• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권4호
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• pp.285-293
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• 2009

By using the notion of fuzzy functions introduced by Dib and Youssef, we obtain fuzzy analogues of some results concerning ordinary functions. In particular, we give the denition dierent from one of invertible fuzzy function introduced by Dib and Youssef. And we show that the two denitions are equivalent. Furthermore, we introduce the concepts of fuzzy increasing functions and fuzzy isomorphisms, and we obtain fuzzy analogues of many results concerning ordinary increasing functions and isomorphisms.

• 한국정보통신학회:학술대회논문집
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• 한국해양정보통신학회 1999년도 추계종합학술대회
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• pp.169-172
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• 1999

수중 음원을 탐지할 때 사용되는 정합장 처리 기법은 복잡한 수중 환경을 고려하여 수행된다. 특히, 최소 분산 처리기를 적용할 경우 행렬의 고유치 문제로 인해 그 성능이 크게 저하될 수 있다. 본 논문에서는 변환 행렬을 이용하여 최소 분산 정합장 처리기의 성능을 개선하였다 이 변환 행렬은 입력 신호의 공분산 행렬이 역행렬을 구할 수 있도록 하면서 원하는 음원 신호 성분을 향상시키도록 한다. 제안된 방법은 NATO 산하 SACLANT 센터에서 수집된 실측 데이터를 이용하여 그 효율성을 입증하였다.

• Kyungpook Mathematical Journal
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• 제56권2호
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• pp.387-396
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• 2016

An $n{\times}n$ matrix A over a commutative ring is strongly clean provided that it can be written as the sum of an idempotent matrix and an invertible matrix that commute. Let R be an arbitrary commutative ring, and let $A(x){\in}M_n(R[[x]])$. We prove, in this note, that $A(x){\in}M_n(R[[x]])$ is strongly clean if and only if $A(0){\in}M_n(R)$ is strongly clean. Strongly clean matrices over quotient rings of power series are also determined.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제16권4호
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• pp.405-416
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• 2009

In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [5]-[7]. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before [5]-[7]. The results obtained here improve our earlier ones reported in [4]. Numerical examples are also provided.

• 대한수학회지
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• 제56권2호
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• pp.507-521
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• 2019

For any $m{\times}n$ nonbinary Boolean matrix A, its spanning column rank is the minimum number of the columns of A that spans its column space. We have a characterization of spanning column rank-1 nonbinary Boolean matrices. We investigate the linear operators that preserve the spanning column ranks of matrices over the nonbinary Boolean algebra. That is, for a linear operator T on $m{\times}n$ nonbinary Boolean matrices, it preserves all spanning column ranks if and only if there exist an invertible nonbinary Boolean matrix P of order m and a permutation matrix Q of order n such that T(A) = PAQ for all $m{\times}n$ nonbinary Boolean matrix A. We also obtain other characterizations of the (spanning) column rank preserver.

• 대한수학회보
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• 제58권4호
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• pp.973-981
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• 2021

Let R be a commutative ring with identity 1, n ≥ 3, and let 𝒯_n(R) be the linear Lie algebra of all upper triangular n × n matrices over R. A linear map 𝜑 on 𝒯_n(R) is called to be strong commutativity preserving if [𝜑(x), 𝜑(y)] = [x, y] for any x, y ∈ 𝒯_n(R). We show that an invertible linear map 𝜑 preserves strong commutativity on 𝒯_n(R) if and only if it is a composition of an idempotent scalar multiplication, an extremal inner automorphism and a linear map induced by a linear function on 𝒯_n(R).

• Journal of Multimedia Information System
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• 제8권1호
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• pp.45-56
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• 2021

This document traces the new technologies development based on a deep classical Hill method improvement. Based on the chaos, this improvement begins with the 256 element body construction, which is to replace the classic ring used by all encryption systems. In order to facilitate the application of algebraic operators on the pixels, two substitution tables will be created, the first represents the discrete logarithm, while the second represents the discrete exponential. At the same time, a large invertible matrix whose structure will be explained in detail will be the subject of the advanced classical Hill technique improvement. To eliminate any linearity, this matrix will be accompanied by dynamic vectors to install an affine transformation. The simulation of a large number of images of different sizes and formats checked by our algorithm ensures the robustness of our method.

• 대한수학회보
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• 제59권1호
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• pp.1-13
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• 2022

The main aim of the article is to introduce new generalizations of Fredholm and Browder classes of spectra when the underlying Hilbert space is not necessarily separable and study their properties. To achieve the goal the notions of 𝛼-Browder operators, 𝛼-B-Fredholm operators, 𝛼-B-Browder operators and 𝛼-Drazin invertibility have been introduced. The relation of these classes of operators with their corresponding weighted spectra has been investigated. An equivalence of 𝛼-Drazin invertible operators with 𝛼-Browder operators and 𝛼-B-Browder operators has also been established. The weighted Browder spectrum of the sum of two bounded linear operators has been characterised in the case when the Hilbert space (not necessarily separable) is a direct sum of its closed invariant subspaces.

• 대한수학회보
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• 제59권2호
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• pp.277-283
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• 2022

Let 𝒜 be a unital Banach algebra, 𝓜 a unital 𝒜-bimodule, and 𝛿 a linear mapping from 𝒜 into 𝓜. We prove that if 𝛿 satisfies 𝛿(A)A^-1+A^-1𝛿(A)+A𝛿(A^-1)+𝛿(A^-1)A = 0 for every invertible element A in 𝒜, then 𝛿 is a Jordan derivation. Moreover, we show that 𝛿 is a Jordan derivable mapping at the unit element if and only if 𝛿 is a Jordan derivation. As an application, we answer the question posed in [4, Problem 2.6].

• 대한수학회보
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• 제60권4호
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• pp.1071-1083
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• 2023

The main motivation of this paper is to introduce and study the notions of strong Dedekind rings and semi-regular injective modules. Specifically, a ring R is called strong Dedekind if every semi-regular ideal is Q₀-invertible, and an R-module E is called a semi-regular injective module provided Ext¹_R(T, E) = 0 for every 𝓠-torsion module T. In this paper, we first characterize rings over which all semi-regular injective modules are injective, and then study the semi-regular injective envelopes of R-modules. Moreover, we introduce and study the semi-regular global dimensions sr-gl.dim(R) of commutative rings R. Finally, we obtain that a ring R is a DQ-ring if and only if sr-gl.dim(R) = 0, and a ring R is a strong Dedekind ring if and only if sr-gl.dim(R) ≤ 1, if and only if any semi-regular ideal is projective. Besides, we show that the semi-regular dimensions of strong Dedekind rings are at most one.