• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.1-11
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• 2020

In this paper we determine conditions which a function a(t) must satisfy to insure that the function a'(t) is an element of the separable Hilbert space L²_a,b[0, T]. We then proceed to illustrate our results with several pertinent examples and counter-examples.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.2
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• pp.140-144
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• 2005

We investigate the P-generating functions, L-generating functions, and A-generating function, respectively induced by product t-norms, Lukasiewicz t-norms and additive semi-groups. Furthermore, we investigate the relations among them.

• East Asian mathematical journal
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• v.33 no.1
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• pp.83-102
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• 2017

The main purpose of this paper is to introduce a pair new class of primal and dual problem associated with an operator. We prove the sufficient optimality theorem, weak duality theorem and strong duality theorem for these problems. The equivalence between the generalized optimization problems and the generalized variational inequality problems is studied in ordered topological vector space modeled in Hilbert spaces. We introduce the concept of partial differential associated (PDA)-operator, PDA-vector function and PDA-antisymmetric function to show the existence of a new class of function called, ($T_{\eta};{\xi}_{\theta}$)-invex functions. We discuss first and second kind of ($T_{\eta};{\xi}_{\theta}$)-invex functions and establish their existence theorems in ordered topological vector spaces.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
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• 2012.10a
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• pp.918-919
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• 2012

This paper present a method of function decomposition and input variable manipulation method based on modular design techniques. We obtain the column multiplicity of decomposition function according to row decomposition method. Also, the proposed partial decomposition function have advantage which is able to omit control function using t-Gate. We find the advantage for internal connection decrement 12% and T-gate number 16%, therefore we find the simple design circuit.

• The Pure and Applied Mathematics
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• v.28 no.4
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• pp.281-296
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• 2021

In this paper, we suggest a representation for an inverse transform of the generalized Fourier-Feynman transform on the function space C_a,b[0, T]. The function space C_a,b[0, T] is induced by the generalized Brownian motion process with mean function a(t) and variance function b(t). To do this, we study the generalized Fourier-Feynman transform associated with the Gaussian process Ƶ_k of exponential-type functionals. We then establish that a composition of the Ƶ_k-generalized Fourier-Feynman transforms acts like an inverse generalized Fourier-Feynman transform.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.1
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• pp.37-48
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• 2010

In this paper we use a generalized Brownian motion process to defined an analytic operator-valued generalized Feynman integral. We then obtain explicit formulas for the analytic operatorvalued generalized Feynman integrals for functionals of the form $$F(x)=f\({\int}^T_0{\alpha}_1(t)dx(t),{\cdots},{\int}_0^T{\alpha}_n(t)dx(t)\)$$, where x is a continuous function on [0, T] and {${\alpha}_1,{\cdots},{\alpha}_n$} is an orthonormal set of functions from ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2021-2026
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• 2013

Let G = (V,E) be a graph. A function $f:V{\rightarrow}\{-1,+1\}$ defined on the vertices of G is a signed total dominating function if the sum of its function values over any open neighborhood is at least one. The signed total domination number of G, ${\gamma}^s_t(G)$, is the minimum weight of a signed total dominating function of G. In this paper, we study the signed total domination number of generalized Petersen graphs P(n, 2) and prove that for any integer $n{\geq}6$, ${\gamma}^s_t(P(n,2))=2[\frac{n}{3}]+2t$, where $t{\equiv}n(mod\;3)$ and $0 {\leq}t{\leq}2$.

• Communications of the Korean Mathematical Society
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• v.36 no.4
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• pp.685-704
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• 2021

The purpose of this paper is to establish a very general Cameron-Storvick theorem involving the generalized analytic Feynman integral of functionals on the product function space C²_a,b[0, T]. The function space C_a,b[0, T] can be induced by the generalized Brownian motion process associated with continuous functions a and b. To do this we first introduce the class ${\mathcal{F}}^{a,b}_{A_1,A_2}$ of functionals on C²_a,b[0, T] which is a generalization of the Kallianpur and Bromley Fresnel class ${\mathcal{F}}_{A_1,A_2}$. We then proceed to establish a Cameron-Storvick theorem on the product function space C²_a,b[0, T]. Finally we use our Cameron-Storvick theorem to obtain several meaningful results and examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.27 no.1
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• pp.59-64
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• 2017

In this paper, a controller for discrete Takagi-Sugeno(T-S) fuzzy model under imperfect premise matching is proposed. Most of previous papers have obtained the stabilization condition using common quadratic Lyapunov function. However, the stabilization condition may be conservative due to the typical disadvantage of the common quadratic Lyapunov function. Hence, in order to solve this problem, we propose the stabilization condition of discrete T-S fuzzy model using fuzzy Lyapunov function. Finally, the proposed approach is verified by the simulation experiments.

• Communications for Statistical Applications and Methods
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• v.4 no.1
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• pp.281-292
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• 1997

In this paper we are concered with the counting processes with intersity function $g_n(t)$, where $g_n(t)$ not only depends on t but n. It is shown that under certain conditions the number of events in [0, t] follows a generalizes Poisson distribution. A counting process is also provided such that $g_i(t)$$\neq$$g_i(t)$ for i$\neq$j and the number of events in [0, t] has a transformed geometric distribution.