• Proceedings of the Korean Statistical Society Conference
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• 2002.11a
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• pp.79-83
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• 2002

A phase III clinical trial of a new drug for neutropenia induced by chemotherapy is presented and consider adding random effects in crossover design which was used in the clinical study. The diagnostics for its heteroscedasticity based on score statistic is derived for detecting homoscedasticity of errors in crossover design. A small simulation study is peformed to investigate the finite sample behaviour of the test statistic which is known to have an asymptotic chi-square distribution under the null hypothesis.

• Kyungpook Mathematical Journal
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• v.58 no.1
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• pp.9-17
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• 2018

Let $R ={\oplus}_{n{\in}Z}R_n$ be a graded commutative Noetherian ring and let I be a graded ideal of R and J be an arbitrary ideal. It is shown that the i-th generalized local cohomology module of graded module M with respect to the (I, J), is graded. Also, the asymptotic behaviour of the homogeneous components of $H^i_{I,J}(M)$ is investigated for some i's with a specified property.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.31-37
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• 2003

In this Paper, we investigate local stability, oscillation and bounde-ness character of positive solutions of the difference equation $X_{N+l}$ = $\alpha$ + ( $X_{N-1}$$^{P/)}$( $X_{N}$$^{P}$), n = 0, 1, … under specified conditions.s.tions.s.

• Journal of applied mathematics & informatics
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• v.11 no.1_2
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• pp.173-183
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• 2003

In this paper, we give a classification of nonoscillatory solution of a second-order neutral delay difference equation of the form △²(x/sub n/-c/sub n/x/sub n-r/)=f(n, x/sub g1(n)/, …, x/sub gm(n)/). Some existence results for each kind of nonoscillatory solutions we also established.

• Journal of the Korean Mathematical Society
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• v.58 no.5
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• pp.1261-1277
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• 2021

An inertial manifold is often constructed as a graph of a function from low Fourier modes to high ones and one used to consider backward bounded (in time) solutions for that purpose. We here show that the proof of the uniqueness of such solutions is crucial in the existence theory of inertial manifolds. Avoiding contraction principle, we mainly apply the Arzela-Ascoli theorem and Laplace transform to prove their existence and uniqueness respectively. A non-self adjoint example is included, which is related to a differential system arising after Kwak transform for Navier-Stokes equations.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.665-684
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• 2008

Runge-Kutta-Nystr$\"{o}$m (RKN) methods provide a popular way to solve the initial value problem (IVP) for a system of ordinary differential equations (ODEs). Users of software are typically asked to specify a tolerance ${\delta}$, that indicates in somewhat vague sense, the level of accuracy required. It is clearly important to understand the precise effect of changing ${\delta}$, and to derive the strongest possible results about the behaviour of the global error that will not have regular behaviour unless an appropriate stepsize selection formula and standard error control policy are used. Faced with this situation sufficient conditions on an algorithm that guarantee such behaviour for the global error to be asympotatically linear in ${\delta}$ as ${\delta}{\rightarrow}0$, that were first derived by Stetter. Here we extend the analysis to cover a certain class of ODEs with low-order derivative discontinuities, and the class of ODEs with constant delays. We show that standard error control techniques will be successful if discontinuities are handled correctly and delay terms are calculated with sufficient accurate interpolants. It is perhaps surprising that several delay ODE algorithms that have been proposed do not use sufficiently accurate interpolants to guarantee asymptotic proportionality. Our theoretical results are illustrated numerically.

• Tribology and Lubricants
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• v.36 no.3
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• pp.147-152
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• 2020

This paper is within the framework of an adhered complete contact problem wherein the contact between a half plane and sharp edged indenter, both of which are elastic in character, is constituted. The eigensolutions of the contact shear and normal stresses, σ_rq and σ_q, respectively, are evaluated via asymptotic analysis. The ratio of σ_rq/σ_qq is investigated and compared with the coefficient of friction, μ, of the contact surface to observe the propensity to slip on the contact surface. Interestingly, there exists a region of |σ_rθ/σ_θθ| ≥ |μ|. Thus, slipping can occur, although the problem is solved under the condition of an adhered contact without slipping. Given that a tribological failure potentially occurs at the slipping region, it is important to determine the size of the slipping region. This aspect is also factored in the paper. A simple example of the adhered contact between two elastically dissimilar squares is considered. Finite element analysis is used to evaluate generalized stress intensity factors. Furthermore, it is repeatedly observed that slipping occurs on the contact surface although the size of it is extremely small compared with that of the contacting squares. Therefore, as a contribution to the field of contact mechanics, this problem must be further explained logically.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.157-172
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• 2004

An age-dependent branching process where disasters occur as a renewal process leading to annihilation or survival of all the cells, is considered. For such a process, the total mean sojourn time of all the cells in the system is analysed using the regeneration point technique. The mean number of cells which die in time t and its asymptotic behaviour are discussed. When the disasters arrival as a Poisson process and the lifetime of the cells follows exponential distribution, elegant inter- relationships are found among the means of (i) the total number of cells which die in time t (ii) the total sojourn time of all cells in the system upto time t and (iii) the number of living cells at time t. Some of the existing results are deduced as special cases for related processes.

• Journal of applied mathematics & informatics
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• v.29 no.3_4
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• pp.721-741
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• 2011

In this paper we have considered a dynamical mathematical model of the sub-populations of potential smokers (non-smokers), smokers, smokers who temporarily quit smoking, smokers who permanently quit smoking and a class of smoking associated illness by introducing time dependent parameters and distributed time delay to acquire smoking habit. Here, we have established some sufficient conditions on the permanence and extinction of the smoking class in the community by using inequality analytical technique. We have introduced some new threshold values $R_0$ and $R^*$ and further obtained that the smoking class in the community will be permanent when $R_0$ > 1 and the smoking class in the community will be going to extinct when $R^*$ < 1. By Lyapunov functional method, we have also obtained some sufficient conditions for global asymptotic stability of this model. Computer simulations are carried out to explain the analytical findings. The aim of the analysis of this model is to identify the parameters of interest for further study, with a view to informing and assisting policy-maker in targeting prevention and treatment resources for maximum effectiveness.

• Bulletin of the Korean Mathematical Society
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• v.55 no.5
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• pp.1463-1481
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• 2018

Let $X=\{X_t\}_{t{\geq}0}$ be a $L{\acute{e}}vy$ process in ${\mathbb{R}}^d$ and ${\Omega}$ be an open subset of ${\mathbb{R}}^d$ with finite Lebesgue measure. The quantity $H_{\Omega}(t)={\int_{\Omega}}{\mathbb{P}}^x(X_t{\in}{\Omega})$ dx is called the heat content. In this article we consider its generalized version $H^{\mu}_g(t)={\int_{\mathbb{R}^d}}{\mathbb{E}^xg(X_t){\mu}(dx)$, where g is a bounded function and ${\mu}$ a finite Borel measure. We study its asymptotic behaviour at zero for various classes of $L{\acute{e}}vy$ processes.