• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.24 no.3
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• pp.293-303
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• 2020

The present work aims to analyzed the transient thermoelastic stress analysis of a thin circular plate with uniform internal heat generation. Initially, the plate is characterized by a parabolic temperature distribution along the z-direction given by T = T₀(r, z) and perfectly insulated at the ends z = 0 and z = h. For times t > 0, the surface r = a is subjected to convection heat transfer with convection coefficient h_c and fluid temperature T_∞. The integral transform method used to obtain the analytical solution for temperature, displacement, and thermal stresses. The associated thermoelastic field is analyzed by making use of the temperature and thermoelastic displacement potential function. Numerical results are carried out with the help of computational software PTC Mathcad Prime-3.1 and shown in figures.

• Communications of the Korean Mathematical Society
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• v.30 no.4
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• pp.505-513
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• 2015

The present paper deals with the determination of displacement and thermal stresses in a semi-infinite circular cylinder defined as $0{\leq}r{\leq}b$, $0{\leq}z<{\infty}$, due to internal heat generation within it. A circular cylinder is considered having arbitrary initial temperature and subjected to time dependent heat flux at the fixed circular boundary (r = b) whereas the zero temperature at the lower surface (z = 0) of the semi-infinite circular cylinder. The governing heat conduction equation has been solved by using integral transform method. The results are obtained in series form in terms of Bessel functions. The results for displacement and stresses have been computed numerically and illustrated graphically.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.1
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• pp.67-75
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• 2022

Analysis of non-integer order thermoelastic temperature distribution and it's thermal deflection of thin hollow circular disk under the axi-symmetric heat supply is investigated. Initially, the disk is kept at zero temperature. For t > 0 the parametric surfaces are thermally insulated and axi-symmetric heat supply on the thickness of the disk. The governing heat conduction equation has been solved by integral transform technique, including Mittag-Leffler function. The results have been computed numerically and illustrated graphically with the help of PTC-Mathcad.

• Structural Engineering and Mechanics
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• v.80 no.6
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• pp.669-675
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• 2021

A GN model with and without energy dissipations is used to discuss the waves propagation in a two-dimension orthotropic half space by the eigenvalues approach. Using the Laplace-Fourier integral transforms to get the solutions of the problem analytically, the basic formulations of the two-dimension problem are given by matrices-vectors differential forms, which are then solved by the eigenvalues scheme. Numerical techniques are used for the inversion processes of the Laplace-Fourier transform. The results for physical quantities are represented graphically. The numerical outcomes show that the characteristic time of pulse heat flux have great impacts on the studied fields values.

• Honam Mathematical Journal
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• v.46 no.2
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• pp.313-334
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• 2024

In the current study, our aim is to define new generalized extended beta and hypergeometric types of functions. Next, we methodically determine several integral representations, Mellin transforms, summation formulas, and recurrence relations. Moreover, we provide log-convexity, Turán type inequality for the generalized extended beta function and differentiation formulas, transformation formulas, differential and difference relations for the generalized extended hypergeometric type functions. Also, we additionally suggest a generating function. Further, we provide the generalized extended beta distribution by making use of the generalized extended beta function as an application to statistics and obtaining variance, coefficient of variation, moment generating function, characteristic function, cumulative distribution function, and cumulative distribution function's complement.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.16 no.5 s.96
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• pp.465-471
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• 2005

A method of calculation fur propagating and focusing of focused beams generated in antenna arrays, using BPM(Beam Propagation Method), is presented in this paper. Based on the diffraction theory, the beam focusing and Propagation is studied specially for the case of the antenna way fed by the Rotman lens that is able to focus microwave power on its focal arc or generate multiple beams. There are difficulties in performing a full-wave simulation using a commercial EM simulation tool for propagating and focusing of beams because of the structural complexity and the feeding assignment of the antenna array. Therefore, as an alternative solution, the BPM is presented to calculate the beam propagation from the aperture-type antennas. From the point of view of optics, the propagations of the lens have been simplified from the Fresnel diffraction integral to the Fourier transform. Using Fourier Transform, a beam propagation method is developed to show improvement of the resolution by controlling the wavefront of wave Propagating from an aperture-type antenna array. The beam width(or spot size) and the intensity are calculated for a focused beam propagating from an array having $10\lambda$ of its size. For the beams with $20\lambda,\;30\lambda$, and $50\lambda$ of geometrical focal length, the half-power beam widths(or spot size) are about 1.1\lambda,\;1.3\lambda,\;and\;1.9\lambda$ respectively.

• International Journal of Computer Science & Network Security
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• v.22 no.8
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• pp.269-274
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• 2022

Economy of Ukraine is characterized by the rapidly increased level of financial failures at a corporate level. Conditions of doing business in Ukraine become tighter year after year and it should motivate the business owners not only to watch more accurately the state in which their business is but also to introduce new, more precise, more tight systems of crisis management and economic security. The experience shows that in order to stay afloat and not to suffer losses companies should pay more attention to different areas of economic security, such as production potential, financial indicators, logistics, staff, etc. For this purpose companies should use a system of valuation of the most important for their activity indicators and transform their values in an integral one in order to use this assessment in making managerial decisions. Such a valuation is one of the components which the article presents. The article also reveals the key points which characterize crisis management as an integral part of enterprise development and economic security. There are specified the essence and problems of crisis management and proposed the ways of raising the level of economic security of a company based on the example of an industrial and commercial enterprise. The key focus of the enterprise's economic security management is defined as constructive responses to threats from the external environment and, as a result, ensuring stable functioning and effective realization of untapped potential in the future. The current assumption is to explain the scheme of strategic management of an industrial and commercial enterprise and to calculate the methodology of an express assessment of the level of enterprise economic security, taking into account the components of crisis management. To assess the level of economic security of the enterprise, it is proposed to use the method of point assessment, which is based on a multi-level system of indicators, which covers the main areas of the enterprise's activity.

• Computers and Concrete
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• v.25 no.6
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• pp.551-563
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• 2020

This paper investigates the artificial neural network (ANN) to predict the dimensionless parameters for the maximum contact pressures and contact areas of a contact problem. Firstly, the problem is formulated and solved theoretically by using Theory of Elasticity and Integral Transform Technique. Secondly, the contact problem has been extended based on the ANN. The multilayer perceptron (MLP) with three-layer was used to calculate the contact distances. External load, distance between the two quarter planes, layer heights and material properties were created by giving examples of different values were used at the training and test stages of ANN. Program code was rewritten in C++. Different types of network structures were used in the training process. The accuracy of the trained neural networks for the case was tested using 173 new data which were generated via theoretical solutions so as to determine the best network model. As a result, minimum deviation value (difference between theoretical and C++ ANN results) of was obtained for the network model. Theoretical results were compared with artificial neural network results and well agreements between them were achieved.

• Proceedings of the KIPE Conference
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• 2001.10a
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• pp.174-178
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• 2001

An improved stationary frame-based digital current control technique for a permanent magnet (PM) synchronous motor is presented. Generally, the stationary frame current controller is known to provide the advantage of a simple implementation. However, there are some unavoidable limitations such as a steady-state error and a phase delay in the steady-state. On the other hand, in the synchronous frame current regulator, the regulated currents are dc quantities and a zero steady-state error can be obtained through the integral control. However, the need to transform the signals between the stationary and synchronous frames makes the implementation of a synchronous frame regulator complex. Although the PI controller in the stationary frame gives a steady-state error and a phase delay, the control performance can be greatly improved by employing the exact decoupling control inputs for the back EMF, resulting in an ideal steady-state control characteristics irrespective of an operating condition as in the synchronous PI decoupling controller. However, its steady-state response may be degraded due to the inexact cancellation inputs under the parameter variations. To improve the control performance in the stationary frame, the disturbance is estimated using the time delay control. The proposed scheme is implemented on a PM synchronous motor using DSP TMS320C31 and the effectiveness is verified through the comparative simulations and experiments.

• The Pure and Applied Mathematics
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• v.5 no.2
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• pp.123-132
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• 1998

Let F and G denote the distribution functions of the failure times and the censoring variables in a random censorship model. Susarla and Van Ryzin(1978) verified consistency of $F_{\alpha}$, he NPBE of F with respect to the Dirichlet process prior D($\alpha$), in which they assumed F and G are continuous. Assuming that A, the cumulative hazard function, is distributed according to a beta process with parameters c, $\alpha$, Hjort(1990) obtained the Bayes estimator $A_{c,\alpha}$ of A under a squared error loss function. By the theory of product-integral developed by Gill and Johansen(1990), the Bayes estimator $F_{c,\alpha}$ is recovered from $A_{c,\alpha}$. Continuity assumption on F and G is removed in our proof of the consistency of $A_{c,\alpha}$ and $F_{c,\alpha}$. Our result extends Susarla and Van Ryzin(1978) since a particular transform of a beta process is a Dirichlet process and the class of beta processes forms a much larger class than the class of Dirichlet processes.