• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.208-213
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• 1992

In this paper we are concerned with optimal control problems whose costs am quadratic and whose states are governed by linear delay equations and general boundary conditions. The basic new idea of this paper is to Introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• 대한수학회보
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• 제51권5호
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• pp.1469-1484
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• 2014

In this paper we are concerned with a class of stochastic partial functional differential equations with infinite delay. Supposing that the linear part is a Hille-Yosida operator but not necessarily densely defined and employing the integrated semigroup and random dynamics theory, we present some appropriate conditions to guarantee the existence of a random attractor.

• 대한수학회지
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• 제57권1호
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• pp.61-88
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• 2020

In this paper, we investigate the existence of mild solutions for a class of fractional impulsive evolution equation with periodic boundary condition by means of the method of upper and lower solutions and monotone iterative method. Using the theory of Kuratowski measure of noncompactness, a series of results about mild solutions are obtained. Finally, two examples are given to illustrate our results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제16권2호
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• pp.93-105
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• 2012

In this paper, we consider the controllability of a certain class of impulsive neutral evolution differential equations in Banach spaces. Sufficient conditions for controllability are obtained by using the Hausdorff measure of noncompactness and Monch fixed point theorem under the assumption of noncompactness of the evolution system.

• 충청수학회지
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• 제7권1호
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• pp.123-139
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• 1994

In this paper we are concerned with optimal control problems whose costs are quadratic and whose states are governed by linear delay differential equations and general boundary conditions. The basic new idea of this paper is to introduce a new class of linear operators in such a way that the state equation subject to a starting function can be viewed as an inhomogeneous boundary value problem in the new linear operator equation. In this way we avoid the usual semigroup theory treatment to the problem and use only linear operator theory.

• Journal of Applied and Pure Mathematics
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• 제5권3_4호
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• pp.129-164
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• 2023

The aim of this work is to present some interesting results on weighted ergodic functions and prove the existence and uniqueness of Stepanov-like pseudo almost automorphic solutions using the spectral decomposition of the phase space developed by Adimy and co-authors. We also give the next challenge of this work.

• 대한수학회논문집
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• 제38권4호
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• pp.1153-1162
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• 2023

In this paper, for the bounded solution of the non-densely defined non-autonomous evolution equation, we present the condition for asymptotic periodicity by using the circular spectral theory of functions on the half line and the extrapolation theory of non-densely defined evolution equation.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.865-876
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• 2023

This paper presents properties of the cocycle equations via cochains on a semigroup. And then we offer hyperstability results of related functional equations using the properties of cocycle equations via cochains. These results generalize hyperstability results of a class of linear functional equation by Maksa and Páles. The obtained results can be applied to obtain hyperstability of various functional equations such as Euler-Lagrange type quadratic equations.

• 한국전자통신학회논문지
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• 제13권4호
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• pp.737-744
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• 2018

RSA 암호계는 가장 널리 쓰이는 공개키 암호계로서, 암호화뿐만 아니라 전자서명이 가능한 최초의 알고리즘으로 알려져 있다. RSA 암호계의 안정성은 큰 수를 소인수 분해하는 것이 어렵다는 것에 기반을 두고 있다. 이러한 이유로 큰 정수의 소인수분해 방법에 많은 연구가 진행되고 있으나, 지금까지 알려진 연구 결과는 모두 실험적이거나 확률적이다. 본 논문에서는, 복소 이차체의 order의 류 반군의 구조와 비 가역 이데알의 성질을 이용하여 인수분해를 하지 않으면서 큰 정수의 소인수를 구하는 알고리즘을 구성한 다음, RSA 암호계에 대한 결정적 공격법을 제안하기로 한다.

• 한국IT서비스학회지
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• 제9권4호
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• pp.219-229
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• 2010

The Green's equivalence relations have played a fundamental role in the development of semigroup theory. They are concerned with mutual divisibility of various kinds, and all of them reduce to the universal equivalence in a group. Boolean matrices have been successfully used in various areas, and many researches have been performed on them. Studying Green's relations on a monoid of boolean matrices will reveal important characteristics about boolean matrices, which may be useful in diverse applications. Although there are known algorithms that can compute Green relations, most of them are concerned with finding one equivalence class in a specific Green's relation and only a few algorithms have been appeared quite recently to deal with the problem of finding the whole D or J equivalence relations on the monoid of all $n{\times}n$ Boolean matrices. However, their results are far from satisfaction since their computational complexity is exponential-their computation requires multiplication of three Boolean matrices for each of all possible triples of $n{\times}n$ Boolean matrices and the size of the monoid of all $n{\times}n$ Boolean matrices grows exponentially as n increases. As an effort to reduce the execution time, this paper shows an isomorphism between the R relation and L relation on the monoid of all $n{\times}n$ Boolean matrices in terms of transposition. introduces theorems based on it discusses an improved algorithm for the J relation computation whose design reflects those theorems and gives its execution results.