• Steel and Composite Structures
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• v.18 no.4
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• pp.909-924
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• 2015

This paper investigates the vibration phenomenon of a nanobeam subjected to a time-dependent heat flux. Material properties of the nanobeam are assumed to be graded in the thickness direction according to a novel exponential distribution law in terms of the volume fractions of the metal and ceramic constituents. The upper surface of the functionally graded (FG) nanobeam is pure ceramic whereas the lower surface is pure metal. A nonlocal generalized thermoelasticity theory with dual-phase-lag (DPL) model is used to solve this problem. The theories of coupled thermoelasticity, generalized thermoelasticity with one relaxation time, and without energy dissipation can extracted as limited and special cases of the present model. An analytical technique based on Laplace transform is used to calculate the variation of deflection and temperature. The inverse of Laplace transforms are computed numerically using Fourier expansion techniques. The effects of the phase-lags (PLs), nonlocal parameter and the angular frequency of oscillation of the heat flux on the lateral vibration, the temperature, and the axial displacement of the nanobeam are studied.

• Smart Structures and Systems
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• v.18 no.4
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• pp.707-731
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• 2016

A unified mathematical model of the equations of generalized magneto-thermoelasticty based on fractional derivative heat transfer for isotropic perfect conducting media is given. Some essential theorems on the linear coupled and generalized theories of thermoelasticity e.g., the Lord- Shulman (LS) theory, Green-Lindsay (GL) theory and the coupled theory (CTE) as well as dual-phase-lag (DPL) heat conduction law are established. Laplace transform techniques are used. The method of the matrix exponential which constitutes the basis of the state-space approach of modern theory is applied to the non-dimensional equations. The resulting formulation is applied to a variety of one-dimensional problems. The solutions to a thermal shock problem and to a problem of a layer media are obtained in the present of a transverse uniform magnetic field. According to the numerical results and its graphs, conclusion about the new model has been constructed. The effects of the fractional derivative parameter on thermoelastic fields for different theories are discussed.

• Proceedings of the Korean Society of Broadcast Engineers Conference
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• 2009.01a
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• pp.246-249
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• 2009

Due to the additive white Gaussian noise (AWGN), images are often corrupted. In recent days, Bayesian estimation techniques to recover noisy images in the wavelet domain have been studied. The probability density function (PDF) of an image in wavelet domain can be described using highly-sharp head and long-tailed shapes. If a priori probability density function having the above properties would be applied well adaptively, better results could be obtained. There were some frequently proposed PDFs such as Gaussian, Laplace distributions, and so on. These functions model the wavelet coefficients satisfactorily and have its own of characteristics. In this paper, mixture distributions of Gaussian and Laplace distribution are proposed, which attempt to corporate these distributions' merits. Such mixture model will be used to remove the noise in images by adopting Maximum a Posteriori (MAP) estimation method. With respect to visual quality, numerical performance and computational complexity, the proposed technique gained better results.

• Journal of the Korean Statistical Society
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• v.30 no.4
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• pp.661-666
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• 2001

In this paper we consider an M/G/1 queue where the server of the system has a vacation time and the service policy is limited-1. In this system, upon termination of a vacation the server returns to the queue and serves at most one message in the queue before taking another vacation. We consider two models. In the first, if the sever finds the queue empty at the end of a cacation, then the sever immediately takes another vacation. In the second model, if no message have arrived during a vacation, the sever waits for the first arrival to serve. The analysis of this system is particularly useful for a priority class polling system. We derive Laplace-Stieltjes transforms of the waiting time for both models, and compare their mean waiting times.

• International Journal of Reliability and Applications
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• v.15 no.1
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• pp.1-9
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• 2014

Let X and $X_t$ denote the lifetime and the residual life at age t, respectively. X is said to be a NBUL (new better than used in Laplace transform order) random variable if $X_t$ is smaller than X in Laplace order, i.e., $X_t{\leq}_{LT}X$. We propose a new test statistics for testing exponentiality versus NBUL class of life distribution. The tests by Hollender and Proschan (1975) and the generalized Hollender and Proschan test by Ains and Mitra (2011) are considered as special cases of the our of test statistics. Our proposed test statistics is simple, consistent and asymptotically normal. Efficiency and powers of the test statistics for some commonly used distributions in reliability are discussed. Finally, real examples are presented to illustrate the theoretical results.

• Journal of the Korean Institute of Telematics and Electronics
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• v.3 no.4
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• pp.16-24
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• 1966

The LASER Amplifier is treated in the manner of a Fabry-Perot Resonator with an active media, five layers are considered: air, reflector, active medium(ruby), reflector and air. One dimensional scalar wave equations are derived using the method of boundary value probrems in which it is assumed that incident coherent radiation falls normally on the surface wall. All equations are treated from the transient analysis point of view using the Laplace transform nethods, and are arranged steady state region as an amplifier and transient region as a self excited oscillator. Also some remarks are given on the design problem of LASER amplifier in connection with the transient terms involved.

• Geomechanics and Engineering
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• v.4 no.1
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• pp.67-78
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• 2012

Soil foundations exhibit significant creeping deformation, which may result in excessive settlement and failure of superstructures. Based on the theory of viscoelasticity and fractional calculus, a fractional Kelvin-Voigt model is proposed to account for the time-dependent behavior of soil foundation under vertical line load. Analytical solution of settlements in the foundation was derived using Laplace transforms. The influence of the model parameters on the time-dependent settlement is studied through a parametric study. Results indicate that the settlement-time relationship can be accurately captured by varying values of the fractional order of differential operator and the coefficient of viscosity. In comparison with the classical Kelvin-Voigt model, the fractional model can provide a more accurate prediction of long-term settlements of soil foundation. The determination of influential distance also affects the calculation of settlements.

• International Journal of Ocean System Engineering
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• v.1 no.1
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• pp.28-31
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• 2011

An attempt was made to compute the free surface deformation due to the impact of a water droplet. The Cauchy Poisson, i.e. the initial value problem, was solved with the kinematic and dynamic free surface boundary conditions linearized. The zero order Hankel transformation and Laplace transform were applied to the related equations. The initial condition for the free surface profile was derived from a captured video image. The effect of the surface tension was not significant with the water mass used in this investigation. The computed and observed free surface deformations were compared.

• Steel and Composite Structures
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• v.34 no.2
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• pp.309-319
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• 2020

The objective is to study the deformation in a homogeneous isotropic modified couple stress thermoelastic medium with mass diffusion and with two temperatures due to a thermal source and mechanical force. Laplace and Fourier transform techniques are applied to obtain the solutions of the governing equations. The displacements, stress components, conductive temperature, mass concentration and couple stress are obtained in the transformed domain. Numerical inversion technique has been used to obtain the solutions in the physical domain. Isothermal boundary and insulated boundaryconditions are used to investigate the problem. Some special cases of interest are also deduced.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.10a
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• pp.239-242
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• 2004

In this paper, the general mathematical model of LRE(Liquid Rocket Engine) is presented. For the analysis about the trend of dynamics and the stability of open type LRE, it is transformed to linear model by Laplace transform and synthesized to the linear complex model of LRE with Matlab/Simulink.