• The Journal of Korea Institute of Information, Electronics, and Communication Technology
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• v.11 no.1
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• pp.40-44
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• 2018

As the information society developed rapidly now, office software based on IoT has released along with office appliances that we encountered in everyday life, providing more convenient services. Now a days, in addition to writing documents for recording, it has importance to create documents for effective document presentation and information transmission. In this paper, we have been presented and designed in 3D virtual space from 2D for effective information transmission in real time. The suggested program, which implements part of the design, enables the voice and visual information to be effectively communicated while conveniently exploring or showing documents in a virtual 3D space. It provides a method of automatically placing documents in 3D virtual space, designing virtual camera movements that effectively explore them, and suggesting how to connect voice information to each document in real time.

• Journal of The Korean Astronomical Society
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• v.53 no.6
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• pp.149-159
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• 2020

Gravitational lensing of point sources located inside the lens caustic is known to produce four images in a configuration closely related to the source position. We study this relation in the particular case of a sample of quadruply-imaged quasars observed by the Hubble Space Telescope. Strong correlations between the parameters defining the image configuration are revealed. The relation between the image configuration and the source position is studied. Some simple features of the selected data sample are exposed and commented upon. In particular, evidence is found for the selected sample to be biased in favor of large magnification systems. While having no direct impact on practical analyses of specific systems, our results have pedagogical value and deepen our understanding of the mechanism of gravitational lensing.

• The Mathematical Education
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• v.26 no.1
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• pp.41-45
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• 1987

In this paper, we give several fixed point theorems in a complete metric space for two multi-valued mappings commuting with two single-valued mappings. In fact, our main theorems show the existence of solutions of functional equations f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ and $\chi$=f($\chi$)=g($\chi$)$\in$S$\chi$∩T$\chi$ under certain conditions. We also answer an open question proposed by Rhoades-Singh-Kulsherestha. Throughout this paper, let (X, d) be a complete metric space. We shall follow the following notations : CL(X) = {A; A is a nonempty closed subset of X}, CB(X)={A; A is a nonempty closed and founded subset of X}, C(X)={A; A is a nonempty compact subset of X}, For each A, B$\in$CL(X) and $\varepsilon$>0, N($\varepsilon$, A) = {$\chi$$\in$X; d($\chi$, ${\alpha}$) < $\varepsilon$ for some ${\alpha}$$\in$A}, E$\sub$A, B/={$\varepsilon$ > 0; A⊂N($\varepsilon$ B) and B⊂N($\varepsilon$, A)}, and (equation omitted). Then H is called the generalized Hausdorff distance function fot CL(X) induced by a metric d and H defined CB(X) is said to be the Hausdorff metric induced by d. D($\chi$, A) will denote the ordinary distance between $\chi$$\in$X and a nonempty subset A of X. Let R$\^$+/ and II$\^$+/ denote the sets of nonnegative real numbers and positive integers, respectively, and G the family of functions ${\Phi}$ from (R$\^$+/)$\^$s/ into R$\^$+/ satisfying the following conditions: (1) ${\Phi}$ is nondecreasing and upper semicontinuous in each coordinate variable, and (2) for each t>0, $\psi$(t)=max{$\psi$(t, 0, 0, t, t), ${\Phi}$(t, t, t, 2t, 0), ${\Phi}$(0, t, 0, 0, t)} $\psi$: R$\^$+/ \longrightarrow R$\^$+/ is a nondecreasing upper semicontinuous function from the right. Before sating and proving our main theorems, we give the following lemmas:

• Bulletin of the Korean Mathematical Society
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• v.49 no.4
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• pp.799-813
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• 2012

In this paper, we first show that the iteration {$x_n$} defined by $x_{n+1}=P((1-{\alpha}_n)x_n +{\alpha}_nTP[{\beta}_nTx_n+(1-{\beta}_n)x_n])$ converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with errors when E is a real uniformly convex Banach space and T is a quasi-nonexpansive self-mapping satisfying Condition A, which generalizes the result due to Senter-Dotson [10]. Finally, we show that the iteration {$x_n$} defined by $x_{n+1}={\alpha}_nSx_n+{\beta}_nT[{\alpha}^{\prime}_nSx_n+{\beta}^{\prime}_nTx_n+{\gamma}^{\prime}_n{\upsilon}_n]+{\gamma}_nu_n$ converges strongly to a common fixed point of T and S when E is a real uniformly convex Banach space and T, S are two quasi-nonexpansive self-mappings satisfying Condition D, which generalizes the result due to Ghosh-Debnath [3].

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.4
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• pp.489-494
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• 2013

In analysis of power transformer loss using calculation of magnetic field, Finite element method is commonly used. When using this method, calculation of magnetic field needs the very large number of elements and the performance of common work station is not sufficient to calculate the magnetic fields. In addition, the definition of boundary conditions may arise. However, When using Integral equation method, only ferromagnetic materials need to be modeled, since the domain is infinite. All the space in which the primary and secondary sources exist is regarded as free(${\mu}={\mu}_0$).

• Honam Mathematical Journal
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• v.24 no.1
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• pp.35-41
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• 2002

The solutions of a homogeneous system in state space form $\dot{x}=Ax$ are to the form $x=e^{At}x_0$ and the solutions of an inhomogeneous system $\dot{x}=Ax(t)+f(t)$ are to the form $x=e^{At}x_0+{{\int}_0^t}\;e^{A(t-{\tau})}f({\tau})d{\tau}$. In this note we show that the solution of descriptor systems under some conditions exists, and is unique, moreover it is interesting to know the solutions of descriptor system are schematically like the solutions as in the state space form. Also we will give some algorithms to compute these solutions.

• Kyungpook Mathematical Journal
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• v.55 no.2
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• pp.345-353
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• 2015

Subnormality of bounded weighted composition operators on $L^2({\Sigma})$ of the form $Wf=uf{\circ}T$, where T is a nonsingular measurable transformation on the underlying space X of a ${\sigma}$-finite measure space (X, ${\Sigma}$, ${\mu}$) and u is a weight function on X; is studied. The standard moment sequence characterizations of subnormality of weighted composition operators are given. It is shown that weighted composition operators are subnormal if and only if $\{J_n(x)\}^{+{\infty}}_{n=0}$ is a moment sequence for almost every $x{{\in}}X$, where $J_n=h_nE_n({\mid}u{\mid}^2){\circ}T^{-n}$, $h_n=d{\mu}{\circ}T^{-n}/d{\mu}$ and $E_n$ is the conditional expectation operator with respect to $T^{-n}{\Sigma}$.

• Kyungpook Mathematical Journal
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• v.58 no.4
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• pp.637-650
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• 2018

In this paper first we show properties of isosymmetric operators given by M. Stankus [13]. Next we introduce an [m, C]-symmetric operator T on a complex Hilbert space H. We investigate properties of the spectrum of an [m, C]-symmetric operator and prove that if T is an [m, C]-symmetric operator and Q is an n-nilpotent operator, respectively, then T + Q is an [m + 2n - 2, C]-symmetric operator. Finally, we show that if T is [m, C]-symmetric and S is [n, D]-symmetric, then $T{\otimes}S$ is [m + n - 1, $C{\otimes}D$]-symmetric.

• Journal of the Korean Mathematical Society
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• v.38 no.6
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• pp.1191-1204
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• 2001

The paper is devoted to the study of fractional integration and differentiation on a finite interval [a, b] of the real axis in the frame of Hadamard setting. The constructions under consideration generalize the modified integration $\int_{a}^{x}(t/x)^{\mu}f(t)dt/t$ and the modified differentiation ${\delta}+{\mu}({\delta}=xD,D=d/dx)$ with real $\mu$, being taken n times. Conditions are given for such a Hadamard-type fractional integration operator to be bounded in the space $X^{p}_{c}$(a, b) of Lebesgue measurable functions f on $R_{+}=(0,{\infty})$ such that for c${\in}R=(-{\infty}{\infty})$, in particular in the space $L^{p}(0,{\infty})\;(1{\le}{\le}{\infty})$. The existence almost every where is established for the coorresponding Hadamard-type fractional derivative for a function g(x) such that $x^{p}$g(x) have $\delta$ derivatives up to order n-1 on [a, b] and ${\delta}^{n-1}[x^{\mu}$g(x)] is absolutely continuous on [a, b]. Semigroup and reciprocal properties for the above operators are proved.

• Communications of the Korean Mathematical Society
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• v.9 no.4
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• pp.819-823
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• 1994

If H is a Hilbert space, then an operator $T : D(T) \subset H \to H$ is said to be monotone if $$ (x-y, Tx-Ty) \geq 0$$ for any x, y in D(T). Many authors [1], [4] obtained the existence theorem for the equation $y = x + Tx$ for x, given an element y in H and a monotone operator T. On the other hand some iterative methods were applied to the approximations for the solution of the above equation [6], [8]. For example Bruck [2] obtained the iterative solution of the above equation with an explicit error estimate as follows.