• 대한기계학회논문집A
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• 제27권11호
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• pp.1809-1814
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• 2003

Differential evolution (DE) algorithm is presented and applied to global optimization in this research. DE suggested initially fur the solution to Chebychev polynomial fitting problem is similar to genetic algorithm(GA) including crossover, mutation and selection process. However, differential evolution algorithm is simpler than GA because it uses a vector concept in populating process. And DE turns out to be converged faster than CA, since it employs the difference information as pseudo-sensitivity In this paper, a trial vector and its control parameters of DE are examined and unconstrained optimization problems of highly nonlinear multimodal functions are demonstrated. To illustrate the efficiency of DE, convergence rates and robustness of global optimization algorithms are compared with those of simple GA.

• 대한수학회지
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• 제41권6호
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• pp.1049-1070
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• 2004

We classify all partial differential equations with polynomial coefficients in $\chi$ and y of the form A($\chi$) $u_{{\chi}{\chi}}$ ＋ 2B($\chi$, y) $u_{{\chi}y}$ ＋ C(y) $u_{yy}$ ＋ D($\chi$) $u_{{\chi}}$ ＋ E(y) $u_{y}$ = λu, which has weak orthogonal polynomials as solutions and show that partial derivatives of all orders are orthogonal. Also, we construct orthogonal polynomials in d-variables satisfying second order partial differential equations in d-variables.s.

• Journal of Mechanical Science and Technology
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• 제20권2호
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• pp.191-196
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• 2006

This paper presents the application of techniques of differential transformation method (DTM) to analyze the transverse vibration of a uniform Euler-Bernoulli beam under varying axial force. The governing differential equation of the transverse vibration of a uniform Euler-Bernoulli beam under varying axial force is derived and verified. The varying axial force was extended to the more general case which was high polynomial consisted of many terms. The concepts of DTM were briefly introduced. Numerical calculations are carried out and compared with previous published results. The accuracy and the convergence in solving the problem by DTM are discussed.

• Structural Engineering and Mechanics
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• 제17권1호
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• pp.1-14
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• 2004

Numerical solution to linear bending analysis of circular plates is obtained by the method of harmonic differential quadrature (HDQ). In the method of differential quadrature (DQ), partial space derivatives of a function appearing in a differential equation are approximated by means of a polynomial expressed as the weighted linear sum of the function values at a preselected grid of discrete points. The method of HDQ that was used in the paper proposes a very simple algebraic formula to determine the weighting coefficients required by differential quadrature approximation without restricting the choice of mesh grids. Applying this concept to the governing differential equation of circular plate gives a set of linear simultaneous equations. Bending moments, stresses values in radial and tangential directions and vertical deflections are found for two different types of load. In the present study, the axisymmetric bending behavior is considered. Both the clamped and the simply supported edges are considered as boundary conditions. The obtained results are compared with existing solutions available from analytical and other numerical results such as finite elements and finite differences methods. A comparison between the HDQ results and the finite difference solutions for one example plate problem is also made. The method presented gives accurate results and is computationally efficient.

• 대한수학회보
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• 제49권1호
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• pp.197-204
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• 2012

In this paper, we study the problem of normal families and deduce some results, which improve and generalize several related theorems obtained by Pang [7], Fang and Xu [3], L$\ddot{u}$, Xu, and Yi [6]. Mean-while, some examples are given to show the sharpness of our results.

• 전기학회논문지
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• 제64권9호
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• pp.1337-1346
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• 2015

In this paper, pattern classifier is designed to classify precipitation and non-precipitation events from weather radar data. The proposed classifier is based on Fuzzy Neural Network(FNN) and consists of three FNNs which operate in parallel. In the proposed network, the connection weights of the consequent part of fuzzy rules are expressed as two polynomial types such as constant or linear polynomial function, and their coefficients are learned by using Least Square Estimation(LSE). In addition, parametric as well as structural factors of the proposed classifier are optimized through Differential Evolution(DE) algorithm. After event classification between precipitation and non-precipitation echo, non-precipitation event is to get rid of all echo, while precipitation event including non-precipitation echo is to get rid of non-precipitation echo by classifier that is also based on Fuzzy Neural Network. Weather radar data obtained from meteorological office is to analysis and discuss performance of the proposed event and echo patter classifier, result of echo pattern classifier compare to QC(Quality Control) data obtained from meteorological office.

• 전기학회논문지
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• 제61권5호
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• pp.744-752
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• 2012

In this study, the Polynomial-based Radial Basis Function Neural Networks is proposed as an one of the recognition part of overall face recognition system that consists of two parts such as the preprocessing part and recognition part. The design methodology and procedure of the proposed pRBFNNs are presented to obtain the solution to high-dimensional pattern recognition problems. In data preprocessing part, Principal Component Analysis(PCA) which is generally used in face recognition, which is useful to express some classes using reduction, since it is effective to maintain the rate of recognition and to reduce the amount of data at the same time. However, because of there of the whole face image, it can not guarantee the detection rate about the change of viewpoint and whole image. Thus, to compensate for the defects, Linear Discriminant Analysis(LDA) is used to enhance the separation of different classes. In this paper, we combine the PCA&LDA algorithm and design the optimized pRBFNNs for recognition module. The proposed pRBFNNs architecture consists of three functional modules such as the condition part, the conclusion part, and the inference part as fuzzy rules formed in 'If-then' format. In the condition part of fuzzy rules, input space is partitioned with Fuzzy C-Means clustering. In the conclusion part of rules, the connection weight of pRBFNNs is represented as two kinds of polynomials such as constant, and linear. The coefficients of connection weight identified with back-propagation using gradient descent method. The output of the pRBFNNs model is obtained by fuzzy inference method in the inference part of fuzzy rules. The essential design parameters (including learning rate, momentum coefficient and fuzzification coefficient) of the networks are optimized by means of Differential Evolution. The proposed pRBFNNs are applied to face image(ex Yale, AT&T) datasets and then demonstrated from the viewpoint of the output performance and recognition rate.

• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.473-485
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• 2010

We consider the differential equation $$(x^2\;-\;1)u_{xx}\;+\;2xyu_{xy}\;+\;(y^2\;-\;1)u_{yy}\;+\;gxu_x\;+\;gyu_y\;=\;\lambda_nu,\;(*)$$ where $\lambda_n\;=\;n(n\;+\;9\;-\;1)$. We show that the differential equation (*) has a polynomial set as solutions if $g\;{\neq}\;-1$, -3, -5, $\cdots$. Also, we construct an orthogonalizing distributional weight for g < 1 and $g\;{\neq}\;1$, 0, -1, $\cdots$ by regularizing a one-dimensional integral with a singularity on the endpoint of the interval.

• 대한수학회보
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• 제51권5호
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• pp.1281-1289
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• 2014

In this paper, we consider the differential equation $$F^{\prime}-Q_1=Re^{\alpha}(F-Q_2)$$, where $Q_1$ and $Q_2$ are polynomials with $Q_1Q_2{\neq}0$, R is a rational function and ${\alpha}$ is an entire function. We consider solutions of the form $F=f^n$, where f is an entire function and $n{\geq}2$ is an integer, and we prove that if f is a transcendental entire function, then $\frac{Q_1}{Q_2}$ is a polynomial and $f^{\prime}=\frac{Q_1}{nQ_2}f$. This theorem improves some known results and answers an open question raised in [16].

• Journal of applied mathematics & informatics
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• 제24권1_2호
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• pp.231-243
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• 2007

The existence of solutions of a class of two-point boundary value problems for higher order differential equations is studied. Sufficient conditions for the existence of at least one solution are established. It is of interest that the nonlinearity f in the equation depends on all lower derivatives, and the growth conditions imposed on f are allowed to be super-linear (the degrees of phases variables are allowed to be greater than 1 if it is a polynomial). The results are different from known ones since we don't apply the Green's functions of the corresponding problem and the method to obtain a priori bound of solutions are different enough from known ones. Examples that can not be solved by known results are given to illustrate our theorems.