• Journal of Integrative Natural Science
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• v.10 no.1
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• pp.33-39
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• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}(p-q{\geq}3)$, $q=rank(P_V)$ with a projection matrix $P_v$ under the quadratic loss, based on a sample $X_1$, $X_2$, ${\cdots}$, $X_n$. We find a James-Stein type decision rule which shrinks towards projection vector when the underlying distribution is that of a variance mixture of normals and when the norm ${\parallel}{\theta}-P_V{\theta}{\parallel}$ is restricted to a known interval, where $P_V$ is an idempotent and projection matrix and rank $(P_V)=q$. In this case, we characterize a minimal complete class within the class of James-Stein type decision rules. We also characterize the subclass of James-Stein type decision rules that dominate the sample mean.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.435-442
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• 2017

Consider the problem of estimating a $p{\times}1$ mean vector ${\theta}$ (p ${\geq}$ 3) under the quadratic loss from multi-variate normal population. We find a James-Stein type estimator which shrinks towards the projection vectors when the underlying distribution is that of a variance mixture of normals. In this case, the norm ${\parallel}{\theta}-K{\theta}{\parallel}$ is known where K is a projection vector with rank(K) = q. The class of this type estimator is quite general to include the class of the estimators proposed by Merchand and Giri (1993). We can derive the class and obtain the optimal type estimator. Also, this research can be applied to the simple and multiple regression model in the case of rank(K) ${\geq}2$.

• International Journal of Reliability and Applications
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• v.2 no.4
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• pp.263-268
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• 2001

Shanmugam(1991) generalized the Poisson distribution to capture a restriction on the incidence rate $\theta$ (i.e. $\theta$ ＜ $\beta$, an unknown upper limit), and named it incidence rate restricted Poisson (IRRP) distribution. Using Neyman's C($\alpha$) concept, Shanmugam then devised a hypothesis testing procedure for $\beta$ when $\theta$ remains unknown nuisance parameter. Shanmugam's C ($\alpha$) based .results involve inverse moments which are not easy tools, This article presents an alternate testing procedure based on likelihood ratio concept. It turns out that likelihood ratio test statistic offers more power than the C($\alpha$) test statistic. Numerical examples are included.

• Steel and Composite Structures
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• v.13 no.2
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• pp.187-206
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• 2012

In this study, fracture analysis of orthotropic FGM (Functionally Graded Material) plate having center crack is performed, numerically. Material axis arbitrarily oriented and there is an angle ${\theta}^{\circ}$ between material and crack axes. Stress intensity factors at the crack tips for Mode I are calculated using Displacement Correlation Method (DCM). In numerical analysis, effects of material properties and variation of angle ${\theta}^{\circ}$ between material and crack axes on the fracture behavior are investigated for four different boundary conditions. Consequently, it is found that the effect of ${\theta}^{\circ}$ on stress intensity factor depends on variation of material properties.

• Kyungpook Mathematical Journal
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• v.51 no.4
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• pp.385-393
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• 2011

The aim of this paper is to introduce and study the sequence spaces [w, ${\theta}$, F, p, q]$_{\infty}({\Delta}_{\upsilon}^m)$, [w, ${\theta}$, F, p, q]$_1({\Delta}_{\upsilon}^m)$ and [w, ${\theta}$, F, p, q]$_0({\Delta}_{\upsilon}^m)$, which arise from the notions of generalized difference sequence space, lacunary convergence, invariant mean and a sequence of Moduli $F=(f_k)$. We establish some inclusion relations between these spaces under some conditions.

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.1809-1810
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• 2007

본 논문에서는 뇌파인식을 위한 입력패턴을 추출하고 패턴 인식을 위한 뇌파 학습 알고리즘을 설계하였다. 입력패턴의 구성은 일반적인 상황에서 인식률을 더욱 높이기 위하여 기존의 Alpha-wave, Beta-wave, Theta-wave, Delta-wave등의 비율을 비교하는 방식에서 Delta-wave와 Theta-wave의 합, Alpha-wave, Delta-wave와 Theta-wave의 합에 Alpha-wave로 나눈 값, Beta-wave의 4가지 입력패턴으로 구성하였다. 그리고 신경망의 한 종류인 역전파 알고리즘을 이용하여 동일 조건이나 비슷한 조건에서의 수면과 비수면의 구분이 아닌 각기 다른 조건 상태에서의 수면과 비수면에 대한 패턴분류를 시뮬레이션 하였고 일반적인 조건에서도 감성 상태를 분류 할 수 있음을 보였다.

• Korean Journal of Hydrosciences
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• v.5
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• pp.85-97
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• 1994

A hybrid finite difference method for the longitudinal dispersion equation, which is based on combining the Holly-Preissmann scheme with fifth-degree Hermite interpolating polynomial and the generalized Crank-Nicholson scheme, is described and comparatively evaluated with other characteristics-based numerical methods. Longitudinal dispersion of an instantaneously-loaded pollutant source is simulated, and computational results are compared with the exact solution. The present method is free from wiggles regardless of the Courant number, and exactly reproduces the location of the peak concentration. Overall accuracy of the computation increases for smaller value of the weighting factor, $\theta$of the model. Larger values of $\theta$ overestimates the peak concentration. Smaller Courant number yields better accuracy, in general, but the sensitivity is very low, especially when the value of $\theta$ is small. From comparisons with the hybrid method using cubic interpolating polynomial and with splitoperator methods, the present method shows the best performance in reproducing the exact solution as the advection becomes more dominant.

• The Pure and Applied Mathematics
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• v.12 no.4 s.30
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• pp.253-274
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• 2005

An additive regular Semiring S is left inversive if the Set E+ (S) of all additive idempotents is left regular. The set LC(S) of all left inversive semiring congruences on an additive regular semiring S is a lattice. The relations $\theta$ and k (resp.), induced by tr. and ker (resp.), are congruences on LC(S) and each $\theta$-class p$\theta$ (resp. each k-class pk) is a complete modular sublattice with $p_{min}$ and $p_{max}$ (resp. With $p^{min}$ and $p^{max}$), as the least and greatest elements. $p_{min},\;p_{max},\;p^{min}$ and $p^{max}$, in particular ${\epsilon}_{max}$, the maximum additive idempotent separating congruence has been characterized explicitly. A semiring is quasi-inversive if and only if it is a subdirect product of a left inversive and a right inversive semiring.

• Journal of the Korean Magnetics Society
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• v.5 no.5
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• pp.720-725
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• 1995

Bi-substituted gadolinium iron garnet films were deposited on GGG(111) and NGG (111) substrates by irradiating KrF excimer laser onto targets having compositions of $Bi_{x}Gd_{3-x}Fe_{5}O_{12}$ ($2.0{\leq}x{\leq}3.0$) under substrate temperature of $580~620^{\circ}C$. Analysis on structure, composition and angle of Faraday rotation, ${\theta}_{F}$, were carried out. The composition, the structure and the magneto-optical properties of the obtained films were found to be strongly dependent both on the compositions of the targets and on the pressure of oxygen. Before annealing in air, all films showed ${\theta}_{F}{\geq}0$ at ${\lambda}=6328{\AA}$, while several films showed ${\theta}_{F}{\leq}0$ after the annealing. The highest value of Bi-substitution up to x = 1.76 with uniform composition was obtained.

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.669-688
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• 2021

The aim of this paper is to prove the existence of an admissible inertial manifold for mild solutions to infinite delay evolution equation of the form $$\{{\frac{du}{dt}}+Au=F(t,\;u_t),\;t{\geq}s,\\\;u_s({\theta})={\phi}({\theta}),\;{\forall}{\theta}{\in}(-{{\infty}},\;0],\;s{\in}{\mathbb{R}},$$ where A is positive definite and self-adjoint with a discrete spectrum, the Lipschitz coefficient of the nonlinear part F may depend on time and belongs to some admissible function space defined on the whole line. The proof is based on the Lyapunov-Perron equation in combination with admissibility and duality estimates.