• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.973-1008
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• 1997

We reconsider the problem of calssifying all classical orthogonal polynomial sequences which are solutions to a second-order differential equation of the form $$ \ell_2(x)y"(x) + \ell_1(x)y'(x) = \lambda_n y(x). $$ We first obtain new (algebraic) necessary and sufficient conditions on the coefficients $\ell_1(x)$ and $\ell_2(x)$ for the above differential equation to have orthogonal polynomial solutions. Using this result, we then obtain a complete classification of all classical orthogonal polynomials : up to a real linear change of variable, there are the six distinct orthogonal polynomial sets of Jacobi, Bessel, Laguerre, Hermite, twisted Hermite, and twisted Jacobi.cobi.

• Journal of applied mathematics & informatics
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• v.38 no.1_2
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• pp.113-132
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• 2020

In this paper, a class of linear second order singularly perturbed delay differential turning point problems containing a small delay (or negative shift) on the reaction term and when the solution of the problem exhibits twin boundary layers are examined. A hybrid finite difference scheme on an appropriate piecewise-uniform Shishkin mesh is constructed to discretize the problem. We proved that the method is almost second order ε-uniformly convergent in the maximum norm. Numerical experiments are considered to illustrate the theoretical results.

• Bulletin of the Korean Mathematical Society
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• v.55 no.4
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• pp.1065-1092
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• 2018

This manuscript is involved with a category of second-order impulsive functional integro-differential equations with nonlocal conditions in Banach spaces. Sufficient conditions for existence and approximate controllability of mild solutions are acquired by making use of the theory of cosine family, Banach contraction principle and Leray-Schauder nonlinear alternative fixed point theorem. An illustration is additionally furnished to prove the attained principles.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.997-1030
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• 2015

This paper is concerned with integral type boundary value problems of second order singular differential equations with quasi-Laplacian on whole lines. Sufficient conditions to guarantee the existence and non-existence of positive solutions are established. The emphasis is put on the non-linear term $[{\Phi}({\rho}(t)x^{\prime}(t))]^{\prime}$ involved with the nonnegative singular function and the singular nonlinearity term f in differential equations. Two examples are given to illustrate the main results.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.183-193
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• 2000

In this paper we use measure theory to solve a wide range of second-order boundary value ordinary differential equations. First, we transform the problem to a first order system of ordinary differential equations(ODE's)and then define an optimization problem related to it. The new problem in modified into one consisting of the minimization of a linear functional over a set of Radon measures; the optimal measure is then approximated by a finite combination of atomic measures and the problem converted approximatly to a finite-dimensional linear programming problem. The solution to this problem is used to construct the approximate solution of the original problem. Finally we get the error functional E(we define in this paper) for the approximate solution of the ODE's problem.

• KIEE International Transactions on Power Engineering
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• v.2A no.4
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• pp.153-159
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• 2002

Power transformer protective relay should block the tripping during magnetizing inrush and rapidly operate the tripping during internal faults. Recently, the frequency environment of power system has been made more complicated and the quantity of 2nd frequency component in inrush state has been decreased because of the improvement of core steel. And then, traditional approaches will likely be maloperate in the case of magnetizing inrush with low second harmonic component and internal faults with high second harmonic component. This paper proposes a new relaying algorithm to enhance the fault detection sensitivities of conventional techniques by using a fuzzy logic approach. The proposed fuzzy based relaying algorithm consists of flux-differential current derivative curve, harmonic restraint, and percentage differential characteristic curve. The proposed relaying was tested with relaying signals obtained from EMTP simulation package and showed a fast and accurate trip operation.

• The Transactions of the Korean Institute of Electrical Engineers A
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• v.53 no.7
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• pp.382-388
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• 2004

The most widely used primary protection for the internal fault detection of power transformers is current percentage differential relaying(PDR). However, the harmonic components could be decreased by magnetizing inrush when there have been changes to the material of iron core or its design methodology. The higher the capacitance of high voltage status and underground distribution, the more differential current includes the second harmonic component during occurrence of an internal fault. Therefore, the conventional harmonic restraint methods need modification. This paper proposes an advanced protective relaying algorithm by fluxt-differential current slope characteristic and trend of voltage and differential current. To evaluate the performance of proposed algorithm, we have made comparative studies of PDR fuzzy relaying, and DWT relaying. The paper is constructed power system model including power transformer, utilizing the WatATP99, and data collection is made through simulation of various internal faults and inrush. As the results of test. the new proposed algorithm was proven to be faster and more reliable.

• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.463-474
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• 2001

We find Rodrigues type formula for multi-variate orthogonal polynomial solutions of second order partial differential equations.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.145-164
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• 2011

In the paper, we study with weighted sharing method the uniqueness of entire functions concerning nonlinear differential polynomials sharing one value and prove two uniqueness theorems, first one of which generalizes some recent results in [10] and [16]. Our second theorem will supplement a result in [17].

• East Asian mathematical journal
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• v.40 no.1
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• pp.37-50
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• 2024

We establish the existence, multiplicity and uniqueness of positive solutions to nonlocal boundary value systems with strongly coupled integral boundary condition by using the global continuation theorem and Banach's contraction principle.