• Korean Journal of Mathematics
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• 제29권3호
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• pp.483-492
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• 2021

This article concerns the property that for any element a in a ring, if a²ⁿ = aⁿ for some n ≥ 2 then a² = a. The class of rings with this property is large, but there also exist many kinds of rings without that, for example, rings of characteristic ≠2 and finite fields of characteristic ≥ 3. Rings with such a property is called reduced-over-idempotent. The study of reduced-over-idempotent rings is based on the fact that the characteristic is 2 and every nonzero non-identity element generates an infinite multiplicative semigroup without identity. It is proved that the reduced-over-idempotent property pass to polynomial rings, and we provide power series rings with a partial affirmative argument. It is also proved that every finitely generated subring of a locally finite reduced-over-idempotent ring is isomorphic to a finite direct product of copies of the prime field {0, 1}. A method to construct reduced-over-idempotent fields is also provided.

• 대한설비공학회지:설비저널
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• 제14권2호
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• pp.138-149
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• 1985

The heat diffusion equation for an annular fin is analyzed using Laplace transformations. The fin has a uniform thickness with its edge heat loss and two temperature profiles at the base such as a step change in temperature or heat flux. To obtain the exact solutions for temperature distribution, this paper can detect the eigenvalues which satisfy the roots of transcendental equations in above two cases during inverse Laplace transformations. The exact solutions for temperature and heat flux are obtained with the infinite Series by dimensionless factors. The solutions are developed for small and large values of times. These series solutions converge rapidly for large values of time, but slowly for small.

• 대한수학교육학회지:학교수학
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• 제16권2호
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• pp.317-334
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• 2014

이 연구는 예비교사들을 대상으로 테일러급수와 그 수렴에 대한 이해 실태를 살펴보았고 그 결과로 얻어진 취약점을 보완하고자 GeoGebra를 이용하여 실험적 맥락에서 테일러급수의 수렴 개념에 대한 교수 방안을 모색하였다. 예비교사들은 형식적 측면에서 테일러급수를 구하고 수렴 반경을 계산하는 것에는 익숙했지만 개념적이고 과정적 요소엔 취약하였으며 테일러급수를 다루는 시각적이고 역동적 경험을 갖고 있지 못했다. 특히 부분합의 개념으로 테일러다항식들의 수렴과 원함수간의 관계가 잘 정립되어 있지 않았다. 이에 GeoGebra를 도구로 활용하여 시각적이고 직관적 측면에서 테일러다항식의 차수와 중심이 테일러급수의 수렴에 미치는 영향을 중심으로 교수실험을 하였다. 이 연구의 결과는 예비중등 수학교사들이 무한급수와 테일러급수에 대한 교수 내용적 지식을 높이고 유연한 지식을 가지는 데 공학을 활용한 교수법이 도움이 될 수 있음을 보여주었다.

• 전력전자학회:학술대회논문집
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• 전력전자학회 2001년도 추계학술대회 논문집
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• pp.97-101
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• 2001

Recently, as the development of industry, the nonlinear load becomes increased. Because of nonlinear load, the variation of source voltage is generated by the impedace of source side flowed harmonic currents. For blocking harmonic currents by nonlinear load, a series active power filter operates blocking resistance of harmonic currents. The value of blocking resistance shows ideal compensating characteristic out of theoretically infinite value. But the blocking resistance is limited by the problem of the system stability and the capacity of inverter. In this paper, the value of optimum blocking resistance is found by a simulation in the applied system. In the case of unbalanced source voltages, each relation of the blocking resistance is shown. It is proved that blocking resistance of series active power filter relates to a passive filter.

• Journal of Electrical Engineering and Technology
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• 제10권5호
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• pp.2062-2069
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• 2015

In the series hybrid active power filter (SHAPF) with magnetic flux compensation (MFC), the system current oscillate in the experimental results when adding the same phase harmonic current command in current control block. This condition endangers the security of the SHAPF. Taking the digit period average arithmetic as example, this paper explains the inter-harmonics current oscillation in the experiment. The conclusion is that the SHAPF is unstable to the inter-harmonics current in theory. Limited by the capacity of the inverter, the system current and the inverter output current do not increase to infinite. At last, some methods are proposed to solve this problem. From the practical viewpoint, the voltage feed-forward control is easy to achieve. It can suppress the current oscillation problems, and also improve the filtering effect. The feasibility of the methods is validated by both the emulation and experiment results.

• 한국생산제조학회지
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• 제7권1호
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• pp.41-50
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• 1998

The detemination of sound pressure radiated from peoriodic plate structures is fundamental in the estimation of noise levels in aircraft fuselages and ship hull structures. As a robust approach to this problem, here a very general and comprehensive analytical model for predicting the sound radiated by a vibrating plate stiffened by periodically spaced orthogonal symmetric beams subjected to a sinusoidally time varying point load is developed. The plate is assumed to be infinite in extent, and the beams are considered to exert both line force and moment reactions on it. Structural damping is included in both plate and beam materials. A space harmonic series representation of the spatial variables is used in conjunction with the Fourier transform to find the sound pressure in terms of harmonic coefficients. From this theoretical model. the sound pressure levels on axis in a semi-infinite fluid (water) bounded by the plate with the variation in the locations of an external time harmonic point force on the plate can be calculated efficiently using three numerical tools such as the Gauss-Jordan method, the LU decomposition method and the IMSL numerical package.

• Journal of applied mathematics & informatics
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• 제29권5_6호
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• pp.1583-1602
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• 2011

A special system of partial differential equations (PDEs) occur in a natural way while studying a class of irrotational inviscid fluid flow problems involving infinite channels. Certain aspects of solutions of such PDEs are analyzed in the context of flow problems involving multiple layers of fluids of different constant densities in a channel associated with arbitrary bottom topography. The whole analysis is divided into two parts-part A and part B. In part A the linearized theory is employed along with the standard Fourier analysis to understand such flow problems and physical quantities of interest are derived analytically. In part B, the same set of problems handled in part A are examined in the light of a weakly non-linear theory involving perturbation in terms of a small parameter and it is shown that the original problems can be cast into KdV type of nonlinear PDEs involving the bottom topography occurring in one of the coefficients of these equations. Special cases of bottom topography are worked out in detail and expressions for quantities of physical importance are derived.

• 대한기계학회논문집A
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• 제26권6호
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• pp.1143-1148
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• 2002

This paper analyses the transient response of a spherical elastic shell located near fee surface and impinged by spherical step-exponential acoustic shock waves. The problem is solved through extension of a method (Huang, 1969) previously formulated for the excitation in an infinite domain, which employs the classical separation of variables, series solutions, and Laplace transform technique The effect of the free surface reflection is taken into account using the image source method. The reflection of the incident wave has been treated by the same image formulation. If the reflection of the pressure field scattered and radiated by the shell is considered, the problem becomes that of multiple scattering by two spheres. However, this is in general negligible considering errors inherent from other sources and that the scattered and radiated pressure waves emanating from the shell are small. Thus, the problem is reduced to that of a structure immersed in an infinite fluid and impinged upon the origin and the image incident.

• 정보학연구
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• 제8권2호
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• pp.77-84
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• 2005

In this paper, electromagnetic scattering problems by a resistive strip grating with tapered resistivity on a grounded dielectric plane according to strip width and spacing, relative permittivity and thickness of dielectric layers, and incident angles of a electric wave are analyzed by applying the Fourier-Galerkin Moment Method known as a numerical procedure. The boundary conditions are applied to obtain the unknown field coefficients and the resistive boundary condition is used for the relationship between the tangential electric field and the electric current density on the strip. The resistivity of resistive strips in this paper varies from zeroes at one edge to infinite at the other edge, then the induced surface current density on the resistive strip is expanded in a series of Jacobi polynomials of the order ${\alpha}=0.2,\;{\beta}=-0.2$ as a orthogonal polynomials. The numerical results of the geometrically normalized reflected power in this paper are compared with those for the existing perfectly conducting strip. The numerical results of the normalized reflected power for conductive strips case with zero resistivity in this paper show in good agreement with those of existing papers.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제19권1호
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• pp.69-81
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• 2015

The present paper deals with the determination of temperature, displacement and thermal stresses in a semi-infinite hollow circular disk due to internal heat generation within it. Initially the disk is kept at arbitrary temperature F(r, z). For times t > 0 heat is generated within the circular disk at a rate of g(r, z, t) $Btu/hr.ft^3$. The heat flux is applied on the inner circular boundary (r = a) and the outer circular boundary (r = b). Also, the lower surface (z = 0) is kept at temperature $Q_3(r,t)$ and the upper surface ($Z={\infty}$) is kept at zero temperature. Hollow circular disk extends in the z-direction from z = 0 to infinity. The governing heat conduction equation has been solved by using finite Hankel transform and the generalized finite Fourier transform. As a special case mathematical model is constructed for different metallic disk have been considered. The results are obtained in series form in terms of Bessel's functions. These have been computed numerically and illustrated graphically.