• 대한수학회지
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• 제41권5호
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• pp.821-864
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• 2004

Both parametric and parameter-free necessary and sufficient optimality conditions are established for a class of nondiffer-entiable nonconvex optimal control problems with generalized fractional objective functions, linear dynamics, and nonlinear inequality constraints on both the state and control variables. Based on these optimality results, ten Wolfe-type parametric and parameter-free duality models are formulated and weak, strong, and strict converse duality theorems are proved. These duality results contain, as special cases, similar results for minmax fractional optimal control problems involving square roots of positive semi definite quadratic forms, and for optimal control problems with fractional, discrete max, and conventional objective functions, which are particular cases of the main problem considered in this paper. The duality models presented here contain various extensions of a number of existing duality formulations for convex control problems, and subsume continuous-time generalizations of a great variety of similar dual problems investigated previously in the area of finite-dimensional nonlinear programming.

• Journal of applied mathematics & informatics
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• 제31권5_6호
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• pp.835-852
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• 2013

In this paper, we have considered a class of constrained non-smooth multiobjective fractional programming problem involving support functions under generalized convexity. Also, second order Mond Weir type dual and Schaible type dual are discussed and various weak, strong and strict converse duality results are derived under generalized class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions. Also, we have illustrated through non-trivial examples that class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions extends the definitions of generalized convexity appeared in the literature.

• 한국수학교육학회지시리즈D:수학교육연구
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• 제14권3호
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• pp.211-218
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• 2010

It is a truism that mathematics is about relations (cf. [Halford, G. S. (1999). The properties of representations used in higher cognitive processes: Developmental implications. In: Sigel, I. E. (Ed.), The Development of Mental Representation: Theories and Applications (pp. 147-168). Mahwah, New Jersey: Erlbaum]). In this article we are considering few problems related to the Viviani's and Routh's Theorems. All Problems are connected by the relation which exists between the distances of the point inside the triangle to it sides. We show how reasoning about the relations could lead the student's problem solving process and give easy to understand solutions of the problems. Among the problems being considered are the proof of the Converse to Viviani's Theorem, the formulas for areas of all figures formed by the sides of triangle and its cevians.

• Korean Journal of Mathematics
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• 제15권2호
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• pp.87-100
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• 2007

We introduce a concept of countably strong inclusions ${\triangleleft}$ and that of ${\triangleleft}-{\sigma}$-ideals and prove that the subframe $S({\triangleleft})$ of the frame ${\sigma}IdL$ of ${\sigma}$-ideals is a Lindel$\ddot{o}$fication of a frame L. We also deal with conditions for which the converse holds. We show that any countably approximating regular $D({\aleph}_1)$ frame has the smallest countably strong inclusion and any frame which has the smallest $D({\aleph}_1)$ Lindel$\ddot{o}$fication is countably approximating regular $D({\aleph}_1)$.

• 한국실내디자인학회논문집
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• 제19호
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• pp.30-37
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• 1999

This study presents a methods on the construction of integrated system for the purpose of automation of design plans, calculation of quantity of materials and estimation by abstracting information on building materials which is produced on the course of three dimension modeling by using computer. Therefore, an object oriented methodology is introduced to compose design informations in three dimension, space for unifying building informations, and expressing properties of building factors and materials, and to construct a database for computers to recognize architecture informations. An object indicates a conceptual individual existing in real world or existence of individual and necessity in composing a building could be called as objects such as column, wall, beam, slab, door and window and these contain materiality and immateriality. It is systemized to which properties of these building's objects are installed by the user of computer and by API(Application Programming Interface), chosen informations automatically converse to each unit work such as design plan structure plan, calculation of amount of materials, etc.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2007년도 춘계학술대회논문집
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• pp.934-937
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• 2007

This study focused on investigating the effect of aligned cellulose fibers to the performance of EAPap actuator. The performance of EAPap is dependant on the material direction of cellulose film. Electrospinning was used to improve material directionality of EAPap. DMAc cellulose solution which cotton pulp was resolved in DMAc solvent was used for electrospinning cellulose film. To increase directionality of nano fibers, the Electrospun film was stretched by 10 % strain during drying process. Induced in-plane strain of Electrospun EAPap was proportional to the applied voltage and larger than that of spincast EAPap. It is concluded that the performance of EAPap was improved by aligning cellulose fibers.

• 조명전기설비학회논문지
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• 제27권6호
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• pp.68-74
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• 2013

Induction-heated system is innovative system which applied IH(Induction Heating) magnetic induction heating generated from induction-heated metallic package and high-frequency power circuit technique for thermal converse technique. In this occurs not burning, so that the working environment and deterioration of products can be improved. This technique is used high frequency inverter. By using high frequency inverter high frequency in the range of kHz can be made with conventional alternative current. In this contribution IGBT module is used for high frequency inverter. In this paper are discussed analysis of characteristics according to the each frequency and produced Flat plate induction heating system using 1.5kW-class half-bridge resonant inverter. In addition, operating characteristics of the system to changes in the distance between the coil and the heater, applications of system are also discussed.

• 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.

• 무역상무연구
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• 제42권
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• pp.3-32
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• 2009

As we know, Incoterms are reflecting only the greatest common measure of practice in int'l trade. Therefore we can think them as the commercial practice most widely used in trade. They contain a number of detail under converse mirror image terms because they connect each other like a thread as to all oversea's commercial transactions between importing buyers and exporting sellers. Therefore they afford convenience to exporters and importers in the world because they tell the parties what to do as to transfer of risk and costs, responsibilities in connection with delivery of the goods. Nonetheless, since Incoterms 1936, they have been periodically revising in order to represent contemporary commercial practice. Therefore, according to change of Int'l trade environment, ICC plans to modify to the 2000 Incoterms. I hope to contribute to revising works by reference of above mentioned revision, that to say, aspects of provision, reflection of prevailing most commonly used, promotion of status as uniform rules, provision of convenience of int'l buyers and sellers. harmony with existing int'l instruments, presentation of criteria in variation of Incoterms.

• 대한수학회논문집
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• 제25권1호
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• pp.139-147
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• 2010

A generalized nondifferentiable fractional optimization problem (GFP), which consists of a maximum objective function defined by finite fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions, is considered. Recently, Kim et al. [Journal of Optimization Theory and Applications 129 (2006), no. 1, 131-146] proved optimality theorems and duality theorems for a nondifferentiable multiobjective fractional programming problem (MFP), which consists of a vector-valued function whose components are fractional functions with differentiable functions and support functions, and a constraint set defined by differentiable functions. In fact if $\overline{x}$ is a solution of (GFP), then $\overline{x}$ is a weakly efficient solution of (MFP), but the converse may not be true. So, it seems to be not trivial that we apply the approach of Kim et al. to (GFP). However, modifying their approach, we obtain optimality conditions and duality results for (GFP).