• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제27권1호
• /
• pp.1-11
• /
• 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
• /
• 제5권2호
• /
• pp.140-144
• /
• 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
• /
• 제33권1호
• /
• pp.83-102
• /
• 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.

• 한국정보통신학회:학술대회논문집
• /
• 한국정보통신학회 2012년도 추계학술대회
• /
• pp.918-919
• /
• 2012

본 논문에서는 모듈러 설계기법에 기반을 둔 함수분해방법과 입력변수 처리 방법에 관한 설계기법을 제안하였다. 부분 분해방법으로서 행 분할 변수 중 1-열 변수의 입력 값에 따라 함수를 분할하여 컬럼 곱을 구하였다. 또한 제안한 부분 함수는 단일 T-gate를 사용하므로 모듈 라이브러리 방식에서의 제어함수를 생략할 수 있는 장점이 있다. 이를 함수에 적용한 결과 주어진 함수가 비대칭, 불규칙인 경우 기존의 방식에 비래 내부 결선이 약 12%정도, T-gate 수는 16% 정도 감소되어 더욱 간단한 회로설계가 이루어지는 장점이 있음을 보였다.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제28권4호
• /
• pp.281-296
• /
• 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.

• 충청수학회지
• /
• 제23권1호
• /
• pp.37-48
• /
• 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 ($L^2_{a,b}[0,T]$, ${\parallel}{\cdot}{\parallel}_{a,b}$).

• 대한수학회보
• /
• 제50권6호
• /
• pp.2021-2026
• /
• 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 $0 {\leq}t{\leq}2$.

• 대한수학회논문집
• /
• 제36권4호
• /
• pp.685-704
• /
• 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.

• 한국지능시스템학회논문지
• /
• 제27권1호
• /
• pp.59-64
• /
• 2017

본 논문은 이산 Takagi-Sugeno (T-S) 퍼지 모델의 제어기 설계 시 시스템과 제어기가 상이한 소속 함수를 가지는 불완전한 전반부 정합 하에서의 제어기 설계에 대해 다룬다. 이산 T-S 퍼지 모델의 안정화 조건을 구할 때, 단일 Lyapunov 함수를 이용하여 구한 기존의 보수적인 안정화 조건보다 완화된 안정화 조건을 구하기 위해 퍼지 Lyapunov 함수를 고려한다. 퍼지 Lyapunov 함수를 이용하여 선형 행렬 부등식 기반의 완화된 안정화 조건을 구하고 시뮬레이션을 통해 제안한 방법의 타당성을 검증한다.

• Communications for Statistical Applications and Methods
• /
• 제4권1호
• /
• pp.281-292
• /
• 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.