• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.13-30
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• 2010

Let C be a nonempty closed convex subset of a real Hilbert space H. Consider the following iterative algorithm given by $x_0\;{\in}\;C$ arbitrarily chosen, $x_{n+1}\;=\;{\alpha}_n{\gamma}f(W_nx_n)+{\beta}_nx_n+((1-{\beta}_n)I-{\alpha}_nA)W_nP_C(I-s_nB)x_n$, ${\forall}_n\;{\geq}\;0$, where $\gamma$ > 0, B : C $\rightarrow$ H is a $\beta$-inverse-strongly monotone mapping, f is a contraction of H into itself with a coefficient $\alpha$ (0 < $\alpha$ < 1), $P_C$ is a projection of H onto C, A is a strongly positive linear bounded operator on H and $W_n$ is the W-mapping generated by a finite family of nonexpansive mappings $T_1$, $T_2$, ${\ldots}$, $T_N$ and {$\lambda_{n,1}$}, {$\lambda_{n,2}$}, ${\ldots}$, {$\lambda_{n,N}$}. Nonexpansivity of each $T_i$ ensures the nonexpansivity of $W_n$. We prove that the sequence {$x_n$} generated by the above iterative algorithm converges strongly to a common fixed point $q\;{\in}\;F$ := $\bigcap^N_{i=1}F(T_i)\;\bigcap\;VI(C,\;B)$ which solves the variational inequality $\langle({\gamma}f\;-\;A)q,\;p\;-\;q{\rangle}\;{\leq}\;0$ for all $p\;{\in}\;F$. Using this result, we consider the problem of finding a common fixed point of a finite family of nonexpansive mappings and a strictly pseudocontractive mapping and the problem of finding a common element of the set of common fixed points of a finite family of nonexpansive mappings and the set of zeros of an inverse-strongly monotone mapping. The results obtained in this paper extend and improve the several recent results in this area.

• 호남수학학술지
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• 제32권3호
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• pp.525-536
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• 2010

Let $X_1,X_2,\cdots$ be identically distributed $\rho$-mixing random variables with mean zeros and positive finite variances. In this paper, we prove $$\array{\lim\\{\in}\downarrow0}{\in}^2 \sum\limits_{n=3}^\infty\frac{1}{nlogn}P({\mid}S_n\mid\geq\in\sqrt{nloglogn}=1$$, $$\array{\lim\\{\in}\downarrow0}{\in}^2 \sum\limits_{n=3}^\infty\frac{1}{nlogn}P(M_n\geq\in\sqrt{nloglogn}=2 \sum\limits_{k=0}^\infty\frac{(-1)^k}{(2k+1)^2}$$ where $S_n=X_1+\cdots+X_n,\;M_n=max_{1{\leq}k{\leq}n}{\mid}S_k{\mid}$ and $\sigma^2=EX_1^2+ 2\sum\limits{^{\infty}_{i=2}}E(X_1,X_i)=1$.

• 한국정보과학회논문지:시스템및이론
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• 제34권5_6호
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• pp.176-186
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• 2007

상호연결망은 그래프로 모델링 할 수 있다: 노드는 정점으로 대응시키고, 링크는 에지로 대응시킨다. 상호연결망(그래프)의 지름은 서로 다른 모든 두 정점 사이의 최단경로 길이 중 최대이다. 상호연결망의 고장지름이란 연결도-1 개 이하의 임의의 정점에 고장이 있을 경우, 이들 고장 정점들을 제거한 연결망에서 모든 두 정점사이의 최단경로 길이 중 최대이다. 지름이 3이상이고 연결도가 r인 r-정규(regular) 그래프의 고장지름은 지름+1이상이다. 이 논문에서는 $m,n{\geq}3$ 인 2-차원 $m{\times}n$ 토러스에서 m=3 혹은 n=3일 때 고장지름은 max(m,n)이고, m,n>3일 때 고장지름은 지름 +1임을 보인다. 그리고 $k_i{\geq}3(1{\leq}i{\leq}d)$이고 $d{\geq}3$인 d- 차원 $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ 토러스에서 서로 다른 임의의 두 정점 사이에 길이가 지름+1이하인 서로소인 경로들이 2d 개 존재함을 보인다. 두 정점 u와 v 사이의 서로소인 경로들이란, 공통의 정점들이 u와 v만 있는 경로들을 말한다. 이들 서로소인 경로들을 이용하여 $k_i{\geq}3(1{\leq}i{\leq}d)$이고 $d{\geq}3$인 d-차원 $k_1{\times}k_2{\times}{\cdots}{\times}k_d$ 토러스의 고장지름이 지름+1임을 보인다.

• 대한화학회지
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• 제21권6호
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• pp.395-403
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• 1977

액체이론(Significant Structure Theory)를 단원자 분자로부터 다원자 분자에 이르는 여러 액체혼합물에 적용하여 전 농도 범위에서 액체 혼합물의 활동도 계수를 계산했다. 단원자 분자계(Ar-Kr, Kr-Xe)와 이원자 분자계$(Ar-O_2,\;N_2-CO)$와 메탄-크립톤계의 액체혼합물의 활동도 계수는 ${\delta}E_s$ 수정 변수에 의해 좋은 결과를 얻었다. 아르곤-질소, 산소-질소, 그리고 메탄-프로판계에 대해서는 이 외에 ${\delta}$V, ${\delta}$n 수정 변수가 더 필요했다.

• Journal of applied mathematics & informatics
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• 제35권1_2호
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• pp.121-130
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• 2017

This study is concerned with the existence of positive solution for the following nonlinear elliptic system $$\{-M_1(\int_{\Omega}{\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^pdx)div({\mid}x{\mid}^{-ap}{\mid}{\nabla}u{\mid}^{p-2}{\nabla}u)\\{\hfill{120}}={\mid}x{\mid}^{-(a+1)p+c_1}\({\alpha}_1A_1(x)f(v)+{\beta}_1B_1(x)h(u)\),\;x{\in}{\Omega},\\-M_2(\int_{\Omega}{\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^qdx)div({\mid}x{\mid}^{-bq}{\mid}{\nabla}v{\mid}^{q-2}{\nabla}v)\\{\hfill{120}}={\mid}x{\mid}^{-(b+1)q+c_2}\({\alpha}_2A_2(x)g(u)+{\beta}_2B_2(x)k(v)\),\;x{\in}{\Omega},\\{u=v=0,\;x{\in}{\partial}{\Omega},$$ where ${\Omega}$ is a bounded smooth domain of ${\mathbb{R}}^N$ with $0{\in}{\Omega}$, 1 < p, q < N, $0{\leq}a$ < $\frac{N-p}{p}$, $0{\leq}b$ < $\frac{N-q}{q}$ and ${\alpha}_i,{\beta}_i,c_i$ are positive parameters. Here $M_i,A_i,B_i,f,g,h,k$ are continuous functions and we discuss the existence of positive solution when they satisfy certain additional conditions. Our approach is based on the sub and super solutions method.

• 대한수학회지
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• 제41권4호
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• pp.717-735
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• 2004

A problem raised by Selfridge and solved by Pomerance asks to find the pairs (a, b) of natural numbers for which $2^a\;-\;2^b$ divides $n^a\;-\;n^b$ for all integers n. Vajaitu and one of the authors have obtained a generalization which concerns elements ${\alpha}_1,\;{\cdots},\;{{\alpha}_{\kappa}}\;and\;{\beta}$ in the ring of integers A of a number field for which ${\Sigma{\kappa}{i=1}}{\alpha}_i{\beta}^{{\alpha}i}\;divides\;{\Sigma{\kappa}{i=1}}{\alpha}_i{z^{{\alpha}i}}\;for\;any\;z\;{\in}\;A$. Here we obtain a further generalization, proving the corresponding finiteness results in a multidimensional setting.

• Natural Product Sciences
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• 제13권1호
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• pp.6-10
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• 2007

The ethanolic (50% v/v) extracts of Carissa carandas (fruits) (Apocynaceae) and Microstylis wallichii (tubers) (Orchidaceae) were examined for anti-inflammatory and analgesic activities in experimental animals. Carissa carandas and Microstylis wallichii (50-200 mg/kg) caused a dose dependent inhibition of swelling caused by carrageenin significantly in cotton pellet induced granuloma in rats (P < 0.05 to P < 0.001). There was a significant increase in the analgesy meter induced pain in rats. The extracts of Carissa carandas and Microstylis wallichii resulted in an inhibition of stretching episodes and percentage protection was 16.05-17.58%respectively in acetic acid induced writhing.

• Transactions on Electrical and Electronic Materials
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• 제14권5호
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• pp.250-253
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• 2013

In this paper, we fabricated 3D pillar type silicon-oxide-nitride-oxide-silicon (SONOS) devices for high density flash applications. To solve the limitation between erase speed and data retention of the conventional SONOS devices, bandgap-engineered (BE) tunneling oxide of oxide-nitride-oxide configuration is integrated with the 3D structure. In addition, the tunneling oxide is modulated by another method of $N_2$ ion implantation ($N_2$ I/I). The measured data shows that the BE-SONOS device has better electrical characteristics, such as a lower threshold voltage ($V_{\tau}$) of 0.13 V, and a higher $g_{m.max}$ of 18.6 ${\mu}A/V$ and mobility of 27.02 $cm^2/Vs$ than the conventional and $N_2$ I/I SONOS devices. Memory characteristics show that the modulated tunneling oxide devices have fast erase speed. Among the devices, the BE-SONOS device has faster program/erase (P/E) speed, and more stable endurance characteristics, than conventional and $N_2$ I/I devices. From the flicker noise analysis, however, the BE-SONOS device seems to have more interface traps between the tunneling oxide and silicon substrate, which should be considered in designing the process conditions. Finally, 3D structures, such as the pillar type BE-SONOS device, are more suitable for next generation memory devices than other modulated tunneling oxide devices.

• 정보과학회 논문지
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• 제43권2호
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• pp.229-236
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• 2016

세타조인은 데이터베이스에 있어서 가장 기본적이면서도 중요한 질의 중 하나이다. 최근 처리해야 하는 데이터의 양이 증가함에 따라, 맵리듀스와 같은 분산 병렬 처리 프레임워크를 사용한 데이터베이스의 질의처리가 많이 연구되고 있다. 대표적인 연구로 M-Bucket-I 휴리스틱을 이용한 세타조인이 있으나, 이 알고리즘은 수행시간이 입력 데이터의 크기를 n이라 할 때, 각 레코드를 $r_{max}$개의 리듀서 중 어느 리듀서로 보낼지 정하는 리듀서맵핑을 구하는데 O(n)의 시간이 걸려 쉽게 사용할 수 없다는 문제가 있다. 본 논문에서는 기존의 M-Bucket-I 휴리스틱을 개선하여, 같은 리듀서 매핑 결과를 내놓더라도 수행시간이 $O(r_{max}log\;n)$으로 보다 짧은 새로운 알고리즘을 제시한다. 다양한 실험을 통하여 기존의 맵리듀스를 이용한 세타조인보다 성능을 10% 정도 향상시킬 수 있음을 보였다.

• East Asian mathematical journal
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• 제5권2호
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• pp.191-198
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• 1989

It is shown that a near-ring N which has no nonzero nilpotent elements is a partially ordered set where $x{\leq}y$ if and only if $yx=x^2$. Also it is shown that $(N,{\leq})$ is infinitely distributive for central elements that is $r(supx_i)=sup(rx_i)$ for every central element r of N and any subset $\{x_i\}$ of N. By using some lemmas we showed that a near-ring without nilpotent elements is isomorphic to a direct product of near-fields if and only if N is hyperatomic and orthogonally complete under the condition that every idempotent of N is central.