• Journal of the Korean Society of Combustion
• /
• v.9 no.2
• /
• pp.1-9
• /
• 2004

Activation energy asymptotics (AEA) for Linan#s diffusion-flame regime is revisited in this paper. The main purpose of the paper is to carefully re-examine each AEA analysis step in order to clarify the some concepts that are often misunderstood among the ordinary practitioners of the AEA. Particular attention is focused on the different AEA regimes arising from the double limit of large Zel#dovich and Damkohler numbers. In addition, the expansion procedures are shown in detail and the method that the turning point condition, commonly known as the Linan#s extinction condition, is found is explained.

• Journal of the Korean Mathematical Society
• /
• v.35 no.4
• /
• pp.1019-1043
• /
• 1998

In this paper we study some asymptotics for solutions of the Ginzburg-Landau equations with Dirichlet boundary conditions. We consider the solutions ( $u_{\in}$, $A_{\in}$) which minimize the Ginzburg-Landau energy functional $E_{\in}$(u, A). We show that the solutions ( $u_{\in$}$ , $A_{\in}$) converge to some ( $u_{*}$, $A_{*}$) in various norms as the coupling parameter $\in$longrightarrow0.ow0.

• Journal of applied mathematics & informatics
• /
• v.33 no.3_4
• /
• pp.343-350
• /
• 2015

We consider an M^X/G/1 retrial queue, where the batch size and service time distributions have finite exponential moments. We show that the tail of the queue size distribution is asymptotically given by a geometric function multiplied by a power function. Our result generalizes the result of Kim et al. (2007) to the M^X/G/1 retrial queue.

• Journal of the Korean Mathematical Society
• /
• v.61 no.1
• /
• pp.91-107
• /
• 2024

We determine the N → ∞ asymptotics of the expected value of entanglement entropy for pure states in H_1,N ⊗ H_2,N, where H_1,N and H_2,N are the spaces of holomorphic sections of the N-th tensor powers of hermitian ample line bundles on compact complex manifolds.

• Honam Mathematical Journal
• /
• v.32 no.3
• /
• pp.525-536
• /
• 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 $\sigma^2=EX_1^2+ 2\sum\limits{^{\infty}_{i=2}}E(X_1,X_i)=1$.

• Honam Mathematical Journal
• /
• v.31 no.3
• /
• pp.369-380
• /
• 2009

Let $X,X_1,X_2,\;{\cdots}$ be identically distributed and negatively associated random variables with mean zeros and positive, finite variances. We prove that, if $E{\mid}X_1{\mid}^r$ < ${\infty}$, for 1 < p < 2 and r > $1+{\frac{p}{2}}$, and $lim_{n{\rightarrow}{\infty}}n^{-1}ES^2_n={\sigma}^2$ < ${\infty}$, then $lim_{{\epsilon}{\downarrow}0}{\epsilon}^{{2(r-p}/(2-p)-1}{\sum}^{\infty}_{n=1}n^{{\frac{r}{p}}-2-{\frac{1}{p}}}E\{{{\mid}S_n{\mid}}-{\epsilon}n^{\frac{1}{p}}\}+={\frac{p(2-p)}{(r-p)(2r-p-2)}}E{\mid}Z{\mid}^{\frac{2(r-p)}{2-p}}$, where $S_n\;=\;X_1\;+\;X_2\;+\;{\cdots}\;+\;X_n$ and Z has a normal distribution with mean 0 and variance ${\sigma}^2$.

• Communications for Statistical Applications and Methods
• /
• v.12 no.3
• /
• pp.557-587
• /
• 2005

This paper elucidates the limiting Gaussian distribution of a class of rank order statistics {$T_N$} for two sample problem pertaining to empirical processes of the squared residuals from two independent samples of GARCH processes. A distinctive feature is that, unlike the residuals of ARMA processes, the asymptotics of {$T_N$} depend on those of GARCH volatility estimators. Based on the asymptotics of {$T_N$}, we empirically assess the relative asymptotic efficiency and effect of the GARCH specification for some GARCH residual distributions. In contrast with the independent, identically distributed or ARMA settings, these studies illuminate some interesting features of GARCH residuals.

• Bulletin of the Korean Mathematical Society
• /
• v.50 no.2
• /
• pp.611-626
• /
• 2013

In the paper we study the finite-time ruin probability in a general risk model with constant interest force, in which the claim sizes are pairwise quasi-asymptotically independent and arrive according to an arbitrary counting process, and the premium process is a general stochastic process. For the case that the claim-size distribution belongs to the consistent variation class, we obtain an asymptotic formula for the finite-time ruin probability, which holds uniformly for all time horizons varying in a relevant infinite interval. The obtained result also includes an asymptotic formula for the infinite-time ruin probability.

• 한국데이터정보과학회:학술대회논문집
• /
• 2006.04a
• /
• pp.43-47
• /
• 2006

Consider a multitype queue where queued customers arc served in their order of arrival at a rate which depends on the customer type. Here we calculate the sharp asymptotics of the probability the total number of customers in the queue reaches a high level before emptying. The natural state space to describe this queue is a tree whose branches increase in length as the number of customers in the queue grows. Consequently it is difficult to prove a large deviation principle. Moreover, since service rates depend on the customer type the stationary distribution is not of product form so there is no simple expression for the stationary distribution. Instead, we use a change of measure technique which increases the arrival rate of customers and decreases the departure rate thus making large deviations common.

• Bulletin of the Korean Mathematical Society
• /
• v.54 no.3
• /
• pp.1023-1036
• /
• 2017

In this paper, we study the existence of positive solutions to the p-Kirchhoff elliptic equation involving general subcritical growth $(a+{\lambda}{\int_{\mathbb{R}^N}{\mid}{\nabla}u{\mid}^pdx+{\lambda}b{\int_{\mathbb{R}^N}{\mid}u{\mid}^pdx)(-{\Delta}_pu+b{\mid}u{\mid}^{p-2}u)=h(u)$, in ${\mathbb{R}}^N$, where a, b > 0, ${\lambda}$ is a parameter and the nonlinearity h(s) satisfies the weaker conditions than the ones in our known literature. We also consider the asymptotics of solutions with respect to the parameter ${\lambda}$.