• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.729-737
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• 2008

In this paper we characterize multi-Jensen functions f : $V^n\;{\rightarrow}\;W$, where n is a positive integer, V, W are commutative groups and V is uniquely divisible by 2. Moreover, under the assumption that f : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$ is Borel measurable, we obtain representation of f (respectively, f, g, h : $\mathbb{R}\;{\rightarrow}\;\mathbb{R}$) such that the Jensen difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;f(x)\;-\;f(y)$$ (respectively, the Pexider difference $$2f\;\(\frac{x\;+\;y}{2}\)\;-\;g(x)\;-\;h(y))$$ takes values in a countable subgroup of $\mathbb{R}$.

• Transactions of the Korean Society of Automotive Engineers
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• v.1 no.1
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• pp.131-139
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• 1993

Low cycle fatigue characteristics of cast aluminum alloy A356 with a yield strength and ultimate strength of 229 and 283 MPa respectively was evaluated using smooth axial specimen under strain controlled condition. Reversals to failure ranged from 16 to 107. The cast aluminum alloy exhibited cyclically strain-gardening behavior. The results of low cycle fatigue tests indicated that the conventional low cycle fatigue tests indicated that the conventional low cycle fatigue life model was not a satisfactory representation of the data. This occurred because the elastic strain-life curve was not-log-log linear and this phenomena caused a nonconservative and unsafe fatigue life prediction at both extremes of long and short lives. A linear log-log total strain-life model and a bilinear log-log elastic strain-life model were proposed in order to improve the representation of data compared to the conventional low cycle fatigue life model. Both proposed fatigue life models were statistically analyzed using F tests and successfully satisfied. However, the low cycle fatigue life model generated by the bilinear log-log elastic strain-life equation yielded a discontinuous curve with nonconservatism in the region of discontinuity. Among the models examined, the linear log-log total strain-life model provided the best representation of the low cycle fatigue data. Low cycle fatigue life prediction method based on the local strain approach could conveniently incorporated both proposed fatigue life models.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.9-9
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• 2003

Let $\Omega$ be a bounded, open, and polygonal domain in $R^2$ with re-entrant corners. We consider the following Partial Differential Equations: $$(I-\nabla\nabla\cdot+\nabla^{\bot}\nabla\times)u\;=\;f\;in\;\Omega$$, $$n\cdotu\;0\;0\;on\;{\Gamma}_{N}$$, $${\nabla}{\times}u\;=\;0\;on\;{\Gamma}_{N}$$, $$\tau{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$, $$\nabla{\cdot}u\;=\;0\;on\;{\Gamma}_{D}$$ where the symbol $\nabla\cdot$ and $\nabla$ stand for the divergence and gradient operators, respectively; $f{\in}L^2(\Omega)^2$ is a given vector function, $\partial\Omega=\Gamma_{D}\cup\Gamma_{N}$ is the partition of the boundary of $\Omega$; nis the outward unit vector normal to the boundary and $\tau$represents the unit vector tangent to the boundary oriented counterclockwise. For simplicity, assume that both $\Gamma_{D}$ and $\Gamma_{N}$ are nonempty. Denote the curl operator in $R^2$ by $$\nabla\times\;=\;(-{\partial}_2,{\partial}_1$$ and its formal adjoint by $${\nabla}^{\bot}\;=\;({-{\partial}_1}^{{\partial}_2}$$ Consider a weak formulation(WF): Find $u\;\in\;V$ such that $$a(u,v):=(u,v)+(\nabla{\cdot}u,\nabla{\cdot}v)+(\nabla{\times}u,\nabla{\times}V)=(f,v),\;A\;v{\in}V$$. (2) We assume there is only one singular corner. There are many methods to deal with the domain singularities. We introduce them shortly and we suggest a new Finite Element Methods by using Singular representation for the solution.

• Journal of Korea Multimedia Society
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• v.10 no.8
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• pp.1017-1028
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• 2007

In this paper we propose an effective method to represent, store, and retrieve video streams efficiently from a video database. We extract features from each video frame, normalize the feature values, and represent them as values in the range [0,1]. In this way a video frame with f features can be represented by a point in the f-dimensional space $[0,1]^f$, and thus the video stream is represented by a trail of points in the multidimensional space. The video stream is partitioned into video segments based on camera shots, each of which is represented by a trend vector which encapsulates the moving trend of points in a segment. The video stream query is processed depending on the comparison of those trend vectors. We examine our method using a collection of video streams that are composed of sports, news, documentary, and educational videos. Experimental results show that our trend vector representation reduces a reconstruction error remarkably (average 37%) and the retrieval using a trend vector achieves the high precision (average 2.1 times) while maintaining the similar response time and recall rate as existing methods.

• Bulletin of the Korean Mathematical Society
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• v.20 no.1
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• pp.9-13
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• 1983

M$_{n}$(F) denotes the set of all n*n matrices over F={0, 1}. For a, b.mem.F, define a+b=max{a, b} and ab=min{a, b}. Under these operations a+b and ab, M$_{n}$(F) forms a multiplicative semigroup (see [1], [4]) and we call it the semigroup of the n*n boolean matrices over F={0, 1}. Since the semigroup M$_{n}$(F) is the matrix representation of the semigroup B$_{n}$ of the binary relations on the set X with n elements, we may identify M$_{n}$(F) with B$_{n}$ for finding all D-classes.l D-classes.

• Proceedings of the Korean Institute of Interior Design Conference
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• 2006.11a
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• pp.115-120
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• 2006

This study concentrates on a new idea that is formulated as a creative space recognition in contemporary architecture and painting. It is stimulated from Deleuze's philosophy, which is expressed with the philosophical instrument, "Non-Representation". After discussing the concept of non-representation used in Deleuze's philosophy, case example in contemporary architecture are analysed to comparatively Investigate the relationship between the architectures by Rem Koolhaas and painting by Francis Bacon. Therefore, he founds expressions of "diagram" and "movement" in painting of F. Bacon. Diagram meansit is a power that is comprised of various points of wiew with the kind experiences that one has in life. Movement that were extracted form the Instrument in space recognition of Deleuze's panting theory were of topology, insertion of geometry, reiteration of layers, transparency and translucency, reflection effect.

• Journal of the Korean Society for Precision Engineering
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• v.13 no.4
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• pp.43-52
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• 1996

This paper describes interactive computer procedures for design the forming sequences in cold forging. This system is implemented on the personal computer and its environment is a commercial AutoCAD system. The programming language. AutoLISP, was used for the configuration of the system. Since the process of metal forming can be considered as a transformation of geometry, treatment of the geometry of the part is a key in process planning. To recognize the part section geometry, the section entity representation, the section coordinate-redius representation and the section primitive geometru were adopted. This system includes six major modules such as input module, forging design module, forming sequence design module, die design module, FEM verification module and output module which are used independently or in all. The sequence drawing wigh all dimensions, which includes the dimensional tolerances and the proper sequence of operations, can generate under the environment of AutoCAD. The acceptable forming sequences can be verified further, using the FE simulation.

• Honam Mathematical Journal
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• v.19 no.1
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• pp.21-27
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• 1997

We shall define three kinds of points for algebraic varieties associated to the center 3 of U(L) which is the universal enveloping algebra of a finite-dimensional modular Lie algebra over an algebraically closed field F of prime characteristic p. We announce here that $sp_4$(F) with p = 2 has a subregular point.

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.667-677
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• 2017

Let $F{\subseteq}{\mathbb{P}}^3$ be a smooth surface of degree $3{\leq}d{\leq}9$ whose equation can be expressed as either the determinant of a $d{\times}d$ matrix of linear forms, or the pfaffian of a $(2d){\times}(2d)$ matrix of linear forms. In this paper we show that F supports families of dimension p of pairwise non-isomorphic, indecomposable, Ulrich bundles for arbitrary large p.

• Honam Mathematical Journal
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• v.33 no.3
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• pp.381-391
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• 2011

One of the main interesting things of a matroid theory is the representability by a matroid from a matrix over some field F. The representability of uniform matroid $U_{m,n}$ over some field are studied by many authors. In this paper we construct a matrix representing $U_{3,6}$ over the field GF(4). Also we find out matrix of the affine matroid AG(2, 3) over the field GF(4).