• 한국콘텐츠학회:학술대회논문집
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• 한국콘텐츠학회 2003년도 춘계종합학술대회논문집
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• pp.406-410
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• 2003

B.M. Schen([2])은 함수의 합성 "${\circ}$" 과 차집합 연산 "-"에 대하여 닫혀있는 함수들의 집합 ${\Phi}$에서의 대수적 구조인 subtraction semigroup (${\Phi}$; ${\circ}$,-)를 정의하였다. 이 구조에서 (${\Phi}$; ${\circ}$)는 semgroup, (${\Phi}$; -)는 [1]에서 정의한 subtraction algebra를 이룬다. B.M. Schen은 [2]에서 모든 subtraction semigroup은 invertible function들의 difference semigroup과 동형이라는 사실을 밝혔다. 본 논문에서는 이 subtraction semigroup의 일반화로써 near subtraction semigroupd을 정의하고 이의 한 특수한 형태인 strong near subtraction semigroup의 개념을 정의하여 이들의 일반적인 성질과 ideal의 특성을 조사하고 이들의 응용도를 조사하고자 한다.

• 대한수학회지
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• 제42권5호
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• pp.1031-1056
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• 2005

In this paper, we define the conditional first variation over Wiener paths in abstract Wiener space and investigate its properties. Using these properties, we also investigate relationships among first variation, conditional first variation, Fourier-Feynman transform and conditional Fourier-Feynman transforms of functions in a Banach algebra which is equivalent to the Fresnel class. Finally, we provide another method evaluating the Fourier-Feynman transform for the product of a function in the Banach algebra with n linear factors.

• 대한수학회논문집
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• 제20권3호
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• pp.505-509
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• 2005

We show that every $\varepsilon-approximate$ Jordan functional on a Banach algebra A is continuous. From this result we obtain that every $\varepsilon-approximate$ Jordan mapping from A into a continuous function space C(S) is continuous and it's norm less than or equal $1+\varepsilon$ where S is a compact Hausdorff space. This is a generalization of Jarosz's result [3, Proposition 5.5].

• 대한수학회보
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• 제57권5호
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• pp.1231-1240
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• 2020

The asymptotic behavior of graded Betti numbers of powers of homogeneous ideals in a polynomial ring over a field has recently been reviewed. We extend quasi-polynomial behavior of graded Betti numbers of powers of homogenous ideals to ℤ-graded algebra over Noetherian local ring. Furthermore our main result treats the Betti table of filtrations which is finite or integral over the Rees algebra.

• 호남수학학술지
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• 제35권1호
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• pp.1-15
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• 2013

In this paper, we study a sheaf-theoretic analysis of the convolution algebra on quiver varieties. As by-products, we reinterpret the results of H. Nakajima. We also produce a refined form of the BBD decomposition theorem for quiver varieties. Finally, we study a construction of highest weight modules through constructible functions.

• Journal of applied mathematics & informatics
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• 제29권1_2호
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• pp.443-450
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• 2011

In this paper, we construct a Gorenstein Artinian algebra R/J with non-unimodal Hilbert function h = (1, 13, 12, 13, 1) to investigate the algebraic structure of the ideal J in a polynomial ring R. For this purpose, we use a software system Macaulay 2, which is devoted to supporting research in algebraic geometry and commutative algebra.

• 대한수학회지
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• 제57권3호
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• pp.777-792
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• 2020

We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information about lex segment ideals. Moreover, we introduce numerical functions called fractal functions, and we use them to solve the open problem of the classification of the Hilbert functions of any bigraded algebra.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.117-125
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• 2020

In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

• 대한수학회보
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• 제46권1호
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• pp.147-153
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• 2009

In this paper, we give some constructions of implicative/commutative d-algebras which are not BCK-algebras. This demonstrate that the notion of implicative/commutative d-algebras are indeed generalizations of the same in BCK-algebras.

• 대한수학회논문집
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• 제37권3호
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• pp.649-658
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• 2022

In this paper, we introduce the notion of a left-almost-zero groupoid, and we generalize two axioms which play important roles in the theory of BCK-algebra using the notion of a projection. Moreover, we investigate a Smarandache disjointness of semi-leftoids.