• Journal of the Korean Mathematical Society
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• v.50 no.5
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• pp.1067-1082
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• 2013

In this paper, we will find some recurrence relations of classical multiple OPS between the same family with different parameters using the generating functions, which are useful to find structure relations and their connection coefficients. In particular, the differential-difference equations of Jacobi-Pineiro polynomials and multiple Bessel polynomials are given.

• Journal of the Korean Mathematical Society
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• v.8 no.1
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• pp.25-30
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• 1971

Put ($$^*$$) $$G[x,y]={\sum}\limits^{p+q=n}_{p,q=0}[-n]_{p+q}c_{p,q}x^py^q$$, where $[{\lambda}]_m$ is the Pocbhammer symbol and the $c_{p,q}$ are arbitrary constants. Making use of the specialized forms of some of his earlier results (see [8] and [9] the author derives here bilateral generating functions of the type ($$^{**}$$) $${\sum}\limits^{\infty}_{n=0}{\frac{[\lambda]_n}{n!}}_2F_1[\array{{\rho}-n,\;{\alpha};\\{\lambda}+{\rho};}x]\;G[y,z]t^n$$ where ${\alpha}$, ${\rho}$ and ${\lambda}$ are arbitrary complex numbers. In particular, it is shown that when G[y, z] is a double hypergeometric polynomial, the right-band member of ($^{**}$) belongs to a class of general triple hypergeometric functions introduced by the author [7]. An interesting special case of ($^{**}$) when ${\rho}=-m,\;m$ being a nonnegative integer, yields a class of bilateral generating functions for the Jacobi polynomials $\{P_n{^{{\alpha},{\beta}}}(x)\}$ in the form ($$^{***}$$) $${\sum\limits^{\infty}_{n=0}}\(\array{m+n\\n}\)P{^{({\alpha}-n,{\beta}-n)}_{m+n}(x)\;G[y,z]{\frac{t^n}{n!}}$$, which provides a unification of several known results. Further extensions of ($^{**}$) and ($^{***}$) with G[y, z] replaced by an analogous multiple sum $H\[y_1,{\cdots},y_m\]$ are also discussed.

• Journal of applied mathematics & informatics
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• v.7 no.3
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• pp.895-904
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• 2000

The contact problem of two elastic bodies of arbitrary shape with a general kernel form, investigated from Hertz problem, is reduced to an integral equation of the second kind with Cauchy kernel. A numerical method is adapted to determine the unknown potential function between the two surfaces under certain conditions. Many cases are derived and discussed from the work.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.168-173
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• 2003

In this paper, we will present a deeper look on optimal design methods that are related to path-planning for a mobile robot. To control the motion of a mobile robot in a clustered environment, it's necessary to know a suitable trajectory assuming certain start and goal point. Up to now, there are many literatures that concern optimal path planning for an obstacle avoided mobile robot. Among those literatures, we have chosen 2 novel methods for our further analysis. The first approach [4] is based on HJB(Hamilton-Jacobi-Bellman) equation whose solution is the return-function that helps to generate a shortest path to the goal. The later [5] is called polynomial-path-planning approach, in this method, a shortest polynomial-shape path would become a solution if it was a collision-free path. The camera network plays the role as sensors to generate updated map which locates the static and dynamic objects in the space. Therefore, the exhibition of both path planning and dynamic obstacle avoidance by the updated map would be accomplished simultaneously. As we mentioned before, our research will include the motion control of a true mobile robot on those optimal planned paths which were generated by above algorithms. Base on the kinematic and dynamic simulation results, we can realize the affection of moving speed to the stable of motion on each generated path. Also, we can verify the time-optimal trajectory through velocity tuning. To simplify for our analysis, we assumed the obstacles are cylindrical circular objects with the same size.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.935-950
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• 1997

When $\tau$ is a quasi-definite moment functional on P, the vector space of all real polynomials, we consider a symmetric bilinear form $\phi(\cdot,\cdot)$ on $P \times P$ defined by $$ \phi(p,q) = \lambad p(a)q(a) + \mu p(b)q(b) + <\tau,p'q'>, $$ where $\lambda,\mu,a$, and b are real numbers. We first find a necessary and sufficient condition for $\phi(\cdot,\cdot)$ and show that such orthogonal polynomials satisfy a fifth order differential equation with polynomial coefficients.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.8 no.5
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• pp.495-503
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• 1997

In this paper, the E-polarized electromagnetic scattering problems by a resistive strip grating with tapered resistivity on 3 dielectric layers are analyzed to find out the effects for the tapered resistivity of resistive strip and the relative permittivity and thickness of 3 die- lectric layers by applying the Fourier-Galerkin moment methods. The induced surface current density is expanded in a series of Jacobi-polynomial ${P^{(\chi,\beta)}}_p$(.) of the order $\alpha$= 0 and $\beta$=1 as a kind of orthogonal polyomians, and the tapered resistivity assumes to vary linearly from 0 at one edge to finite resistivity at the other edge. The normalized reflected and transmitted powers are obtained by varying the tapered resistivity and the relative permittivity and thickness of dielectric layers. The sharp variation points are observed when the higher order modes are transferred between propagating and evanescent modes, and in general the local minimum positions occur at less grating period for the more relative permittivity of dielectric layers. It should be noted that the patterns of the normalized reflected and transmitted powers for the tapered resistivity are very much different from those of the uniform resistivity and perfectly conducting cases. The proposed method of this paper cna solve the scattering problems for the tapered resistive, uniform resistive, and PEC strip cases.

• The Journal of Engineering Research
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• v.2 no.1
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• pp.113-123
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• 1997

The purpose of this paper is an optimum design of the shaped Cassegrainian antenna system for the base station. The process of the shaped Cassegrainian antenna design is as follows : 1) the aperture field distribution is determined so as to meet design specifications, 2) a proper design parameter is selected, 3) extracting of the dimension data for the main and sub-reflector antenna To do these, Hansen's distribution is chosen as the aperture field, and the far-field pattern from the aperture is predicted by the angular spectrum. Firstly, the aperture field distribution is designed to satisfy the specification for design frequency, it is confirmed if this distribution meet the specification for another frequency band. The main- and the sub-reflectors are synthesized so as for the given beamwaveguide feed pattern to be transformed into the prescribed aperture distribution. The designed system has circular aperture, left-right symmetry and no tilted structure. The continuous surface functions of reflectors are obtained by adopting the global interpolation technique to the discrete reflector profiles. Jacobi polynomial-sinusoidal is used as the basis function. A Ka-band Cassegrainian antenna operates over 17.7 – 20.2 GHz for down-link band and 27.5 – 30 GHz for up-link band is designed.