• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.177-193
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• 2010

Working with the various special functions of mathematical physics and applied mathematics we often encounter inverse relations of the type $F_n(x)=\sum\limits_{k=0}^{n}A^n_kG_k(x)$ and $ G_n(x)=\sum\limits_{k=0}^{n}B_k^nF_k(x)$, where 0, 1, 2,$\cdots$. Here $F_n(x)$, $G_n(x)$ denote special polynomial functions, and $A_k^n$, $B_k^n$ denote coefficients found by use of the orthogonal properties of $F_n(x)$ and $G_n(x)$, or by skillful series manipulations. Typically $G_n(x)=x^n$ and $F_n(x)=P_n(x)$, the n-th Legendre polynomial. We give a collection of inverse series pairs of the type $f(n)=\sum\limits_{k=0}^{n}A_k^ng(k)$ if and only if $g(n)=\sum\limits_{k=0}^{n}B_k^nf(k)$, each pair being based on some reasonably well-known special function. We also state and prove an interesting generalization of a theorem of Rainville in this form.

• Journal for History of Mathematics
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• v.15 no.1
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• pp.83-92
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• 2002

Gator Szego was one of the most brilliant Mathematicians. Mathematical science owes him several fundamental contributions in such fields as theory of functions of a complex variables, conformal mapping, Fourier series, theory of orthogonal polynomials, and many others. He wrote the famous Polya-Szego Problems and Theorem in Analysis which is the two volume of concentrated mathematical beauty. In this paper, we mention Szego's life, Szego's work, and Szego reproducing kernel.

• Structural Engineering and Mechanics
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• v.8 no.6
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• pp.547-560
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• 1999

In this paper an asymptotic iteration method is adopted to analyze non-linear free vibration of reticulated circular plates composed of beam members placed in two orthogonal directions. For the resulting linear ordinary differential equations in the process of iteration, the power series with rapid convergence has been applied to obtain an analytical solution for non-linear characteristic relation between the amplitude and frequency of the structure. Numerical examples are given, and the phenomena indicating hardening of such structures have been presented for the (immovable or movable) simply-supported and clamped circular plates.

• Proceedings of the Korea Water Resources Association Conference
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• 2005.05b
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• pp.867-872
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• 2005

This study introduces a method to evaluate the probability of a specific area to be affected by a drought of a given severity and shows its potential for investigating agricultural drought characteristics. The method is applied to Gyeonggi as a case study. The proposed procedure includes Standard Precipitation Index(SPI) time series, which are linearly transformed by the Empirical Orthogonal Functions(EOF) method, These EOFs are extended temporally with AutoRegressive Moving Average(ARMA) method and spatially with Kriging method. By performing these simulations, long time series of SPI can be simulated for each designed grid cell in whole Gyeonggi area. The probability distribution functions of the area covered by a drought and the drought severity are then derived and combined to produce drought severity-area-frequency(SAF) curves.

• Proceedings of the KIEE Conference
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• 2000.07b
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• pp.867-869
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• 2000

This paper describes the steady state performance of a self-excited wound type induction generator with stator and rotor windings connected in series along with excitation capacitors. For this purpose a mathematical model is developed by means of the well known generalized machine theory utilizing d-q axis orthogonal transformation. This model can be used to analyze short shunt and long shunt generators as well as shunt generator and the algorithm for this analysis is persented. The characteristics of generators are compared one another by using parameters which are validated by Mostafa et al.

• Proceedings of the Acoustical Society of Korea Conference
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• 1994.06a
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• pp.686-691
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• 1994

For evaluating the response fluctuation of the actual environmental acoustic system excited by arbitrary random inputs, it is important to predict a whole probability distribution form closely connected with evaluation indexes Lx, Leq and so on. In this paper, a new type evaluation method is proposed by introducing three functional models matched to the prediction of the response probability distribution from a problem-oriented viewpoint. Because of the positive variable of the sound intensity, the response probability density function can be reasonably expressed theoretically by a statistical Laguerre expansion series form. The relationship between input and output is described by the regression relationship between the distribution parameters(containing expansion coefficients of this expression) and the stochastic input. These regression functions are expressed in terms of the orthogonal series expansion and their parameters are determined based on the least-squares error criterion and the measure of statistical independency.

• Journal of Theoretical and Applied Mechanics
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• v.3 no.1
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• pp.66-80
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• 2002

The bilinear formulation proposed earlier by Peters and Izadpanah to develop finite elements in time to solve undamped linear systems, Is extended (and found to be readily amenable) to develop time finite elements to obtain transient responses of both linear and nonlinear, and damped and undamped systems. The formulation Is used in the h-, p- and hp-versions. The resulting linear and nonlinear algebraic equations are differentiated to obtain the first- and second-order sensitivities of the transient response with respect to various system parameters. The present developments were tested on a series of linear and nonlinear examples and were found to yield, when compared with results obtained using other methods, excellent results for both the transient response and Its sensitivity to system parameters. Mostly. the results were obtained using the Legendre polynomials as basis functions, though. in some cases other orthogonal polynomials namely. the Hermite. the Chebyshev, and integrated Legendre polynomials were also employed (but to no great advantage). A key advantage of the time finite element method, and the one often overlooked in its past applications, is the ease In which the sensitivity of the transient response with respect to various system parameters can be obtained. The results of sensitivity analysis can be used for approximate schemes for efficient solution of design optimization problems. Also. the results can be applied to gradient-based parameter identification schemes.

• Structural Engineering and Mechanics
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• v.40 no.4
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• pp.517-539
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• 2011

This paper presents the seismic responses of a 1:5-scale five-story reinforced concrete building model, which represents a residential apartment building that has a high irregularity of weak story, soft story, and torsion simultaneously at the ground story. The model was subjected to a series of uni- and bi-directional earthquake simulation tests. Analysis of the test results leads to the following conclusions: (1) The model survived the table excitations simulating the design earthquake with the PGA of 0.187 g without any significant damages, though it was not designed against earthquakes; (2) The fundamental mode was the torsion mode. The second and third orthogonal translational modes acted independently while the torsion mode showed a strong correlation with the predominant translational mode; (3) After a significant excursion into inelastic behavior, this correlation disappeared and the maximum torsion and torsion deformation remained almost constant regardless of the intensity of the two orthogonal excitations; And, (4) the lateral resistance and stiffness of the critical columns and wall increased or decreased significantly with the large variation of acting axial forces caused by the high bi-directional overturning moments and rocking phenomena under the bi-directional excitations.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.31 no.5A
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• pp.451-458
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• 2006

In this paper, we propose a novel scheduling algorithm for downlink transmission which utilizes scarce wireless resource efficiently in an Orthogonal Frequency Division Multiple Access/Time Division Duplex system. Scheduling schemes which exploit channel information between a Base Station and terminals have been proposed recently for improved performance. Time series analysis is used to estimate the channel state of mobile terminals. The predicted information is then used for prioritized scheduling of downlink transmissions for improved throughput, delay and jitter performance. Through simulation, we show that the total throughput and mean delay of the proposed scheduling algorithm are improved compared with those of the Proportional Fairness and Maximum Carrier to Interference Ratio schemes.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.12
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• pp.3174-3182
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• 1996

In this paper, a new receiver is proposed for the detection of the OFDM(orthogonal frequency division multiplexing) signals in the time-selective multipath fading channel. For the optimal detection, we estimate the transmitted symbols from OFDM demultiplexing signal using the LMLE(linear masimum likelihold estimation) algorithm. Also, in this paper, the lowerbound for BER(bit error rate) using Taylor series approximation is provided. If the matched filter is used for the OFDM receiver in the time-selectivemultipath fading channel, it is known that the SER(symbol error rate) is always greater than $10^{-1}$, due to the cross-talk between adjacent channels. But, the proposed receiver provides of SER with 15dB SNR. Also, it is found that for the receiver implemented using the LMLE algorithm, the performance is shown to be not affected by the increase of th enumber of subchannel and channel path.