• 대한수학회보
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• 제51권2호
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• pp.531-538
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• 2014

Concentric hyperspheres in the n-dimensional Euclidean space $\mathbb{R}^n$ are the level hypersurfaces of a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$. The magnitude $||{\nabla}f||$ of the gradient of such a radial function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ is a function of the function f. We are interested in the converse problem. As a result, we show that if the magnitude of the gradient of a function f : $\mathbb{R}^n{\rightarrow}\mathbb{R}$ with isolated critical points is a function of f itself, then f is either a radial function or a function of a linear function. That is, the level hypersurfaces are either concentric hyperspheres or parallel hyperplanes. As a corollary, we see that if the magnitude of a conservative vector field with isolated singularities on $\mathbb{R}^n$ is a function of its scalar potential, then either it is a central vector field or it has constant direction.

• Korean Journal of Mathematics
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• 제18권2호
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• pp.141-148
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• 2010

We introduce the concept of fuzzy almost r-M continuous function on fuzzy r-minimal structures and investigate characterizations and properties for such a function.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권2호
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• pp.124-127
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• 2010

In this paper, we introduce the concepts of fuzzy r-minimal continuous function and fuzzy r-minimal open function between a fuzzy r-minimal space and a fuzzy topological space. We also investigate characterizations and properties for such functions.

• 호남수학학술지
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• 제43권2호
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• pp.183-197
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• 2021

Recently several authors have extended the Beta function by using its integral representation. However, in many cases no expression of these extended functions in terms of classic special functions is known. In the present paper, we introduce a further extension by defining a family of functions G_r,s : ℝ^*₊ → ℂ, with r, s ∈ ℂ and ℜ(r) > 0. For given r, s, we prove that this function satisfies a second-order linear differential equation with rational coefficients. Solving this ODE, we express G_r,s as a combination of confluent hypergeometric functions. From this we deduce a new integral relation satisfied by Tricomi's function. We then investigate additional specific properties of G_r,1 which take the form of new non trivial integral relations involving exponential and error functions. We discuss the connection between G_r,1 and Stokes' first problem (or Rayleigh problem) in fluid mechanics which consists in determining the flow created by the movement of an infinitely long plate. For $r{\in}{\frac{1}{2}}{\mathbb{N}}^*$, we find additional relations between G_r,1 and Hermite polynomials. In view of these results, we believe the family of extended beta functions G_r,s will find further applications in two directions: (i) for improving our knowledge of confluent hypergeometric functions and Tricomi's function, (ii) and for engineering and physics problems.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1992년도 한국자동제어학술회의논문집(국제학술편); KOEX, Seoul; 19-21 Oct. 1992
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• pp.164-169
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• 1992

Classical methods for estimating transfer function models have not always been successful. A statistic approach to the identification of transfer function models which is corrupted by disturbances or noise is presented. The estimated impulse response is obtained from the autocorrelation function and cross correlation function between the measured input and output. Several data analysis tools such as R- , S- and GPAC array for the estimated impulse response give us pretty clear information on the order of transfer function models.

• Kyungpook Mathematical Journal
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• 제18권2호
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• pp.311-319
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• 1978

This paper deals with the evaluation of two definite integrals involving spheroidal wave function, H-function of two variables, and the generalized hypergeometric function. Also, an expansion formula for the product of generalized hypergeometric function and the H-function of two variables has been obtained. Since the H-function of two variables, spheroidal wave functions, and the generalized hypergeometric function may be transformed into a number of higher transcendental functions and polynomials, the results obtained in this paper include some known results as their particular cases. As an application of such results, a problem of heat conduction in a non-homogenous bar has been solved by using the generalized Legendre transform [9].

• 대한수학회논문집
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• 제12권2호
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• pp.293-303
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• 1997

The existence theorem for the operator valued function space integral has been studied, when the wave function was in $L_1(R)$ class and the potential energy function was represented as a double integra [4]. Johnson and Lapidus established the existence theorem for the operator valued function space integral, when the wave function was in $L_2(R)$ class and the potential energy function was represented as an integral involving a Borel measure [9]. In this paper, we establish the existence theorem for the operator valued function we establish the existence theorem for the operator valued function space integral as an operator from $L_1(R)$ to $L_\infty(R)$ for certain potential energy functions which involve double integrals with some Borel measures.

• Journal of applied mathematics & informatics
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• 제28권3_4호
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• pp.993-1001
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• 2010

In this paper, we introduce the concept of fuzzy weakly r-M continuous function on r-minimal structures and investigate characterizations and properties for such functions.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1553-1560
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• 2010

We introduce the concept of fuzzy almost r-M continuous function on fuzzy r-minimal structures, and investigate characterizations and properties for such a function.

• 대한화학회지
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• 제37권3호
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• pp.279-286
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• 1993

물-메탄올 혼합용매에서 KCl의 용매화에 미치는 압력의 효과를 알기 위하여 여러 가지 압력하에서 물-메탄올 혼합 용매의 밀도와 점성도 및 이 혼합용매하에서 KCl의 무한희석시 당량 전도도를 측정하여 r-함수를 구하였다. 25$^{\circ}C$, 1기압에서 KCl의 r-함수는 물에서는 0.613이나 메탄올의 양이 증가함에 따라 감소하다가 다시 증가하였으며 고압하에서도 대기압에서와 비슷한 변화의 경향을 보였다. 일정 압력하에서는 메탄올의 양이 증가함에 따라 r-함수가 감소하다가 다시 증가하였으나, 일정 용매조성에서 압력이 증가하면 r-함수는 감소하였다.