• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.317-326
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• 2003

We classify all possible level Artinian O-sequences of socle degree 5 and type 3. Moreover, we show how to construct level Artinian algebras with those Hilbert functions using the sum of two ideals of finite sets of points in $P^2$ such that the ideal of the union of two sets is level.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권2호
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• pp.129-136
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• 2013

We research properties of ternary numbers with values in ${\Lambda}(2)$. Also, we represent dual ternary numbers in the sense of Clifford algebras of real six dimensional spaces. We give generation theorems in dual ternary number systems in view of Clifford analysis, and obtain Cauchy theorems with respect to dual ternary numbers.

• Korean Journal of Mathematics
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• 제29권4호
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• pp.765-774
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• 2021

In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach 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.

• 한국항행학회논문지
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• 제17권6호
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• pp.652-657
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• 2013

논문에서는 두 가지 혼돈맵들을 연결시킨 하나의 합성맵을 기초로 사용하는 독립된 하나의 합성상태머신을 설계하는 방법 및 그 결과를 제시하였다. 혼돈2진스트림발생기로 사용하기 위하여 혼돈합성맵에 관한 디지털회로를 설계하였다. 두 가지 혼돈함수들- 톱니함수와 비뚤어진 로지스틱 함수-로 구성되는 혼돈합성함수의 이산화 진리표를 작성하였고, 디지털회로의 수학적 모델로써 간략화 된 부울대수식들을 제시하였다. 결과로써 혼돈합성함수의 맵에 관한 디지털회로들을 제시하였다.

• 대한수학회지
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• 제49권2호
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• pp.405-417
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• 2012

We find the Hilbert function and the minimal free resolution of a star-configuration in $\mathbb{P}^n$. The conditions are provided under which the Hilbert function of a star-configuration in $\mathbb{P}^2$ is generic or non-generic We also prove that if $\mathbb{X}$ and $\mathbb{Y}$ are linear star-configurations in $\mathbb{P}^2$ of types t and s, respectively, with $s{\geq}t{\geq}3$, then the Artinian k-algebra $R/(I_{\mathbb{X}}+I_{\mathbb{Y})$ has the weak Lefschetz property.

• 대한수학회지
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• 제54권5호
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• pp.1379-1410
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• 2017

Kang and Ko introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4. Let $R=k[w_0,\;w_1,\;w_2,\;{\ldots},\;w_m]$ be the polynomial ring over an algebraically closed field k with indetermiantes $w_l$ and deg $w_l=1$, and $I_i$ a homogeneous perfect ideal of grade 3 with type $t_i$ defined by a skew-symmetrizable matrix $G_i(1{\leq}t_i{\leq}4)$. We show that for m = 2 the Hilbert function of the zero dimensional standard k-algebra $R/I_i$ is determined by CI-sequences and a Gorenstein sequence. As an application of this result we show that for i = 1, 2, 3 and for m = 3 a Gorenstein sequence $h(R/H_i)=(1,\;4,\;h_2,\;{\ldots},\;h_s)$ is unimodal, where $H_i$ is the sum of homogeneous perfect ideals $I_i$ and $J_i$ which are geometrically linked by a homogeneous regular sequence z in $I_i{\cap}J_i$.

• 대한수학회지
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• 제56권5호
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• pp.1333-1354
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• 2019

In authors' paper in 2007, it was shown that the BSE-extension of $C^1_0(R)$, the algebra of continuously differentiable functions f on the real number space R such that f and df /dx vanish at infinity, is the Lipschitz algebra $Lip_1(R)$. This paper extends this result to the case of $C^n_0(R^d)$ and $C^{n-1,1}_b(R^d)$, where n and d represent arbitrary natural numbers. Here $C^n_0(R^d)$ is the space of all n-times continuously differentiable functions f on $R^d$ whose k-times derivatives are vanishing at infinity for k = 0, ${\cdots}$, n, and $C^{n-1,1}_b(R^d)$ is the space of all (n - 1)-times continuously differentiable functions on $R^d$ whose k-times derivatives are bounded for k = 0, ${\cdots}$, n - 1, and (n - 1)-times derivatives are Lipschitz. As a byproduct of our investigation we obtain an important result that $C^{n-1,1}_b(R^d)$ has a predual.

• 대한수학회보
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• 제49권4호
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• pp.715-736
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• 2012

Brown provided a structure theorem for a class of perfect ideals of grade 3 with type ${\lambda}$ > 0. We introduced a skew-symmetrizable matrix to describe a structure theorem for complete intersections of grade 4 in a Noetherian local ring. We construct a class of perfect ideals I of grade 3 with type 2 defined by a certain skew-symmetrizable matrix. We present the Hilbert function of the standard $k$-algebras R/I, where R is the polynomial ring $R=k[v_0,v_1,{\ldots},v_m]$ over a field $k$ with indeterminates $v_i$ and deg $v_i=1$.

• 대한수학회논문집
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• 제9권4호
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• pp.831-836
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• 1994

In this paper we characterize the quasiaffine transforms of quasisubscalar operators. Let H and K be separable, complex Hilbert spaces and L(H,K) denote the space of all linear, bounded operators from H to K. If H = K, we write L(H) in place of L(H,K). A linear bounded operators S on H is called scalar of order m if there is a continuous unital morphism of topological algebras $$ \Phi : C^m_0(C) \to L(H) $$ such that $\Phi(z) = S$, where as usual z stands for identity function on C, and $C^m_0(C)$ stands for the space of compactly supproted functions on C, continuously differentiable of order m, $0 \leq m \leq \infty$.