• Bulletin of the Korean Mathematical Society
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• v.50 no.3
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• pp.983-991
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• 2013

For each real number $n$ > 6, we prove that there is a sequence $\{pk(n,z)\}^{\infty}_{k=1}$ of fourth degree self-reciprocal polynomials such that the zeros of $p_k(n,z)$ are all simple and real, and every $p_{k+1}(n,z)$ has the largest (in modulus) zero ${\alpha}{\beta}$ where ${\alpha}$ and ${\beta}$ are the first and the second largest (in modulus) zeros of $p_k(n,z)$, respectively. One such sequence is given by $p_k(n,z)$ so that $$p_k(n,z)=z^4-q_{k-1}(n)z^3+(q_k(n)+2)z^2-q_{k-1}(n)z+1$$, where $q_0(n)=1$ and other $q_k(n)^{\prime}s$ are polynomials in n defined by the severely nonlinear recurrence $$4q_{2m-1}(n)=q^2_{2m-2}(n)-(4n+1)\prod_{j=0}^{m-2}\;q^2_{2j}(n),\\4q_{2m}(n)=q^2_{2m-1}(n)-(n-2)(n-6)\prod_{j=0}^{m-2}\;q^2_{2j+1}(n)$$ for $m{\geq}1$, with the usual empty product conventions, i.e., ${\prod}_{j=0}^{-1}\;b_j=1$.

• The KIPS Transactions:PartA
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• v.16A no.6
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• pp.501-508
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• 2009

In this paper, we prove that folded hyper-star network FHS(2n,n) is node-symmetric and a bipartite network. We show that FHS(2n,n) can be embedded into odd network On+1 with dilation 2, congestion 1 and Od can be embedded into FHS(2n,n) with dilation 2 and congestion 1. Also, we show that $2n{\time}n$ torus can be embedded into FHS(2n,n) with dilation 2 and congestion 2.

• Bulletin of the Korean Mathematical Society
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• v.33 no.1
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• pp.119-126
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• 1996

In this paper we study the asymptotic behavior of the edge independence number of a random (n,n)-tree. The tools we use include the matrix-tree theorem, the probabilistic method and Hall's theorem. We begin with some definitions. An (n,n)_tree T is a connected, acyclic, bipartite graph with n light and n dark vertices (see [Pa92]). A subset M of edges of a graph is called independent(or matching) if no two edges of M are adfacent. A subset S of vertices of a graph is called independent if no two vertices of S are adjacent. The edge independence number of a graph T is the number $\beta_1(T)$ of edges in any largest independent subset of edges of T. Let $\Gamma(n,n)$ denote the set of all (n,n)-tree with n light vertices labeled 1, $\ldots$, n and n dark vertices labeled 1, $\ldots$, n. We give $\Gamma(n,n)$ the uniform probability distribution. Our aim in this paper is to find bounds on $\beta_1$(T) for a random (n,n)-tree T is $\Gamma(n,n)$.

• Communications of the Korean Mathematical Society
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• v.17 no.3
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• pp.535-540
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• 2002

Let X$_1$, X$_2$‥‥,X$\_$n/ be n independent and identically distributed random variables with continuous cumulative distribution function F(x). Let us rearrange the X's in the increasing order X$\_$1:n/ $\leq$ X$\_$2:n/ $\leq$ ‥‥ $\leq$ X$\_$n:n/. We call X$\_$k:n/ the k-th order statistic. Then X$\_$n:n/ - X$\_$n-1:n/ and X$\_$n-1:n/ are independent if and only if f(x) = 1-e(equation omitted) with some c > 0. And X$\_$j/ is an upper record value of this sequence lf X$\_$j/ > max(X$_1$, X$_2$,¨¨ ,X$\_$j-1/). We define u(n) = min(j|j > u(n-1),X$\_$j/ > X$\_$u(n-1)/, n $\geq$ 2) with u(1) = 1. Then F(x) = 1 - e(equation omitted), x > 0 if and only if E[X$\_$u(n+3)/ - X$\_$u(n)/ | X$\_$u(m)/ = y] = 3c, or E[X$\_$u(n+4)/ - X$\_$u(n)/|X$\_$u(m)/ = y] = 4c, n m+1.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.497-503
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• 2005

This paper presents characterizations on the independence of the exponential and Pareto distributions by record values. Let ${X_{n},\;n {\ge1}$ be a sequence of independent and identically distributed(i.i.d) random variables with a continuous cumulative distribution function(cdf) F(x) and probability density function(pdf) f(x). $Let{\;}Y_{n} = max{X_1, X_2, \ldots, X_n}$ for n \ge 1. We say $X_{j}$ is an upper record value of ${X_{n},{\;}n\ge 1}, if Y_{j} > Y_{j-1}, j > 1$. The indices at which the upper record values occur are given by the record times {u(n)}, n \ge 1, where u(n) = $min{j|j > u(n-1), X_{j} > X_{u(n-1)}, n \ge 2}$ and u(l) = 1. Then F(x) = $1 - e^{-\frac{x}{a}}$, x > 0, ${\sigma} > 0$ if and only if $\frac {X_u(_n)}{X_u(_{n+1})} and X_u(_{n+1}), n \ge 1$, are independent. Also F(x) = $1 - x^{-\theta}, x > 1, {\theta} > 0$ if and only if $\frac {X_u(_{n+1})}{X_u(_n)}{\;}and{\;} X_{u(n)},{\;} n {\ge} 1$, are independent.

• Korean Journal of Materials Research
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• v.28 no.7
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• pp.405-410
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• 2018

TiN and CrN thin films are among the most used coatings in machine and tool steels. TiN and CrN are deposited by arc ion plating(AIP) method. The AIP method inhibits the reaction by depositing a hard, protective coating on the material surface. In this study, the characteristics of multi-layer(TiN/CrN/TiN(TCT), CrN/TiN/CrN(CTC)) are investigated. For comparison, TiN with the same thickness as the multilayer is formed as a single layer and analyzed. Thin films formed as multilayers are well stacked. The characteristics of micro hardness and corrosion resistance are better than those of single layer TiN. The TiN/CrN peak is confirmed because both TCT and CTC are formed of the same component(TiN, CrN), and the phase is first grown in the (111) direction, which is the growth direction. However, the adhesion and abrasion resistance of the multilayer films are somewhat lower.

• Kyungpook Mathematical Journal
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• v.56 no.1
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• pp.83-94
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• 2016

Let M and N be modules over a ring R. The purpose of this paper is to study modules M, N for which the bi-module [M, N] is regular or pi. It is proved that the bi-module [M, N] is regular if and only if a module N is semi M-projective and $Im({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$, if and only if a module M is semi N-injective and $Ker({\alpha}){\subseteq}^{\oplus}N$ for all ${\alpha}{\in}[M,N]$. Also, it is proved that the bi-module [M, N] is pi if and only if a module N is direct M-projective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Im({\alpha}{\beta}){\subseteq}^{\oplus}N$, if and only if a module M is direct N-injective and for any ${\alpha}{\in}[M,N]$ there exists ${\beta}{\in}[M,N]$ such that $Ker({\beta}{\alpha}){\subseteq}^{\oplus}M$. The relationship between the Jacobson radical and the (co)singular ideal of [M, N] is described.

• Archives of Pharmacal Research
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• v.27 no.3
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• pp.273-277
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• 2004

In previous studies for the development of new anticonvulsants, we found that N-Cbz-$\alpha$-amino-N-alkylsuccinimides exhibited significant anticonvulsant activities in the Maximal electroshock seizure (MES) and Pentylenetetrazole induced seizure (PTZ) tests, and also their anticonvulsant activities were dependent on the N-alkyl substituents existent in their structures. Based on these estimations, N-Cbz-$\alpha$-amino-N-hydroxysuccinimide and various N-Cbz-$\alpha$-amino-N-alkoxysuccinimides were prepared in order to develop more active anticonvulsants and to examine the effects of N-hydoxy or N-alkoxy groups on their anticonvulsant activities. The (R)-or (S)-N-Cbz-$\alpha$-amino-N-hydroxysuccinimide and N-Cbz-$\alpha$-amino-N-alkoxysuccinimides were prepared from the corresponding (R)-or (S)-N-Cbz-aspartic acid through the known synthetic procedures. Their anticonvulsant activities in the MES and PTZ test were evaluated. All of these compounds except 3a showed significant anticonvulsant activities against the PTZ test, but these compounds were not active in the MES test. The most active compound in the PTZ test was (R)-N-Cbz-$\alpha$-amino-N-benzyloxysuccinimide (ED$_{50}$=62.5 mg/kg). In addition, the anti-convulsant activities of these compounds were dependent on their N-substited groups. The order of anticonvulsant activity against the PTZ test, as judged from the ED50 values for (R) series was N-benzyloxy > N-hydroxy > N-isopropoxy > N-methoxy > N-ethoxy; for the (S) series N-ethoxy > N-benzyloxy > N-methoxy > N-isopropoxy.y.

• Journal of the Korean Chemical Society
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• v.13 no.3
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• pp.221-228
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• 1969

The nucleophilic addition rate constants of n-amyl-, n-hexyl-, n-octyl-and n-decyl mercaptide ion to 3,4-methylenedioxy-${\beta}$-nitrostyrene were determined and found to be 2.82 ${\times}10^8$ $M^{-2} .sec^{-1}$, 1.00 ${\times}10^8$ $M^{-2}.sec^{-1}$, 2.23 ${\times}10^8$ $M^{-2} .sec^{-1}$ and 1.77 ${\times}10^8$ $M^{-2}.sec^{-1}$ respectively. At low pH, for n-amyl-, n-hexyl-, n-octyl-and n-decyl mercaptan the values determined are 2.82 ${\times}10^{-2}$ $M^{-1} . sec^{-1}$, 1.95 ${\times}10^{-2}$ $M^{-1} . sec^{-1}$, 7.08 ${\times}10^{-2}$ $M^{-1} . sec^{-1}$ and 5.63 ${\times}10^{-2}$ $M^{-1} . sec^{-1}$ respectively. The rate equations which can fully explain the addition mechanism over wide pH range were also be obtained.

• Journal of Nutrition and Health
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• v.24 no.5
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• pp.420-430
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• 1991

To compare the hypolipidemic effects of n6 linoleic acid. n3 $\alpha$-linolenic acid and n3 eicosapentaenoic acid in rats fed high carbohydrate(70% Cal) diet. male Sprague Dawley rats were fed different experimental diets for 6 weeks. which were different only in fatty acid composition. The dietary fats were beer tallow(BT) as a source of saturated fatty acid (SFA), corn oil(CO) for n6 linoleic acid(LA), perilla oil(PO) for n3 $\alpha$-linolenic acid(LL) and fish oil(FO) for n3 eicosapentaenoic acid(EPA) and docosahexaenoic acid (DHA) Plasma total cholesterol(Chol) level was increased by n6 LA but decreased by n3 LL and n3 EPA and most effectively reduced by n3 EPA. HDL-Chol level was raised by n6 LA, but there was no significant change in HDL-Chol levels by n3 LL and was lowered by n3 EPA. Plasma TG level was reduced by n6 LA, but lipogenesis in liver was not affected by n6 LA. However, plasma TG level was lowered by n3 LL and EPA. Both lipogenic enzyme activity and liver TC level were also decreased by n3 PUFA. The relative proportions of TG in VLDL was significantly lowered by n3 EPA. but the proportions of Apo B in VLDL was not changed by n3 EPA. Overall. the hypolipidemic effect was in the order of EPA+ DHA(n3) >LL(n3) >LA(n6) and fish oil and perilla oil rich in n3 PUFA may have important nutritional applications in the prevention and treatment of hypertriglyceridemia.