• Kyungpook Mathematical Journal
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• 제47권3호
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• pp.357-361
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• 2007

A right R-module P is $c$-separative provided that $$P{\oplus}P{{c}\atop{\simeq_-}}P{\oplus}Q{\Longrightarrow}P{\simeq_-}Q$$ for any right R-module Q. We get, in this paper, two sufficient conditions under which a right module is $c$-separative. A ring R is a hereditary ring provided that every ideal of R is projective. As an application, we prove that every projective right R-module over a hereditary ring is $c$-separative.

• 대한수학회지
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• 제55권3호
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• pp.671-694
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• 2018

In this paper, we investigate the weighted vector-valued bounds for a class of multilinear singular integral operators, and its commutators, from $L^{p_1}(l^{q_1};\;{\mathbb{R}}^n,\;w_1){\times}{\cdots}{\times}L^{p_m}(l^{q_m};\;{\mathbb{R}}^n,\;w_m)$ to $L^p(l^q;\;{\mathbb{R}}^n,\;{\nu}_{\vec{w}})$, with $p_1,{\cdots},p_m$, $q_1,{\cdots},q_m{\in}(1,\;{\infty})$, $1/p=1/p_1+{\cdots}+1/p_m$, $1/q=1/q_1+{\cdots}+1/q_m$ and ${\vec{w}}=(w_1,{\cdots},w_m)$ a multiple $A_{\vec{P}}$ weights. Our argument also leads to the weighted weak type endpoint estimates for the commutators. As applications, we obtain some new weighted estimates for the $Calder{\acute{o}}n$ commutator.

• Management Science and Financial Engineering
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• 제15권1호
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• pp.33-49
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• 2009

We examine the effectiveness of the conventional (Q, r) model in managing production-inventory systems with finite capacity, stochastic demand, and stochastic order processing times. We show that, for systems with finite production capacity, order replenishment lead times are highly sensitive to loading and order quantity. Consequently, the choice of optimal order quantity and optimal reorder point can vary significantly from those obtained under the usual assumption of a load-independent lead time. More importantly, we show that for a given (Q, r) policy the conventional model can grossly under or over-estimate the actual cost of the policy. In cases where a setup time is associated with placing a production order, we show that the optimal (Q, r) policy derived from the conventional model can, in fact, be infeasible.

• 대한수학회지
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• 제34권4호
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• pp.1029-1036
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• 1997

Let ${A_t)}_{t>0}$ be a dilation group given by $A_t = exp(-P log t)$, where P is a real $n \times n$ matrix whose eigenvalues has strictly positive real part. Let $\nu$ be the trace of P and $P^*$ denote the adjoint of pp. Suppose that $K$ is a function defined on $R^n$ such that $$\mid$K(x)$\mid$ \leq k($\mid$x$\mid$_Q)$ for a bounded and decreasing function $k(t) on R_+$ satisfying $k \diamond $\mid$\cdot$\mid$_Q \in \cup_{\varepsilon >0}L^1((1 + $\mid$x$\mid$)^\varepsilon dx)$ where $Q = \int_{0}^{\infty} exp(-tP^*) exp(-tP)$ dt and the norm $$\mid$\cdot$\mid$_Q$ stands for $$\mid$x$\mid$_Q = \sqrt{}, x \in R^n$. For $f \in L^1(R^n)$, define $mf(x) = sup_{t>0}$\mid$K_t * f(x)$\mid$$ where $K_t(X) = t^{-\nu}K(A_{1/t}^* x)$. Then we show that $m$ is a bounded operator of $L^1(R^n) into L^{1, \infty}(R^n)$.

• Kyungpook Mathematical Journal
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• 제53권3호
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• pp.435-457
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• 2013

Using the Lukasiewicz 3-valued implication operator, the notion of an (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring is introduced, where ${\alpha},{\beta}{\in}\{{\in},q,{\in}{\wedge}q,{\in}{\vee}q\}$. We define intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of a hemiring R and investigate their various properties. We characterize intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) and (${\alpha},{\beta}$)-intuitionistic fuzzy left (right) $h$-ideal of a hemiring R by its level sets. We establish that an intuitionistic fuzzy set A of a hemiring R is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$)-intuitionistic fuzzy left (right) $h$-ideal of R if and only if A is an intuitionistic fuzzy left (right) $h$-ideal with thresholds (0, 1) (or (0, 0.5) or (0.5, 1)) of R respectively. It is also shown that A is a (${\in},{\in}$) (or (${\in},{\in}{\vee}q$) or (${\in}{\wedge}q,{\in}$))-intuitionistic fuzzy left (right) $h$-ideal if and only if for any $p{\in}$ (0, 1] (or $p{\in}$ (0, 0.5] or $p{\in}$ (0.5, 1] ), $A_p$ is a fuzzy left (right) $h$-ideal. Finally, we prove that an intuitionistic fuzzy set A of a hemiring R is an intuitionistic fuzzy left (right) $h$-ideal with thresholds ($s,t$) of R if and only if for any $p{\in}(s,t]$, the cut set $A_p$ is a fuzzy left (right) $h$-ideal of R.

• East Asian mathematical journal
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• 제18권2호
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• pp.271-282
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• 2002

Let R be a ring with an endomorphism $\sigma$ and a derivation $\delta$. An ideal I of R is ($\sigma,\;\delta$)-ideal of R if $\sigma(I){\subseteq}I$ and $\delta(I){\subseteq}I$. An ideal P of R is a ($\sigma,\;\delta$)-prime ideal of R if P(${\neq}R$) is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideals I and J of R, $IJ{\subseteq}P$ implies that $I{\subseteq}P$ or $J{\subseteq}P$. An ideal Q of R is ($\sigma,\;\delta$)-semiprime ideal of R if Q is a ($\sigma,\;\delta$)-ideal and for ($\sigma,\;\delta$)-ideal I of R, $I^2{\subseteq}Q$ implies that $I{\subseteq}Q$. The ($\sigma,\;\delta$)-prime radical (resp. prime radical) is defined by the intersection of all ($\sigma,\;\delta$)-prime ideals (resp. prime ideals) of R and is denoted by $P_{(\sigma,\delta)}(R)$(resp. P(R)). In this paper, the following results are obtained: (1) $P_{(\sigma,\delta)}(R)$ is the smallest ($\sigma,\;\delta$)-semiprime ideal of R; (2) For every extended endomorphism $\bar{\sigma}$ of $\sigma$, the $\bar{\sigma}$-prime radical of an Ore extension $P(R[x;\sigma,\delta])$ is equal to $P_{\sigma,\delta}(R)[x;\sigma,\delta]$.

• 대한수학회논문집
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• 제39권3호
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• pp.785-802
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• 2024

Given M a monoid with a neutral element e. We show that the solutions of d'Alembert's functional equation for n × n matrices Φ(pr, qs) + Φ(sp, rq) = 2Φ(r, s)Φ(p, q), p, q, r, s ∈ M are abelian. Furthermore, we prove under additional assumption that the solutions of the n-dimensional mixed vector-matrix Wilson's functional equation $$\begin{cases}f(pr, qs) + f(sp, rq) = 2\phi(r, s)f(p, q),\\Φ(p, q) = \phi(q, p),{\quad}p, q, r, s {\in} M\end{cases}$$ are abelian. As an application we solve the first functional equation on groups for the particular case of n = 3.

• 대한수학회논문집
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• 제33권4호
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• pp.1141-1158
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• 2018

Hahn difference operator $D_{q,{\omega}}$ which is defined by $$D_{q,{\omega}}g(t)=\{{\frac{g(gt+{\omega})-g(t)}{t(g-1)+{\omega}}},{\hfill{20}}\text{if }t{\neq}{\theta}:={\frac{\omega}{1-q}},\\g^{\prime}({\theta}),{\hfill{83}}\text{if }t={\theta}$$ received a lot of interest from many researchers due to its applications in constructing families of orthogonal polynomials and in some approximation problems. In this paper, we investigate sufficient conditions for stability of the abstract linear Hahn difference equations of the form $$D_{q,{\omega}}x(t)=A(t)x(t)+f(t),\;t{\in}I$$, and $$D^2{q,{\omega}}x(t)+A(t)D_{q,{\omega}}x(t)+R(t)x(t)=f(t),\;t{\in}I$$, where $A,R:I{\rightarrow}{\mathbb{X}}$, and $f:I{\rightarrow}{\mathbb{X}}$. Here ${\mathbb{X}}$ is a Banach algebra with a unit element e and I is an interval of ${\mathbb{R}}$ containing ${\theta}$.

• 스마트미디어저널
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• 제4권3호
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• pp.9-15
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• 2015

퍼브/서브 시스템(Pub/Sub System)은 시스템에서 발행되는 정보 중 사용자가 등록한 관심 정보만을 사용자에게 전달해주는 시스템이다. 기존의 퍼브/서브 시스템은 컨텐트의 저장 및 전달을 담당하는 브로커들을 네트워크화 하여 구현되었다. 모바일 사용자가 급증함에 따라 사용자의 관심위치 정보와 같은 지속적으로 변하게 되는 관심정보를 다루기 위한 퍼브/서브 시스템에 대한 수요가 부각 되고 있다. 이 논문에서는 기존의 퍼브/서브 시스템에서 깊이 고려하지 않았던, 관심 위치 정보의 빈번한 변화를 효과적으로 처리하기 위한 브로커 네트워크 기반의 퍼브/서브 시스템을 제안한다. 사용자의 행동 패턴이나 지리적 특성을 고려해 퍼브/서브 시스템에서 관리하는 공간 데이터 영역을 Slow Moving Region과 Normal Moving Region의 두가지 타입으로 구분하고, 각 영역에 대한 사용자의 요청을 효과적으로 지원하기 위해 Q+R트리를 사용하여 브로커를 관리한다. 시뮬레이션을 사용한 실험 결과를 통해 제안하는 Q+R트리 기반의 브로커 네트워크가 불필요한 브로커의 로드와 네트워크 트래픽을 감소시킴으로써 보다 효과적으로 지속적인 사용자의 관심 위치 정보 변화를 지원할 수 있음을 확인하였다.

• Journal of the Korean Statistical Society
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• 제21권1호
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• pp.47-58
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• 1992

The autocorrelation function structures of bilinear time series model BL(p, q, r, s), $r \geq s$ are obtained and shown to be analogous to those of ARMA(p, l), l=max(q, s). Simulation studies are performed to investigate the adequacy of Akaike information criteria for identification between ARMA(p, l) and BL(p, q, r, s) models and for determination of orders of BL(p, q, r, s) models. It is suggested that the model of having minimum Akaike information criteria is selected for a suitable model.