• Bulletin of the Korean Chemical Society
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• v.21 no.12
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• pp.1227-1232
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• 2000

Near the conical intersection for the 1,2 $^{2}A'$ states of $H_3$ the derivative coupling vector is calculated and analyzed on the plane of internal coordinates, (U,V) or its polar coordinates $(S{\theta})$, based on the squares of the internuclear distances. It is shown that in the vicinity of the conical intersection the derivative coupling vector behaves like ${\theta}/2S$, which is responsible for the sign changes of the real-valued electronic wave function when the nuclear configuration traverses a closed path enclosing a conical intersection. The analytic property of the wave functions is studied and especially the observation of the sign change in the configuration state function (CSF) coefficients of the real-valued electronic wave functions is demonstrated.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.359-375
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• 2014

In this paper, a multiobjective nondifferentiable fractional programming problem (MFP) is considered where the objective function contains a term involving the support function of a compact convex set. A vector valued (generalized) ${\alpha}$-univex function is defined to extend the concept of a real valued (generalized) ${\alpha}$-univex function. Using these functions, sufficient optimality criteria are obtained for a feasible solution of (MFP) to be an efficient or weakly efficient solution of (MFP). Duality results are obtained for a Mond-Weir type dual under (generalized) ${\alpha}$-univexity assumptions.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.105-114
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• 2001

In this paper we introduce the concepts of generalized bounded variation with respect to a strictly increasing function and Denjoy-Stieltjes integral of real-valued functions and then prove some properties of them.

• Journal of the Korean Statistical Society
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• v.22 no.1
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• pp.93-111
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• 1993

Let ${X(t) : t \geq 0}$ be a real-valued stochastics process with stationary independent increments. In this paper, under the condition of stochastic compactness, we obtain appropriate function $\alpha(t)$ and random function $\beta(t)$ such that for some positive finite constant C, lim sup${X(t) - \alpha(t)}/\beta(t) = C$ a.s. both as t tends to zero and infinity.

• Communications of the Korean Mathematical Society
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• v.10 no.2
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• pp.409-417
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• 1995

We consider the $R^k$-valued $(k \geq 1)$ process ${X_n}$ generated by $X_n + 1 = f(X_n)+e_{n+1}$, where $f(x) = (h(x),x^{(1)},x^{(1)},\cdots,x{(k-1)})'$. We assume that h is a real-valued measuable function on $R^k$ and that $e_n = (e'_n,0,\cdot,0)'$ where ${e'_n}$ are independent and identically distributed random variables. We obtained a practical criteria guaranteeing a given process to be geometrically ergodic. Sufficient condition for transience is also given.

• Bulletin of the Korean Mathematical Society
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• v.21 no.2
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• pp.99-106
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• 1984

J. Yeh has recently introduced the concept of conditional Wiener integrals which are meant specifically the conditional expectation E$^{w}$ (Z vertical bar X) of a real or complex valued Wiener integrable functional Z conditioned by the Wiener measurable functional X on the Wiener measure space (A precise definition of the conditional Wiener integral and a brief discussion of the Wiener measure space are given in Section 2). In [3] and [4] he derived some inversion formulae for conditional Wiener integrals and evaluated some conditional Wiener integrals E$^{w}$ (Z vertical bar X) conditioned by X(x)=x(t) for a fixed t>0 and x in Wiener space. Thus E$^{w}$ (Z vertical bar X) is a real or complex valued function on R$^{1}$. In this paper we shall be concerned with the random vector X given by X(x) = (x(s$_{1}$),..,x(s$_{n}$ )) for every x in Wiener space where 0=s$_{0}$ $_{1}$<..$_{n}$ =t. In Section 3 we will evaluate some conditional Wiener integrals E$^{w}$ (Z vertical bar X) which are real or complex valued functions on the n-dimensional Euclidean space R$^{n}$ . Thus we extend Yeh's results [4] for the random variable X given by X(x)=x(t) to the random vector X given by X(x)=(x(s$_{1}$).., x(s$_{n}$ )).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.21 no.9
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• pp.2456-2469
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• 1996

A digital satellite communication channel has a nonlinearity with memory due to saturation characeristis of the high poer amplifier in the satellite and transmitter/receiver linear filter used in the overall system. In this paper, we propose a complex radial basis function network(CRBFN) based adaptive equalizer for compensation of nonlinearities in digital satellite communication channels. The proposed CRBFN untilizes a complex-valued hybrid learning algorithm of k-means clustering and LMS(least mean sequare) algorithm that is an extension of Moody Darken's algorithm for real-valued data. We evaluate performance of CRBFN in terms of symbol error rates and mean squared errors nder various noise conditions for 4-PSK(phase shift keying) digital modulation schemes and compare with those of comples pth order inverse adaptive Volterra filter. The computer simulation results show that the proposed CRBFN ehibits good equalization, low computational complexity and fast learning capabilities.

• Journal of the Institute of Electronics Engineers of Korea SD
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• v.46 no.3
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• pp.10-19
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• 2009

In this paper, an efficient optical watermark method using multiple phase wrapping and real-valued decoding key is proposed. In the embedding process, two zero-padded original images placed in two quadrants on input plane are multiplied with two statistically independent random phase patterns and are Fourier transformed, respectively. Two encoded images are obtained by taking the real-valued data from these Fourier transformed images. And then two phase-encoded patterns, used as a hidden image and a decoding key, are generated by the use of multiple phase wrapping from each of the encoded images. A transmitted image is made from the linear superposition of the weighted hidden images and a cover image. In reconstruction process, the mirror reconstructed images can be obtained at all quadrants by the inverse-Fourier transform of the product of the transmitted image and the decoding key. Computer simulation and optical experiment are demonstrated in order to confirm the proposed method.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.243-254
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• 1991

For a given function f.mem.F and a set of functions J.subeq.F, the problem of isotonic optimization is to determine an element in the set nearest to f in some sense. Specifically, let X be a partially ordered finite set with a partial order << and, let F"=F(X) be the linear space of all bounded real valued functions on X. A function g.mem.F is said to be an isotonic function if g(x).leq.g(y) whenever x,y.mem.X and x << y.<< y.

• The Pure and Applied Mathematics
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• v.26 no.3
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• pp.199-208
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• 2019

A necessary and sufficient condition in terms of lower cut sets is given for the insertion of a Baire-.5 function between two comparable real-valued functions on the topological spaces that whose $F_{\sigma}$-kernel of sets are $F_{\sigma}$-sets.