• 한국군사과학기술학회지
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• 제12권5호
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• pp.577-584
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• 2009

Fusion of decisions in wireless sensor networks having flexibility on energy efficiency is studied in this paper. Two representative distributions, the generalized Gaussian and $\alpha$-stable probability density functions, are used to model non-Gaussian noise channels. By incorporating noise channels into the parallel fusion model, the optimal fusion rules are represented and suboptimal fusion rules are derived by using a large signal-to-noise ratio(SNR) approximation. For both distributions, the obtained suboptimal fusion rules are same and have equivalent form to the Chair-Varshney fusion rule(CVR). Thus, the CVR does not depend on the behavior of noise distributions that belong to the generalized Gaussian and $\alpha$-stable probability density functions. The simulation results show the suboptimality of the CVR at large SNRs.

• 대한수학회논문집
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• 제27권4호
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• pp.721-732
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• 2012

The principal aim of the paper is to investigate new integral expression $${\int}_0^{\infty}x^{s+1}e^{-{\sigma}x^2}L_m^{(\gamma,\delta)}\;({\zeta};{\sigma}x^2)\;L_n^{(\alpha,\beta)}\;({\xi};{\sigma}x^2)\;J_s\;(xy)\;dx$$, where $y$ is a positive real number; $\sigma$, $\zeta$ and $\xi$ are complex numbers with positive real parts; $s$, $\alpha$, $\beta$, $\gamma$ and $\delta$ are complex numbers whose real parts are greater than -1; $J_n(x)$ is Bessel function and $L_n^{(\alpha,\beta)}$ (${\gamma};x$) is generalized Laguerre polynomials. Some integral formulas have been obtained. The Maple implementation has also been examined.

• 대한수학회논문집
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• 제31권1호
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• pp.101-113
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• 2016

In this article, we considered the stability of the following (${\alpha}$, ${\beta}$, ${\gamma}$)-derivation $${\alpha}D[x,y]={\beta}[D(x),y]+{\gamma}[x,D(y)]$$ and homomorphisms associated to the quadratic type functional equation $$f(kx+y)+f(kx+{\sigma}(y))=2kg(x)+2g(y),\;x,y{\in}A$$, where ${\sigma}$ is an involution of the Lie $C^*$-algebra A and k is a fixed positive integer. The Hyers-Ulam stability on unbounded domains is also studied. Applications of the results for the asymptotic behavior of the generalized quadratic functional equation are provided.

• 대한수학회지
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• 제42권6호
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• pp.1121-1136
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• 2005

Nonstandard finite difference schemes are considered for a generalization of the Cahn-Hilliard equation with Neumann boundary conditions and the Kuramoto-Sivashinsky equation with periodic boundary conditions, which are of the type $$U_t\;+\;\frac{{\partial}^2}{{\partial}x^2} g(u,\;U_x,\;U_{xx})\;=\;\frac{{\partial}^{\alpha}}{{\partial}x^{\alpha}}f(u,\;u_x),\;{\alpha}\;=\;0,\;1,\;2$$. Stability and error estimate of approximate solutions for the corresponding schemes are obtained using the extended Lax-Richtmyer equivalence theorem. Three examples are provided to apply the nonstandard finite difference schemes.

• 대한수학회보
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• 제53권5호
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• pp.1585-1596
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• 2016

In this paper we investigate the existence of nontrivial solutions for the following fractional boundary value problem (FBVP) $$\{_tD_T^{\alpha}(_0D_t^{\alpha}u(t))={\nabla}W(t,u(t)),\;t{\in}[0,T],\\u(0)=u(T)=0,$$ where ${\alpha}{\in}(1/2,1)$, $u{\in}{\mathbb{R}}^n$, $W{\in}C^1([0,T]{\times}{\mathbb{R}}^n,{\mathbb{R}})$ and ${\nabla}W(t,u)$ is the gradient of W(t, u) at u. The novelty of this paper is that, when the nonlinearity W(t, u) involves a combination of superquadratic and subquadratic terms, under some suitable assumptions we show that (FBVP) possesses at least two nontrivial solutions. Recent results in the literature are generalized and significantly improved.

• International Journal of Reliability and Applications
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• 제2권4호
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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.

• Geomechanics and Engineering
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• 제19권4호
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• pp.295-305
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• 2019

The present paper is concerned with the investigation of disturbances in orthotropic thermoelastic medium by using fractional order heat conduction equation with three phase lags due to thermomechanical sources. Laplace and Fourier transform techniques are used to solve the problem. The expressions for displacement components, stress components and temperature change are derived in transformed domain and further in physical domain using numerical inversion techniques. The effect of fractional parameter based on its conductivity i.e., ($0<{\alpha}<1$ for weak, ${\alpha}=1$ for normal, $1<{\alpha}{\leq}2$ for strong conductivity) is depicted graphically on various components.

• 대한수학회보
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• 제60권6호
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• pp.1567-1605
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• 2023

Let d ∈ ℕ and α ∈ (0, min{2, d}). For any a ∈ [a^*, ∞), the fractional Schrödinger operator 𝓛_a is defined by 𝓛_a := (-Δ)^α/2 + a|x|^-α, where $a^*:={\frac{2^{\alpha}{\Gamma}((d+{\alpha})/4)^2}{{\Gamma}(d-{\alpha})/4)^2}}$. In this paper, we study two-weight Sobolev inequalities associated with 𝓛_a and two-weight norm estimates for several square functions associated with 𝓛_a.

• Bulletin of the Korean Chemical Society
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• 제7권4호
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• pp.257-262
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• 1986

Thixotropy is a time-dependent shear-thinning phenomenon. We derived a new thixotropic formula which is based on the generalized viscosity formula of Ree and Eyring, $f={\Sigma}\frac{X_i}{{\alpha}_i}sinh^{-1}$ () (Refer to the text concerning the notation.) The following is postulated: (1) thixotropy occurs when small flow units attached to a large flow unit separate from the latter under stress (2) elastic energy(${\omega}$) is stored on the large flow unit during the flow process, and (3) the stored energy contributes to decrease the activation energy for flow. A new thixotropic formula was derived by using these postulations, $f={\frac}{X_0{\beta}_0}{\alpha_0}{\dot{s}}+{\frac}{X_1{\beta}_1}{{\alpha}_1}{\dot{s}}+{\frac}{X_2}{{\alpha_x}}sinh^{-1}$[$({\beta}_0)_2$ exp $(-C_2{\dot{s}}^2/RT){\cdot}{\dot{s}}$] f is the shear stress, and s is the rate of shear. In case of concentrated solutions where the Newtonian flow units have little contribution to the viscosity of the system, the above equation becomes, $f=\frac{X_2}{\alpha_2}sinh^{-1}$[$({\beta}_0)_2$ exp $(-C_2{\dot{s}}^2/RT){\cdot}{\dot{s}}$]. In order to confirm these formulas, we applied to TiO2(anatase and rutile)-water, printing ink and mayonnaise systems. Good agreements between the experiment and theory were observed.

• 한국자동차공학회논문집
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• 제4권4호
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• pp.190-200
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• 1996

Step-by-step time integration methods are widely used for solving structural dynamics problem. One difficult yet critical choice an analyst must make is to decide an appropriate time step size. The choice of time step size has a significant effect on solution accuracy and computational expense. The objective of this research is to derive error estimate for newly developed time integration method and develop automatic time step size control algorithm for structural dynamics. A formula for computing error tolerance is derived based on desired period resolution. An automatic time step size control strategy is proposed based on a normalized local error estimate for the generalized-α method. Numerical examples demonstrate the developed strategy satisfies general design criteria for time step size control algorithm for dynamic problem.