• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권2호
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• pp.235-249
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• 2024

We obtain a structured class of frames in separable Hilbert spaces which are generalizations of Gabor frames in L²(ℝ) in their construction aspects. For this, the concept of Gabor type unitary systems in [13] is generalized by considering a system of invertible operators in place of unitary systems. Pseudo Gabor like frames and pseudo Gabor frames are introduced and the corresponding frame operators are characterized.

• Korean Journal of Mathematics
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• 제32권1호
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• pp.1-14
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• 2024

We seek for an invertible map B from L²(Γ) to L²(G), where G is a finite abelian group and Γ is the direct product of finite cyclic groups which is isomorphic to G, so that any Gabor frame in L²(G), is a generalized pseudo B-Gabor frame.

• Korean Journal of Mathematics
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• 제22권1호
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• pp.181-206
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• 2014

Let $R={\bigoplus}_{\alpha{\in}\Gamma}R_{\alpha}$ be a graded integral domain graded by an arbitrary grading torsionless monoid ${\Gamma}$, and ⋆ be a semistar operation on R. In this paper we define and study the graded integral domain analogue of ⋆-Nagata and Kronecker function rings of R with respect to ⋆. We say that R is a graded Pr$\ddot{u}$fer ⋆-multiplication domain if each nonzero finitely generated homogeneous ideal of R is ⋆$_f$-invertible. Using ⋆-Nagata and Kronecker function rings, we give several different equivalent conditions for R to be a graded Pr$\ddot{u}$fer ⋆-multiplication domain. In particular we give new characterizations for a graded integral domain, to be a $P{\upsilon}MD$.

• 대한수학회논문집
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• 제21권3호
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• pp.577-586
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• 2006

In this paper we will propose the methods for finding the non-invertible ideals corresponding to non-primitive quadratic forms and clarify the structures of class SEMIGROUPS of imaginary quadratic orders which were given by Zanardo and Zannier [8], and we will give a general algorithm for calculating power of ideals/classes via the Dirichlet composition of quadratic forms which is applicable to cryptography in the class semigroup of imaginary quadratic non-maximal order and revisit the cryptosystem of Kim and Moon [5] using a Zanardo and Zannier [8]'s quantity as their secret key, in order to analyze Jacobson [7]'s revised cryptosystem based on the class semigroup which is an alternative of Kim and Moon [5]'s.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권3호
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• pp.203-218
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• 2018

An old result of Whitehead says that the set of derivations of a group with values in a crossed G-module has a natural monoid structure. In this paper we introduce derivation of crossed polymodule and actor crossed polymodules by using Lue's and Norrie's constructions. We prove that the set of derivations of a crossed polygroup has a semihypergroup structure with identity. Then, we consider the polygroup of invertible and reversible elements of it and we obtain actor crossed polymodule.

• Kyungpook Mathematical Journal
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• 제48권3호
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• pp.465-472
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• 2008

For a nonnegative real matrix A of rank 1, A can be factored as $ab^t$ for some vectors a and b. The perimeter of A is the number of nonzero entries in both a and b. If B is a matrix of rank k, then B is the sum of k matrices of rank 1. The perimeter of B is the minimum of the sums of perimeters of k matrices of rank 1, where the minimum is taken over all possible rank-1 decompositions of B. In this paper, we obtain characterizations of the linear operators which preserve perimeters 2 and k for some $k\geq4$. That is, a linear operator T preserves perimeters 2 and $k(\geq4)$ if and only if it has the form T(A) = UAV or T(A) = $UA^tV$ with some invertible matrices U and V.

• 한국음향학회지
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• 제19권2호
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• pp.68-72
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• 2000

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 가상 데이터와 NATO 산하 SACLANT 센터에서 수집된 실측 데이터를 이용하여 그 효율성을 입증하였다.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.115-119
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• 2007

Let R be a Krull ring with the unique regular maximal ideal M. We show that R has a regular prime element and reg-$dimR=1{\Leftrightarrow}R$ is a factorial ring and reg-$dim(R)=1{\Rightarrow}M$ is invertible ${\Leftrightarrow}R{\varsubsetneq}[R:M]{\Leftrightarrow}M$ is divisorial ${\Leftrightarrow}$ reg-$htM=1{\Rightarrow}R$ is a rank one discrete valuation ring. We also show that if M is generated by regular elements, then R is a rank one discrete valuation ring ${\Rightarrow}$ R is a factorial ring and reg-dim(R)=1.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.101-114
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• 2007

For an $m$ by $n$ nonnegative real matrix A, the maximal column rank of A is the maximal number of the columns of A which are linearly independent. In this paper, we analyze relationships between ranks and maximal column ranks of matrices over nonnegative reals. We also characterize the linear operators which preserve the maximal column rank of matrices over nonnegative reals.

• 대한수학회보
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• 제37권3호
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• pp.577-586
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• 2000

For a grading monoid S, we prove that (1) if (S, M) is a valuation semigroup, then M is an m-canonical ideal, that is, an ideal M such that M : (M:J)=J for every ideal J of S. (2) if S is an integrally closed semigroup and S has a principal m-canonical ideal, then S is a valuation semigroup, and (3) if S is a completely integrally closed and S has an m-canonical ideal I, then every ideal of S is I-invertible, that is, J+(I+J)=I for every ideal J of S.