• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.509-512
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• 2007

We aim at deriving Gauss's second summation theorem for the series $_2F_1(1/2)$ by using Euler's integral representation for $_2F_1$. It seems that this method of proof has not been tried.

• Communications for Statistical Applications and Methods
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• v.9 no.1
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• pp.1-11
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• 2002

This paper discusses problems of the Poisson Mixture model which Is widely used to decide the effective words in judging relevant document. Gamma Distribution model and Gauss Patterns model as an alternative of the Poisson Mixture model are studied. Classification experiments by using TREC sub-collection, WSJ[1,2] with MGQUERY and AidSearch3.0 system are discussed.

• Journal of the Korean Statistical Society
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• v.4 no.1
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• pp.39-56
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• 1975

Ever since Gauss discussed the least-squares method in 1812 and Bertrand translated Gauss's work in French, the least-squares method has been used for various economic analysis. The justification of the least-squares method was given by Markov in 1912 in connection with the previous discussion by Gauss and Bertrand. The main argument concerned the problem of obtaining the best linear unbiased estimates. In some modern language, the argument can be explained as follow.

• Proceedings of the Korean Information Science Society Conference
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• 2004.04a
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• pp.502-504
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• 2004

이동성이 중요시되는 네트워크에서 특정 프로토콜의 성능 평가를 위해서는 노드의 이동패턴을 정확하게 표현할 수 있는 Mobility Model이 필요하다. 노드의 연속적인 이동패턴을 필요로 하는 Mobile Ad-hoc 네트워크를 위해선 Markov process 기반의 Gauss-Markov Mobility Model이 적절하다. 그러나 맵의 엣지 부근에서 노드 이동의 부적절한 처리로 인해, 기존의 Gauss-Markov Model은 편중된 이동 패턴을 야기한다. 본 논문은 엣지 부근의 평균 이동각도를 랜덤하게 조정함으로써 기존의 모델이 가진 문제를 해결하고, 시뮬레이션을 통해서 이를 검증한다.

• The Pure and Applied Mathematics
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• v.17 no.4
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• pp.307-319
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• 2010

We provide a new semilocal convergence analysis of the Gauss-Newton method (GNM) for solving nonlinear equation in the Euclidean space. Using our new idea of recurrent functions, and a combination of center-Lipschitz, Lipschitz conditions, we provide under the same or weaker hypotheses than before [7]-[13], a tighter convergence analysis. The results can be extented in case outer or generalized inverses are used. Numerical examples are also provided to show that our results apply, where others fail [7]-[13].

• Honam Mathematical Journal
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• v.38 no.1
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• pp.25-37
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• 2016

In 1972, Andrews derived the basic analogue of Gauss's second summation theorem and Bailey's theorem by implementing basic analogue of Kummer's theorem into identity due to Jackson. Recently Lavoie et.al. derived many results closely related to Kummer's theorem, Gauss's second summation theorem and Bailey's theorem and also Rakha et. al. derive the basic analogues of results closely related Kummer's theorem. The aim of this paper is to derive basic analogues of results closely related Gauss's second summation theorem and Bailey's theorem. Some applications and limiting cases are also considered.

• Journal of the Korean Mathematical Society
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• v.34 no.4
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• pp.871-894
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• 1997

For a lifted nontrivial additive character $\lambda'$ and a multiplicative character $\chi$ of the finite field with $q^2$ elements, the 'Gauss' sums $\Sigma\lambda'$(tr $\omega$) over $\omega$ $\in$ SU(2n + 1, $q^2$) and $\Sigma\chi$(det $\omega$)$\lambda'$(tr $\omega$) over $\omega$ $\in$ U(2n + 1, $q^2$) are considered. We show that the first sum is a polynomial in q with coefficients involving certain new exponential sums and that the second one is a polynomial in q with coefficients involving powers of the usual twisted Kloosterman sums and the average (over all multiplicative characters of order dividing q-1) of the usual Gauss sums. As a consequence we can determine certain 'generalized Kloosterman sum over nonsingular Hermitian matrices' which were previously determined by J. H. Hodges only in the case that one of the two arguments is zero.

• Journal of the Korean Institute of Telematics and Electronics
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• v.17 no.3
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• pp.52-56
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• 1980

The Signal -to- Noise Ratio of delta modulation for a fi rEt -order Gauss -Markov signal is derived and an approximate expreession of SND is discussed, in the case that only granular noise arises. Cross covariance of input and error signals are negligible when the adjacent correlation of input signal is larger than the difference between the adjacent correlation and the prediction coefficient of local decoder. The approximately derived SNR is available for any value of adjacent correlation.

• Bulletin of the Korean Mathematical Society
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• v.48 no.2
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• pp.291-302
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• 2011

We first study the generalized Fourier-Gauss transforms of functionals defined on the complexification $\cal{B}_C$ of an abstract Wiener space ($\cal{H}$, $\cal{B}$, ${\nu}$). Secondly, we introduce a new class of convolution products of functionals defined on $\cal{B}_C$ and study several properties of the convolutions. Then we study various relations among the first variation the convolutions, and the generalized Fourier-Gauss transforms.

• Bulletin of the Korean Mathematical Society
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• v.48 no.3
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• pp.601-609
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• 2011

Tensor product immersions of a given Riemannian manifold was initiated by B.-Y. Chen. In the present article we study the tensor product surfaces of two Euclidean plane curves. We show that a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ has harmonic Gauss map if and only if M is a part of a plane. Further, we give necessary and sufficient conditions for a tensor product surface M of a plane circle $c_1$ centered at origin with an Euclidean planar curve $c_2$ to have pointwise 1-type Gauss map.