• 대한수학회지
• /
• 제55권6호
• /
• pp.1337-1358
• /
• 2018

In this paper, we study the solvability of the nonlinear Dirichlet problem with sum of the operators of independent non standard growths $$-div\({\mid}{\nabla}u{\mid}^{p_1(x)-2}{\nabla}u\)-\sum\limits^n_{i=1}D_i\({\mid}u{\mid}^{p_0(x)-2}D_iu\)+c(x,u)=h(x),\;{\in}{\Omega}$$ in a bounded domain ${\Omega}{\subset}{\mathbb{R}}^n$. Here, one of the operators in the sum is monotone and the other is weakly compact. We obtain sufficient conditions and show the existence of weak solutions of the considered problem by using monotonicity and compactness methods together.

• 한국게임학회 논문지
• /
• 제18권2호
• /
• pp.121-130
• /
• 2018

대부분의 빈발 패턴은 패턴이 트랜잭션 데이터베이스에 나타나는 support를 패턴 interestingness의 핵심 척도로 다루어 왔으나 패턴의 횟수는 패턴의 completeness가 가지는 정보를 최대치로 가정하고 있다. 그러나 실제적으로는 임의의 패턴 X의 completeness는 트랜잭션에서 서로 다르게 나타나기 마련이다. 따라서 패턴이 가지는 정보의 손실을 줄이기 위해서는 가중치에 의한 support와 completeness에 의한 유용한 패턴 마이닝을 고려하여야 한다. 즉, 높은 completeness율을 갖는 패턴은 더 높은 recall로 이어질 수 있고 높은 빈도수를 갖는 패턴은 보다 높은 정밀도로 이어진다. 본 논문에서는 동적인 항목들의 가중치에 따른 적응된 support와 completeness를 고려하는 WSCFPM 패턴 마이닝 알고리즘을 제안한다. 제안한 방법은 모노톤 또는 반 모노톤 속성이 가중치에 의한 support와 completeness에 영향을 미치지 않기 때문에 탐색과정을 줄일 수 있다. 실험결과를 통하여 제안된 알고리즘이 효과적이며 확장성이 좋은 것임을 보인다.

• Journal of applied mathematics & informatics
• /
• 제25권1_2호
• /
• pp.1-15
• /
• 2007

Consider a Rayleigh distribution with $$pdf\;p(x/{\theta})\;=\;2x{\theta}^{-1}\;{\exp}\;({-x^2}/{\theta})$$ and mean lifetime ${\mu}\;=\;\sqrt{\pi\theta}/2$. We study the two-action problem of testing the hypotheses $H_{0}\;:\;{\mu}{\leq}{\mu}_{0}$ against $H_{1}\;:\;{\mu}\;>\;{\mu}_{0}$ using a linear error loss of ${\mid}{\mu}\;-\;{\mu}_{0}{\mid}$ via the empirical Bayes approach. We construct a monotone empirical Bayes test ${\delta}^{*}_{n}$ and study its associated asymptotic optimality. It is shown that the regret of ${\delta}^{*}_{n}$ converges to zero at a rate $\frac{{\ln}^{2}n}{n}$, where n is the number of past data available when the present testing problem is considered.

• 대한산업공학회지
• /
• 제17권1호
• /
• pp.117-126
• /
• 1991

When {X(t), t ${\geq}$ 0} is a Markov process representing time-varying system states, we develop efficient bounding methods for some time-dependent performance measures. We use the discretization technique for stochastically monotone Markov processes and a combination of discretization and uniformization for Markov processes with the stochastic convexity(concavity) property. Sufficient conditions for stochastic monotonocity and stochastic convexity of a Markov process are also mentioned. A simple example is given to demonstrate the validity of the bounding methods.

• 대한수학회보
• /
• 제43권3호
• /
• pp.599-610
• /
• 2006

The aim of this paper is to give an existence theorem for a strong solution of generalized vector quasi-equilibrium problems of the weak type II due to Hou et al. using the equilibrium existence theorem for 1-person game, and as an application, we shall give a generalized quasivariational inequality.

• Korean Journal of Mathematics
• /
• 제14권2호
• /
• pp.137-160
• /
• 2006

We describe the weight functions for which Hardy's inequality of nonincreasing functions is satisfied. Further we characterize the pairs of weight functions $(w,v)$ for which the Laplace transform $\mathcal{L}f(x)={\int}^{\infty}_0e^{-xy}f(y)dy$, with monotone function $f$, is bounded from the weighted Lebesgue space $L^p(w)$ to $L^q(v)$.

• 대한수학회보
• /
• 제30권1호
• /
• pp.91-97
• /
• 1993

In this article, we consider the case that S is a topologically complete subspace of $R^{k}$ , and that .GAMMA. is a set of monotone functions on S into S. It is obtained the sugficient condition for the existence of a unique invariant probability to which $P^{(n}$/(x,dy) converges exponentially fast in a metric stronger than the Kolmogorov's distance. This extends the earlier results of Bhattacharya and Lee (1988) who considered the case .GAMMA. a set of nondecreasing functions.tions.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제23권1호
• /
• pp.35-51
• /
• 2016

We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G : X² → X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.

• 대한수학회논문집
• /
• 제12권3호
• /
• pp.655-664
• /
• 1997

The existence and behavior of a bounded solution for a perturbed nonlinear differential equation of the type $$ (DE) x'(t) + Ax(t) \ni G(x(t)), t \in [0, \infty) $$ is considered. First, we consider the existence of a bounded solution with more simple assumptions using the concept of "the method of lines". Then we devote to study its behavior using recent results of almost non-expansive curve which is developed by Djafari Rouhani.i Rouhani.

• East Asian mathematical journal
• /
• 제32권3호
• /
• pp.333-354
• /
• 2016

We present coincidence point theorem for g-non-decreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We show how multidimensional results can be seen as simple consequences of our unidimensional coincidence point theorem. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings $F,G:X^2{\rightarrow}X$ by using obtained coincidence point results. Furthermore, an example and an application to integral equation are also given to show the usability of obtained results. Our results generalize, modify, improve and sharpen several well-known results.