• Journal of applied mathematics & informatics
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• 제7권1호
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• pp.1-28
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• 2000

In the present paper, we introduce fundamental results in the KKM theory for G-convex spaces which are equivalent to the Brouwer theorem, the Sperner lemma, and the KKM theorem. Those results are all abstract versions of known corresponding ones for convex subsets of topological vector spaces. Some earlier applications of those results are indicated. Finally, We give a new proof of the Himmelberg fixed point theorem and G-convex space versions of the von Neumann type minimax theorem and the Nash equilibrium theorem as typical examples of applications of our theory.

• 대한수학회논문집
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• 제38권4호
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• pp.1045-1061
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• 2023

Using variational methods, Krasnoselskii's genus theory and symmetric mountain pass theorem, we introduce the existence and multiplicity of solutions of a parameteric local equation. At first, we consider the following equation $$\{-div[a(x,{\mid}{\nabla}u{\mid}){\nabla}u]\,=\,{\mu}(b(x){\mid}u{\mid}^{s(x)-2}-{\mid}u{\mid}^{r(x)-2})u\;in\;{\Omega},\\u\,=0\,on\;{\partial}{\Omega},$$ where Ω⊆ ℝ^N is a bounded domain, µ is a positive real parameter, p, r and s are continuous real functions on ${\bar{\Omega}}$ and a(x, ξ) is of type |ξ|^p(x)-2. Next, we study boundedness and simplicity of eigenfunction for the case a(x, |∇u|)∇u = g(x)|∇u|^p(x)-2∇u, where g ∈ L^∞(Ω) and g(x) ≥ 0 and the case $a(x,\,{\mid}{\nabla}u{\mid}){{\nabla}u}\,=\,(1\,+\,{\nabla}u{\mid}^2)^{\frac{p(x)-2}{2}}{\nabla}u$ such that p(x) ≡ p.

• International journal of advanced smart convergence
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• 제13권2호
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• pp.7-15
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• 2024

6G network technology represents the next generation of communications, supporting high-speed connectivity, ultra-low latency, and integration with cutting-edge technologies, such as the Internet of Things (IoT), virtual reality, and autonomous vehicles. These advancements promise to drive transformative changes in digital society. However, as technology progresses, the demand for efficient data transmission and energy management between smart devices and network equipment also intensifies. A significant challenge within 6G networks is the optimization of interactions between satellites and smart devices. This study addresses this issue by introducing a new game theory-based technique aimed at minimizing system-wide energy consumption and latency. The proposed technique reduces the processing load on smart devices and optimizes the offloading decision ratio to effectively utilize the resources of Low-Earth Orbit (LEO) satellites. Simulation results demonstrate that the proposed technique achieves a 30% reduction in energy consumption and a 40% improvement in latency compared to existing methods, thereby significantly enhancing performance.

• 대한수학회지
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• 제37권6호
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• pp.901-913
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• 2000

This is a summary of results involving the development of a theory of an index of an isolated critical point for densely defined nonlinear operators of type (S(sub)+)(sub)0,L. This index theory is associated with a degree theory, for such operators, whch has been recently developed by the authors.

• 대한화학회지
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• 제21권5호
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• pp.339-352
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• 1977

소성변형에 대한 저자들의 이론(제1보)을 요업재료, 금속, 합금 및 단결정들에 적용하였다. 그 결과 다중 결정에서는 dislocation 운동과 grain boundary 운동이 실험조건에 따라 함께 또는 분리되어 나타나는 반면 단결정에서는 dislocation 운동만 나타났다. 유동식에 나타나는 파라미터$({\alpha}_{d1},\;1/{\beta}_{d1})와\;({\alpha}_{gj}/X_{gj},\;1/{\beta}_{gj})$ (j = 1 or 2) 및 활성화엔탈피 ${\Delta}H_{k1}^{\neq}$ (k = d 혹은 g)를 구하여 예측한 소성변형은 실험과 잘 일치함을 보았다. 여기서 첨자 d1는 첫번째의 dislocation 유동단위, gj는 j번째 grain boundary 유동단위를 나타낸다. 활성화엔탈피에 대하여 ${\Delta}H_{d1}^{\neq}$는 bulk의 자체확산에 대한 활성화엔탈피와 일치하고 ${\Delta}H_{g1}^{\neq}$는 grain boundary 자체확산에 대한 활성화엔탈피와 일치하였다. 이 사실은 저자들의 이론의 정당성을 보이고 있다.

• 한국지반공학회:학술대회논문집
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• 한국지반공학회 1999년도 연약지반처리위원회 학술세미나
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• pp.36-47
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• 1999

Terzaghi's theory of one-dimensional consolidation is restricted in its applicability to relatively thin layers and small incremental loading. Because it is assumed to infinitesimal strain and linear material function. For this reason, Gibson et al established a rigorous formulation for the one-dimensional nonlinear finite strain consolidation theory. There are some difficulties in the application of finite strain consolidation theory. The developed program consisted of several forms and modules. These forms and modules with graphic-user-interfaced format are used in analysis of consolidation practices. For the purpose of verification of developed program. the results of case study and prediction of developed program are compared. The results of comparison is fairly well with prediction and measured data. And with varying finite strain consolidation parameter, g(e) or λ(e), the sensitivity of predicted values were examined.

• 대한수학회보
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• 제35권4호
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• pp.641-652
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• 1998

Chung and et al. ([2].1991) introduced a new concept of a manifold, denoted by $^{\ast}g-SEX_n$, in Einstein's n-dimensional $^{\ast}g$-unified field theory. The manifold $^{\ast}g-SEX_n$ is a generalized n-dimensional Riemannian manifold on which the differential geometric structure is imposed by the unified field tensor $^{\ast}g^{\lambda \nu}$ through the SE-connection which is both Einstein and semi-symmetric. In this paper, they proved a necessary and sufficient condition for the unique existence of SE-connection and sufficient condition for the unique existence of SE-connection and presented a beautiful and surveyable tensorial representation of the SE-connection in terms of the tensor $^{\ast}g^{\lambda \nu}$. Recently, Chung and et al.([3],1998) obtained a concise tensorial representation of SE-curvature tensor defined by the SE-connection of $^{\ast}g-SEX_n$ and proved deveral identities involving it. This paper is a direct continuations of [3]. In this paper we derive surveyable tensorial representations of constracted curvature tensors of $^{\ast}g-SEX_n$ and prove several generalized identities involving them. In particular, the first variation of the generalized Bianchi's identity in $^{\ast}g-SEX_n$, proved in theorem (2.10a), has a great deal of useful physical applications.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2008년도 추계학술대회 논문집
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• pp.551-552
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• 2008

• Kyungpook Mathematical Journal
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• 제59권3호
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• pp.563-589
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• 2019

Let W and V be manifolds of dimension m + 2, M a locally flat submanifold of V whose dimension is m. Let $f:W{\rightarrow}V$ be a homotopy equivalence. The problem we study in this paper is the following: When is f homotopic to another homotopy equivalence $g:W{\rightarrow}V$ such that g is transverse regular along M and such that $g{\mid}g^{-1}(M):g^{-1}(M){\rightarrow}M$ is a simple homotopy equivalence? $L{\acute{o}}pez$ de Medrano (1970) called this problem the weak h-regularity problem. We solve this problem applying the codimension two surgery theory developed by the author (1973). We will work in higher dimensions, assuming that $$m{\geq_-}5$$.

• 한국도서관정보학회지
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• 제28권
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• pp.447-475
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• 1998

We are seeing a shift of the focus of information service from system-centered(data-centered or intermediary-centered) a n.0, pproach to user-centered a n.0, pproach. Sense-making theory is one of the user- centered a n.0, pproaches. This study focused on user-centered information service paradigm concepts of Dervin's sense-making theory and interpreting sense-making theory in the practical context of library services. The sense-making theory is basically a cognitive a n.0, pproach to information-seeking, in that it recognizes information as something that involves internal cognitive processes. The user of information becomes the focus in this sense-making model. The sense-making theory sees information as subjective, situational, and cognitive. It focuses on understanding information within specific contexts and on understanding how information needs develop and how they are satisfied. It regards the user not as a passive receive of external information but as the center in a active, ongoing process of change. It related to the information needs of users. Dervin's method for studying information needs employs the 'situation-gap-use' metaphor. All information needs stem from a discontinuity or 'gap! in one's knowledge. Dervin believes that information needs can be addressed by understanding the process that each individual goes through in experiencing a gap, in trying to resolve it, and in gaining something (especially new knowledge) from the experience. Sense-making is a process; 'sense' is the product of this process. Sense includes 'knowledge'. However, it includes a host of other subjective factors that reflect an individual's interpretations of a situation including intuitions, opinions, hunches, effective responses, evaluations, questions, etc. For several reasons, however, difficulties are encountered if one attempts a more substantial assessment of the theory. First, it has not yet crystallized into a well-defined theory. Secondly, though the theory has aroused general interest, e.g. within LIS, detailed discussion of its strong and weak points is still lacking. A third source of difficulty is that the basic assumptions of the theory have been explicated metaphorically. If sense-making theory is to be really useful, it needs to be interpreted for library settings. But we have found no attempt to construct an information service based on the theory. Because the research tradition is still relatively young, there are many unanswered questions connected, e.g. with the design of information systems. In any case, e.g. intermediary access systems would be more efficient and effective it their planning could be founded on the user-centered a n.0, pproach.