• Proceedings of the KSME Conference
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• 2001.06e
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• pp.760-765
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• 2001

Some multidimentional generalizations of the Fokker-Planck Equation used by Friedrich and Peinke for description of a turbulent cascade was solved by A.A.Donkov, A.D.Donkov, and G.I.Grancharova. The solutions are two types, isotropic and anisotropic diffusion case. We introduce their methods to solve the Equation and solutions. Furthermore we get the more generalized exact solution as combination of two cases and plot to compare those to experimental results for the isotropic case.

• Journal of the Korean Mathematical Society
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• v.41 no.5
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• Bulletin of the Korean Chemical Society
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• v.24 no.8
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• pp.1111-1118
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• 2003

We present one-color nonlinear wavepacket interferometry (WPI) signal calculations for a system of two electronic levels and one vibrational degree of freedom. We consider two cases, a displaced harmonic oscillator system, which can be treated analytically, and a model photodissociative system, whose WPI signal must be calculated by numerical wavepacket propagation. We show how signals obtained with different combinations of intrapulse-pair phase shifts can be combined to isolate the complex-valued overlap between a given onepulse target wavepacket and a variable three-pulse reference wavepacket. We demonstrate that with a range of inter- and intrapulse-pair delays the complex overlaps and variable reference states can be used to reconstruct the target wavepacket. We compare our results with previous methods for vibronic state reconstruction based on linear WPI and discuss further generalizations of our method.

• Research in Mathematical Education
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• v.8 no.4
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• pp.261-277
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• 2004

Julia sets, their variants and generalizations have been studied extensively by using the Picard iterations. The purpose of this paper is to introduce Mann iterative procedure in the study of Julia sets. Escape criterions with respect to this process are obtained for polynomials in the complex plane. New escape criterions are significantly much superior to their corresponding cousins. Further, new algorithms are devised to compute filled Julia sets. Some beautiful and exciting figures of new filled Julia sets are included to show the power and fascination of our new venture.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.107-120
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• 2008

There has been a recent growth of interest in codes with respect to a newly defined non-Hamming metric grown as the Rosenbloom-Tsfasman metric (RT, or $\rho$, in short). In this paper, the definitions of the Lee complete $\rho$ weight enumerator and the exact complete $\rho$ weight enumerator of a code over $M_n_\times_s(Z_4)$ are given, and the MacWilliams identities with respect to this RT metric for the two weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are proven too. At last, we also prove that the MacWilliams identities for the Lee and exact complete $\rho$ weight enumerators of a linear code over $M_n_\times_s(Z_4)$ are the generalizations of the MacWilliams identities for the Lee and complete weight enumerators of the corresponding code over $Z_4$.

• Journal of applied mathematics & informatics
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• v.26 no.1_2
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• pp.75-106
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• 2008

In this paper, we derive necessary optimality conditions for a continuous programming problem in which both objective and constraint functions contain support functions and is, therefore, nondifferentiable. It is shown that under generalized invexity of functionals, Karush-Kuhn-Tucker type optimality conditions for the continuous programming problem are also sufficient. Using these optimality conditions, we construct dual problems of both Wolfe and Mond-Weir types and validate appropriate duality theorems under invexity and generalized invexity. A mixed type dual is also proposed and duality results are validated under generalized invexity. A special case which often occurs in mathematical programming is that in which the support function is the square root of a positive semidefinite quadratic form. Further, it is also pointed out that our results can be considered as dynamic generalizations of those of (static) nonlinear programming with support functions recently incorporated in the literature.

• Language and Information
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• v.4 no.2
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• pp.55-68
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• 2000

The efficiency and stability of an NLP system depends crucially on how is lexicon is orga- nized . Then lexicon ought to encode linguistic generalizations and exceptions thereof. Nowadays many computational linguists tend to construct such lexical information in an inheritance hierarchy DATR is good for this purpose In this research I will construct a DATR-lexicon in order to parse sentences in Korean using QPATR is implemented on the basis of a unification based grammar developed in Dusseldorf. In this paper I want to show the interface between a syntactic parser(QPATR) and DTAR-formalism representing lexical information. The QPATR parse can extract the lexical information from the DATR lexicon which is organised hierarchically.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.557-562
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• 2009

A module M is said to be SIP-extending if the intersection of every pair of direct summands is essential in a direct summand of M. SIP-extending modules are a proper generalization of both SIP-modules and extending modules. Every direct summand of an SIP-module is an SIP-module just as a direct summand of an extending module is extending. While it is known that a direct sum of SIP-extending modules is not necessarily SIP-extending, the question about direct summands of an SIP-extending module to be SIP-extending remains open. In this study, we show that a direct summand of an SIP-extending module inherits this property under some conditions. Some related results are included about $C_{11}$ and SIP-modules.

• Bulletin of the Korean Mathematical Society
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• v.52 no.1
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• pp.323-333
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• 2015

Let X be a compact metric space and let |A| denote the cardinality of a set A. We prove that if $f:X{\rightarrow}X$ is a homeomorphism and ${\mid}X{\mid}={\infty}$, then for all ${\delta}$ > 0 there is $A{\subset}X$ such that |A| = 4 and for all $k{\in}\mathbb{Z}$ there are $x,y{\in}f^k(A)$, $x{\neq}y$, such that dist(x, y) < ${\delta}$. An observer that can only distinguish two points if their distance is grater than ${\delta}$, for sure will say that A has at most 3 points even knowing every iterate of A and that f is a homeomorphism. We show that for hyperexpansive homeomorphisms the same ${\delta}$-observer will not fail about the cardinality of A if we start with |A| = 3 instead of 4. Generalizations of this problem are considered via what we call (m, n)-expansiveness.

• Korean Journal of Mathematics
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• v.20 no.2
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• pp.213-223
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• 2012

In this paper, we will prove the superstability of the following generalized Pexider type exponential equation $${f(x+y)}^m=g(x)h(y)$$, where $f,g,h\;:\;G{\rightarrow}\mathbb{R}$ are unknown mappings and $m$ is a fixed positive integer. Here G is an Abelian group (G, +), and $\mathbb{R}$ the set of real numbers. Also we will extend the obtained results to the Banach algebra. The obtained results are generalizations of P. G$\check{a}$vruta's result in 1994 and G. H. Kim's results in 2011.