• 스마트미디어저널
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• 제7권2호
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• pp.9-14
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• 2018

The k-ary n-cube $Q^k_n$ is widely used in the design and implementation of parallel and distributed processing architectures. It consists of $k^n$ identical nodes, each node having degree 2n is connected through bidirectional, point-to-point communication channels to different neighbors. On $Q^k_n$ we would like to transmit packets from a source node to 2n destination nodes simultaneously along paths on this network, the $i^{th}$ packet will be transmitted along the $i^{th}$ path, where $0{\leq}i{\leq}2n-1$. In order for all packets to arrive at a destination node quickly and securely, we present an $O(n^3)$ routing algorithm on $Q^k_n$ for generating a set of one-to-many node-disjoint and nearly shortest paths, where each path is either shortest or nearly shortest and the total length of these paths is nearly minimum since the path is mainly determined by employing the Hungarian method.

• Journal of applied mathematics & informatics
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• 제10권1_2호
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• pp.245-250
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• 2002

Consider the Convex Polygon Pm={Al , A2, ‥‥, Am} With Vertex points A$\_$i/ = (a$\_$i/, b$\_$i/),i : 1,‥‥, m, interior P$\^$0/$\_$m/, and length of perimeter denoted by L(P$\_$m/). Let R$\_$n/ = {B$_1$,B$_2$,‥‥,B$\_$n/), where B$\_$i/=(x$\_$i/,y$\_$I/), i =1,‥‥, n, denote a regular polygon with n sides of equal length and equal interior angle. Kaiser[4] used the regular polygon R$\_$n/ to approximate P$\_$m/, and the problem examined in his work is to position R$\_$n/ with respect to P$\_$m/ to minimize the area of the symmetric difference between the two figures. In this paper we give the quality of a approximating regular polygon R$\_$n/ to approximate P$\_$m/.

• Bulletin of the Korean Chemical Society
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• 제26권2호
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• pp.238-240
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• 2005

The enthalpies of transfer, ${\Delta}H_t{\Theta}$, of NaI from water to aqueous methanol, ethanol and isopropanol, iPrOH, systems are reported. These data have been analysed in terms of the new solvation theory. These data are considered in terms of the new developed solvation theory including variable ($\alpha$n + $\beta$N), the net effect of the solute on the solvent-solvent bonding, is positive if there is a net breaking or weakening of solvent-solvent bonds. The solvation parameters recovered from the analyses indicate that the net affect of NaI on solvent structure is a breaking of solvent-solvent bonds and that NaI is preferentially solvated by water in all aqueous alcohol systems considered. ($\alpha$n + $\beta$N) values increase with increasing in the size of the alcohol alkyl residue from methanol to iPrOH.

• 대한수학회논문집
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• 제20권3호
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• pp.531-538
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• 2005

In this paper we derive the central limit theorem for ${\sum}_{i=1}^n\;a_{ni}\xi_i$, where ${a_{ni},\;1\;{\leq}\;i\;{\leq}\;n}$ is a triangular array of nonnegative numbers such that $sup_n{\sum}_{i=1}^n\;a_{ni}^2\;<\;{\infty},\;max_{1{\leq}i{\leq}n}a_{ni}{\rightarrow}0\;as\;n\;{\rightarrow}\;{\infty}\;and\;\xi'_i\;s$ are a linearly negative quadrant dependent sequence. We also apply this result to consider a central limit theorem for a partial sum of a generalized linear process $X_n\;=\;\sum_{j=-\infty}^\infty\;a_k+_j{\xi}_j$.

• 대한수학회보
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• 제43권1호
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• pp.169-178
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• 2006

For double arrays of constants ${a_{ni},\;1{\leq}i{\leq}k_n,\;n{\geq}1}$ and sequences ${X_n,\;n{\geq}1}$ of asymptotically almost negatively associated (AANA) random variables the almost sure convergence of $\sum\limits{_{i=1}}{^{k_n}}\;a_{ni}X_i$ is derived.

• 대한수학회지
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• 제55권5호
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• pp.1031-1043
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• 2018

Let R be a commutative ring with $1{\neq}0$, I a proper ideal of R, and m and n positive integers. In this paper, we define I to be a weakly (m, n)-closed ideal if $0{\neq}x^m\;{\in}I$ for $x{\in}R$ implies $x^n{\in}I$, and R to be an (m, n)-von Neumann regular ring if for every $x{\in}R$, there is an $r{\in}R$ such that $x^mr=x^n$. A number of results concerning weakly(m, n)-closed ideals and (m, n)-von Neumann regular rings are given.

• 대한수학회논문집
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• 제17권4호
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• pp.719-729
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• 2002

Consider the random n $\times$ m assignment problem with m $\geq$ $_{i,j}$ Let $u_{i,j}$ be iid uniform random variables on [0, 1] and exponential random variables with mean 1, respectively, and let $U_{n, m}$ and $T_{n, m}$ denote the optimal assignment costs corresponding to $u_{i, j}$ and $t_{i, j}$. In this paper we first give a comparison result about the discrepancy E $T_{n, m}$ -E $U_{n, m}$. Using this comparison result with a known lower bound for Var( $T_{n, m}$) we obtains a lower bound for Var( $U_{n, m}$). Finally, we study the way that E $U_{n, m}$ and E $T_{n, m}$ vary as m does. It turns out that only when m - n is large enough, the cost decreases significantly.tly.

• Korean Journal of Mathematics
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• 제24권3호
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• pp.307-317
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• 2016

Let R be a ring. It is well-known that R is NI if and only if ${\sum}^n_{i=0}Ra_i$ is a nil ideal of R whenever a polynomial ${\sum}^n_{i=0}a_ix^i$ is nilpotent, where x is an indeterminate over R. We consider a condition which is similar to the preceding one: ${\sum}^n_{i=0}Ra_iR$ contains a nonzero nil ideal of R whenever ${\sum}^n_{i=0}a_ix^i$ over R is nilpotent. A ring will be said to be quasi-NI if it satises this condition. The structure of quasi-NI rings is observed, and various examples are given to situations which raised naturally in the process.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제15권4호
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• pp.401-406
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• 2008

Given operators X and Y acting on a separable complex Hilbert space H, an interpolating operator is a bounded operator A such that AX=Y. In this article, we investigate Hilbert-Schmidt interpolation problems for operators in a tridiagonal algebra and we get the following: Let ${\pounds}$ be a subspace lattice acting on a separable complex Hilbert space H and let X=$(x_{ij})$ and Y=$(y_{ij})$ be operators acting on H. Then the following are equivalent: (1) There exists a Hilbert-Schmidt operator $A=(a_{ij})$ in Alg${\pounds}$ such that AX=Y. (2) There is a bounded sequence $\{{\alpha}_n\}$ in $\mathbb{C}$ such that ${\sum}_{n=1}^{\infty}|{\alpha}_n|^2<{\infty}$ and $$y1_i={\alpha}_1x_{1i}+{\alpha}_2x_{2i}$$ $$y2k_i={\alpha}_{4k-1}x_2k_i$$ $$y{2k+1}_i={\alpha}_{4k}x_{2k}_i+{\alpha}_{4k+1}x_{2k+1}_i+{\alpha}_{4k+2}x_{2k+2}_i\;for\;all\;i,\;k\;\mathbb{N}$$.

• 대한한의진단학회지
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• 제10권2호
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• pp.31-42
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• 2006

Background and Purpose : The concept of $Wux{\'{\i}}ng$(五行) is central to all elements of the Koran traditional medicine. And $Wux{\'{\i}}ng$ is considered to one of the constitution theories in some of oriental medicine fields in South Korea. The aim of this study is to find necessary and concrete estimation factors for distributing patterns of $Wux{\'{\i}}ngr{\'{e}}n$(五行人) respectively. Methods : We translated and summarized the records about distinguishing characteristics and distributing points of Wu-Xing Ren described in <$L{\'{\i}}ngshu$(靈樞)${\cdot}$Yin-Y${\'{a}}$ng ${\`{e}}rsh{\'{\i}}wur{\'{e}}n$(陰陽二十五人)>. Some review articles were identified through searches of KISS and KERIS databases. Results and Conclusion : Concrete distinguishing characteristics and distributing points of Wu-Xing Ren were described in <$Lingshu{\cdot}Yin-Y{\'{a}}ng\;{\`{e}}rsh{\'{\i}}wur{\'{e}}n$>. According to <$Lingshu{\cdot}Yin-Y{\'{a}}ng\;{\`{e}}rsh{\'{\i}}wur{\'{e}}n$>, the most notable characteristics and distributing points are the skin color and shape of face. but the skin color and shape of face are too ambiguous to be used as distributing criteria in a practical manner. In stead size of head, longitudinal length of back, disposition, and width between both shoulders may be used as distributing criteria in practical clinic fields.