• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1393-1404
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• 2008

Let K be a nonempty closed convex subset of a Banach space E. Suppose $\{T_{n}\}$ (n = 1,2,...) is a uniformly asymptotically regular sequence of nonexpansive mappings from K to K such that ${\cap}_{n=1}^{\infty}$ F$\(T_n){\neq}{\phi}$. For $x_0{\in}K$, define $x_{n+1}={\lambda}_{n+1}x_{n}+(1-{\lambda}_{n+1})T_{n+1}x_{n},n{\geq}0$. If ${\lambda}_n{\subset}[0,1]$ satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n=0$, we proved that $\{x_n\}$ weakly converges to some $z{\in}F\;as\;n{\rightarrow}{\infty}$ in the framework of reflexive Banach space E which satisfies the Opial's condition or has $Fr{\acute{e}}chet$ differentiable norm or its dual $E^*$ has the Kadec-Klee property. We also obtain that $\{x_n\}$ strongly converges to some $z{\in}F$ in Banach space E if K is a compact subset of E or there exists one map $T{\in}\{T_{n};n=1,2,...\}$ satisfy some compact conditions such as T is semi compact or satisfy Condition A or $lim_{n{\rightarrow}{\infty}}d(x_{n},F(T))=0$ and so on.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1443-1482
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• 2008

In this paper we define a Myller configuration in a Finsler space and use some special configurations to obtain results about Finsler subspaces. Let $F^{n}$ = (M,F) be a Finsler space, with M a real, differentiable manifold of dimension n. Using the pull back bundle $({\pi}^{*}TM,\tilde{\pi},\widetilde{TM})$ of the tangent bundle $(TM,{\pi},M)$ by the mapping $\tilde{\pi}={\pi}/TM$ and the Cartan Finsler connection of a Finsler space, we obtain an orthonormal frame of sections of ${\pi}^{*}TM$ along a regular curve in $\widetilde{TM}$ and a system of invariants, geometrically associated to the Myller configuration. The fundamental equations are written in a very simple form and we prove a fundamental theorem. Important lines in a Finsler subspace are defined like special lines in a Myller configuration, geometrically associated to the subspace: auto parallels, lines of curvature, asymptotes. Torse forming vector fields with respect to the Cartan Finsler connection are characterized by means of the invariants of the Frenet frame of a versor field along a curve, and the new notion of torse forming vector fields in the sense of Myller is introduced. The particular cases of concurrence and parallelism in the sense of Myller are completely studied, for vector fields from the distribution $T^m$ of the Myller configuration and also from the normal distribution $T^p$.

• Journal of Educational Research in Mathematics
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• v.8 no.2
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• pp.495-507
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• 1998

This article intends to review what problems the terms in calculus have and how those problems are caused. For this purpose We make examinations on the considerations in the analysis of mathematical terminology, which includes the problems of general and technical terms, the meaning and the boundary of words, their consistency, the name and meaning, concept and their concept images, translations and qwerty effects. And in chapter 3, We analyse the textbook which are currently used, through which I was able to find out that the terms in calculus have some problems, In other words, the key terms such as "differentiable", "differential coefficient", "differential" have their roots in the term "differential" but the term "derived function" is very distinct from other terms and thus obstructs the consistency of terms. And the central term "differential" is being used without clear definition. In particular, the fact that "differential", when used in its arbitrary definition, has the image of "splitting minutely" can be an obstacle to understanding the exact concepts of calculus. In chapter 4, We make a review on the history of calculus and the term "differential" currently used in modern mathematics so that I can identify the origin of the problem connected with the usage of the term "differential". We should recognize the specified problems and its causes and keep their instructional implications in mind. Furthermore, following researches and discussions should be made on whether the terminology system of calculus should be reestablished and how the reestablishment should be made.e terminology system of calculus should be reestablished and how the reestablishment should be made.

• Proceedings of the KIEE Conference
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• 1997.07c
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• pp.1009-1011
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• 1997

This paper presents an optimization method which determines locations and size of capacitors simultaneously while minimizing power losses and improving voltage profile in radial distribution systems. Especially, the cost function associated with capacitor placement is considered as step function due to banks of standard discrete capacities. Genetic algorithms(GA) are used to obtain efficiently the solution of the cost function associated with capacitors which is non-continuous and non-differentiable function. The strings in GA consist of the node number index and size of capacitors to be installed. The length mutation operator, which is able to change the length of strings in each generation, is used. The proposed method which determines locations and size of capacitors simultaneously can reduce power losses and improve' voltage profile with capacitors of minimum size. Its efficiency is proved through the application in radial distribution systems.

• Kyungpook Mathematical Journal
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• v.56 no.3
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• pp.777-789
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• 2016

In this paper, we establish some new oscillation criteria for the second-order forced nonlinear functional dynamic equations with damping term $$(r(t)x^{\Delta}(t))^{\Delta}+q({\sigma}(t))x^{\Delta}(t)+p(t)f(x({\tau}(t)))=e(t)$$, and $$(r(t)x^{\Delta}(t))^{\Delta}+q(t)x^{\Delta}(t)+p(t)f(x({\sigma}(t)))=e(t)$$, on a time scale ${\mathbb{T}}$, where r(t), p(t) and q(t) are real-valued right-dense continuous (rd-continuous) functions [1] defined on ${\mathbb{T}}$ with p(t) < 0 and ${\tau}:{\mathbb{T}}{\rightarrow}{\mathbb{T}}$ is a strictly increasing differentiable function and ${\lim}_{t{\rightarrow}{\infty}}{\tau}(t)={\infty}$. No restriction is imposed on the forcing term e(t) to satisfy Kartsatos condition. Our results generalize and extend some pervious results [5, 8, 10, 11, 12] and can be applied to some oscillation problems that not discussed before. Finally, we give some examples to illustrate our main results.

• Journal of Digital Contents Society
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• v.18 no.5
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• pp.969-976
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• 2017

This paper proposes the learning method of an artificial neural network and a convolutional neural network using the WFSO algorithm developed as an optimization algorithm. Since the optimization algorithm searches based on a number of candidate solutions, it has a drawback in that it is generally slow, but it rarely falls into the local optimal solution and it is easy to parallelize. In addition, the artificial neural networks with non-differentiable activation functions can be trained and the structure and weights can be optimized at the same time. In this paper, we describe how to apply WFSO algorithm to artificial neural network learning and compare its performances with error back-propagation algorithm in multilayer artificial neural networks and convolutional neural networks.

• Honam Mathematical Journal
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• v.1 no.1
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• pp.1-9
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• 1979

Positive Local Coordmate($(x^1,x^2,{\cdots}x^n)$)을 갖는 Oriented Manifold M을 생각한다. M이 Compact Carrier를 갖는 경우, M위의 n차(次) Differential Form ${\phi}^{(n)}$의 적분(積分)을 $${\int}{\phi}^{(n)}=\sum_{\alpha}{\int}_{-{\infty}}^{\infty}{\cdots}{\int}_{-{\infty}}^{\infty}f_{\alpha}{\phi}^{(n)}dx^1{\cdots}dx^n$$로 정의(定義)하며 (정의(定義) 7), M위의 p 차(次)의 Differential form $\beta^{(p)}$와 Differential simplex $S^{(p)}=(S^{(p)},\;{\pi},\;{\varepsilon})$에 대하여 $S^{(p)}$위의 $\beta^{(p)}$의 적분(積分)을 $${\int}_{^{(p)}S}{\beta}^{(p)}={\int}_{S^{(p)}}{\varepsilon}{\pi}^*{\beta}^{(p)}={\int}_{E^p}f{\cdot}{\varepsilon}{\cdot}{\pi}^*{\beta}^{(p)}$$로 정의(定義)한다 (정의(定義) 9). 단(但) $\bar{S}^{(p)}$는 $S^{(p)}=(p_0{\cdot}p_1{\cdots}p_p)$에 의(依)하여 Spanning 되는 $E^p$의 Subspace이고 f는 $\bar{S}^{(p)}$의 특성함수(特性函數)이다. 이때 (n-1)차(次)의 Differential Form ${\beta}^{(n-1)}$이 Compart인 Carrier를 가지면 ${\int}d{\beta}^{(n-1)}=0$이 됨을 고찰(考察)하며(정리(定理 8), (p-1)차(次) Differential Form ${\beta}^{(p-1)$과 p차(次) Differential Chain $C^{(p)}$에 관(關)하여 $${\int}_{C^{(p)}}d{\beta}^{(p-1)}={\int}_{{\partial}C^{(p)}}{\beta}^{(p-1)}$$이 성립(成立)함을 구명(究明)하려 한다(정리(定理) 10).

• Proceedings of the KIEE Conference
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• 2007.07a
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• pp.848-849
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• 2007

This paper presents an efficient approach for solving the economic dispatch (ED) problems with valve-point effects using differential evolution (DE). A DE, one of the evolutionary algorithms (EAs), is a novel optimization method capable of handling nonlinear, non-differentiable, and nonconvex functions. And an efficient constraints treatment method (CTM) is applied to handle the equality and inequality constraints. The resultant DE-CTM algorithm is very effective in solving the ED problems with nonconvex cost functions. To verify the superiority of the proposed method, a sample ED problem with valve-point effects is tested and its results are compared with those of previous works. The simulation results clearly show that the proposed DE-CTM algorithm outperforms other state-of-the-art algorithms in solving ED problems with valve-point effects

• Journal of the Korean Mathematical Society
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• v.58 no.6
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• pp.1327-1345
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• 2021

In this paper, we are concerned with a Liouville-type result of the nonlinear integral equation of Chern-Simons-Higgs type $$u(x)=\vec{\;l\;}+C_{\ast}{{\displaystyle\smashmargin{2}{\int\nolimits_{\mathbb{R}^n}}}\;{\frac{(1-{\mid}u(y){\mid}^2){\mid}u(y){\mid}^2u(y)-\frac{1}{2}(1-{\mid}u(y){\mid}^2)^2u(y)}{{\mid}x-y{\mid}^{n-{\alpha}}}}dy.$$ Here u : ℝⁿ → ℝ^k is a bounded, uniformly continuous function with k ⩾ 1 and 0 < α < n, $\vec{\;l\;}{\in}\mathbb{R}^k$ is a constant vector, and C_* is a real constant. We prove that ${\mid}\vec{\;l\;}{\mid}{\in}\{0,\frac{\sqrt{3}}{3},1\}$ if u is the finite energy solution. Further, if u is also a differentiable solution, then we give a Liouville type theorem, that is either $u{\rightarrow}\vec{\;l\;}$ with ${\mid}\vec{\;l\;}{\mid}=\frac{\sqrt{3}}{3}$, when |x| → ∞, or $u{\equiv}\vec{\;l\;}$, where ${\mid}\vec{\;l\;}{\mid}{\in}\{0,1\}$.

• The Journal of the Korea Contents Association
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• v.8 no.12
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• pp.160-167
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• 2008

Animations consist of the created artificial images. To interpret of the meaning from analyzing the style of main images is an important element in understanding of animations. Therefore, to analyze images expressed in works of Miyazaki-hayao, this study substitutes the concept of 'hybridity' for images of characters, backgrounds, and mechanics created by him and explores how they are expressed, how they produce symbolic meanings and functions. It is confirmed that main images in selected works as a scope of research have hybridity of images between 'past, present, and future', 'eastern elements and western elements', 'real and virtual', 'human beings and animal' in narrative. From these results, it is concluded that because of hybridity between images, he can present fresh pleasures to spectators, simultaneously communicate thoughtful messages above mere enjoyment, which is a differentiable point with works of other directors.