Sum of Disjoint Products form. The terminal reliability can then be obtained in a straightforward manner from the Sum of Disjoint Products form. In this paper, we proposed an efficient method to obtain reliability expressions for calculating multiple K terminal-pairs reliability between terminal-pairs of nodes of computers of complex networks. Actual programming results show that the new method is superior with regard to computational efficiency, especially for computing the reliability of multiple terminals.

• 전기의세계
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• v.28 no.11
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• pp.37-44
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• 1979

This paper deals with the computer program of finding the minimal sum-of-products for a switching function by using the MASK method derived from the characteristics of the Boolean algebra. The approach differs from the previous procedures in that all the prime implicants are determined only by the bit operation and the minimal sum-of-products are obtained by the modified Petrick method in this work. The important features are the relatively small amount of the run time and the less memory capacity to solve a problem, as compared to the previous computer programs.

• Proceedings of the Korea Institutes of Information Security and Cryptology Conference
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• 1997.11a
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• pp.315-321
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• 1997

본 논문에서는 임의의 부울함수(Boolean function)에 대한 진리표나 출력 시퀀스로부터 논리곱의 배타적 합(exclusive-or sum of products; ESOP)형의 부울함수를 구성하는 알고리듬을 제안한다. 기존에 알려진 카르노맵이나 Quine HcClusky법에 의하여 구해지는 부울함수는 논리곱의 합(sum of product; SOP) 형으로 주어지며 이들 수식은 부정(NOT)논리를 포함하는 경우가 있다. 제안된 알고리듬에 의하여 구해지는 부울함수는 구조적인 등가성을 판별하는데 편리하므로 해쉬함수용 부울함수의 개발에 이용될 수 있다.

• Proceedings of the Korea Multimedia Society Conference
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• 1998.10a
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• pp.202-207
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• 1998

The network reliability is to be computed in terms of the terminal reliability. The computation of a terminal reliability is started with a Boolean sum of products expression corresponding to simple paths of the pair of nodes. This expression is then transformed into another equivalent expression to be a Disjoint Sum of Products form. But this computation of the terminal reliability obviously does not consider the communication between any other nodes but for the source and the sink. In this paper, we derive the overall network reliability which all other remaining nodes. For this, we propose a method to make the SOP disjoint for deriving the network reliability expression from the system success expression using the modified Sheinman's method. Our method includes the concept of spanning trees to find the system success function by the Cartesian products of vertex cutsets.

• Journal of the Korean Mathematical Society
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• v.30 no.1
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• pp.79-91
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• 1993

• Proceedings of the Korean Institute of Communication Sciences Conference
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• 1995.10a
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• pp.1087-1090
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• 1995

• Bulletin of the Korean Mathematical Society
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• v.60 no.1
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• pp.161-170
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• 2023

We consider dual Toeplitz operators acting on the orthogonal complement of the Dirichlet space on the unit disk. We give a characterization of when a finite sum of products of two dual Toeplitz operators is equal to 0. Our result extends several known results by using a unified way.

• Honam Mathematical Journal
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• v.41 no.3
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• pp.619-629
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• 2019

On the setting of the pluriharmonic Dirichlet space, we describe the essential norm of an operator which is a finite sum of products of several Toeplitz operators.