• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권2호
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• pp.155-185
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• 2021

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of generalized relative order (𝛼, 𝛽), generalized relative type (𝛼, 𝛽) and generalized relative weak type (𝛼, 𝛽) of entire functions with respect to another entire function where 𝛼, 𝛽 are continuous non-negative functions on (-∞, +∞).

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.355-376
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• 2021

In this paper we wish to establish the integral representations of generalized relative order (𝛼, 𝛽) and generalized relative type (𝛼, 𝛽) of entire and meromorphic functions where 𝛼 and 𝛽 are continuous non-negative functions defined on (-∞, +∞). We also investigate their equivalence relation under some certain condition.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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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.

• 대한수학회논문집
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• 제38권4호
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• pp.1141-1151
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• 2023

Let C_a,b[0, T] denote the space of continuous sample paths of a generalized Brownian motion process (GBMP). In this paper, we study the structures which exist between the analytic generalized Fourier-Feynman transform (GFFT) and the generalized convolution product (GCP) for functions on the function space C_a,b[0, T]. For our purpose, we use the exponential type functions on the general Wiener space C_a,b[0, T]. The class of all exponential type functions is a fundamental set in L₂(C_a,b[0, T]).

• 대한수학회논문집
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• 제38권4호
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• pp.1271-1280
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• 2023

The object of the present paper is to introduce a type of non-flat Riemannian manifold, called a weakly cyclic generalized B-symmetric manifold (W CGBS)_n. We obtain a sufficient condition for a weakly cyclic generalized B-symmetric manifold to be a generalized quasi Einstein manifold. Next we consider conformally flat weakly cyclic generalized B-symmetric manifolds. Then we study Einstein (W CGBS)_n (n > 2). Finally, it is shown that the semi-symmetry and Weyl semi-symmetry are equivalent in such a manifold.

• 대한수학회보
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• 제29권1호
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• pp.31-40
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• 1992

We introduce the generalized Runge-Kutta methods with the exponentially dominant order .omega. in [3], and the convergence theorems of the generalized explicit Euler method are derived in [4]. In this paper we will study the convergence of the generalized implicit Euler method.

• 충청수학회지
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• 제24권1호
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• pp.131-135
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• 2011

It is shown that generalized GCD domains satisfy a certain property of injectivity and conversely this property characterizes generalized GCD domains.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1997년도 한국자동제어학술회의논문집; 한국전력공사 서울연수원; 17-18 Oct. 1997
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• pp.1367-1370
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• 1997

This paper presents a vision algorithm for finding the centers of steam generator tubes using the generalized symmetry transform, which is used for ECT(Eddy Current Test) of steam generator tubes in nuclear power plants. The geometrical properties of the image representing steam generator tubes shows that they have amost circular or somewhat elliptic appearances and each tube has strong symmetry about its center. So we apply the generalized symmetry transform to finding centers of steam geneator tubes. But applying the generalized symmetry transform itself without any modification gives difficulties in obtaining the exact centers of steam generator tubes. But applying the generalized symmetry transform itself without any modification gives difficulties in obtaining the exact centers of tubes due to the shadow effect generated by the local light installed inside steam generator. Therefore we make the generalized symmetry transform modified, which uses a modified phase weight function in getting the symmetry magnitude in order to overcome the misleading effect by the local light. The experimental results indicate that the proposed vision algorithm efficiently recongnizes centers of steam generator tubes.

• 충청수학회지
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• 제25권4호
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• pp.703-709
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• 2012

Recently, Kazmi and Khan [7] introduced a kind of equilibrium problem called generalized system (GS) with a single-valued bi-operator F. Next, in [10], the first author considered a generalization of (GS) into a multi-valued circumstance called the multi-valued quasi-generalized system (in short, MQGS). In the current work, we provide an extension of (MQGS) into a system of (MQGS) in general settings. This system is called the generalized multi-valued quasi-generalized system (in short, GMQGS). Using the existence theorem for abstract economy by Kim [8], we prove the existence of solutions for (GMQGS) in the framework of Hausdorff topological vector spaces. As an application, an existence result of a system of generalized vector quasi-variational inequalities is derived.

• 대한수학회지
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• 제54권3호
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• pp.999-1013
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• 2017

In the present study we consider the generalized rotational surfaces in Euclidean spaces. Firstly, we consider generalized tractrices in Euclidean (n + 1)-space $\mathbb{E}^{n+1}$. Further, we introduce some kind of generalized rotational surfaces in Euclidean spaces $\mathbb{E}^3$ and $\mathbb{E}^4$, respectively. We have also obtained some basic properties of generalized rotational surfaces in $\mathbb{E}^4$ and some results of their curvatures. Finally, we give some examples of generalized Beltrami surfaces in $\mathbb{E}^3$ and $\mathbb{E}^4$, respectively.