• Journal of the Korean Mathematical Society
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• v.45 no.1
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• pp.1-27
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• 2008

We introduce a new concept of convex spaces and a multimap class K having certain KKM property. From a basic KKM type theorem for a K-map defined on an convex space without any topology, we deduce ten equivalent formulations of the theorem. As applications of the equivalents, in the frame of convex topological spaces, we obtain Fan-Browder type fixed point theorems, almost fixed point theorems for multimaps, mutual relations between the map classes K and B, variational inequalities, the von Neumann type minimax theorems, and the Nash equilibrium theorems.

• The Journal of Korean Academy of Orthopedic Manual Physical Therapy
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• v.2 no.1
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• pp.39-49
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• 1996

The techniques of joint mobilization and traction are used to improve joint mobility or to decrease pain by restoring accessory movements to the shoulder joints and thus allowing full, nonrestriced, pain-free range of motion. In the glenohumeral joint, the humeral head would be the convex surface, while the glenoid fossa would be the concave surface. The medial end of the clavicle is concave anterioposteriorly and convex superioinferiorly, the articular surface of the sternum is reciprocally curved. The acromioclavicular joint is a plane synovial joint between a small convex facet on lateral end of the clavicle and a small concave facet on the acromion of the scapula. The relationship between the shape of articulating joint surface and the direction of gliding is defined by the convex-concave rule. If the concave joint surface is moving on a stationary convex surface, gliding occur in the same direction as the rolling motion. If the convex surface is moving on a stationary concave surface, gliding will occur in an opposite direction to rolling. Hypomobile shoulder joint are treated be using a gliding technique.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.373-383
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• 2010

New integral inequalities concerning $\gamma$-convex and $\gamma$-concave functions are presented.

• Journal of the Korean Mathematical Society
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• v.36 no.4
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• pp.823-823
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• 1999

• Bulletin of the Korean Mathematical Society
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• v.58 no.3
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• pp.721-727
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• 2021

The convex hull of a generic triple of boundary points has non-zero finite volume in complex hyperbolic 2-space.

• Journal of Advanced Navigation Technology
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• v.20 no.3
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• pp.203-209
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• 2016

Among the various fields in the communications, navigation, and surveillance/air traffic management (CNS/ATM) scheme, the surveillance field, which includes an automatic dependent surveillance - broadcast (ADS-B) system and a multilateration (MLAT) system, is implemented using satellite and digital communications technology. These systems provide better performance than radar, but still incur position error. To reduce the error, we propose an efficient information fusion method called the reweighted convex combination method for ADS-B and MLAT systems. The reweighted convex combination method improves aircraft tracking performance compared to the original convex combination method by readjusting the weights given to these systems. In this paper, we prove that the reweighted convex combination method always provides better performance than the original convex combination method. Performance from the fusion of ADS-B and MLAT improves an average of 51.51% when compared to the original data.

• Journal of the Korea Society of Computer and Information
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• v.25 no.7
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• pp.75-83
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• 2020

We consider the D2D utility optimization problem in the cellular system. More specifically, we develop a concave function decision rule which reduces the complexity of non-convex optimization problem. Typically, utility function, which is a function of the signal and the interference, is non-convex. In this paper, we analyze the utility function from the interference perspective. We introduce the 'relative interference' and the 'interference majorization'. The relative interference captures the level of interference at D2D receiver's perspective. The interference majorization approximates the interference by applying the major interference. Accordingly, we propose a concave function decision rule, and the corresponding convex optimization solution. Simulation results show that the utility function is concave when the relative interference is less than 0.1, which is a typical D2D usage scenario. We also show that the proposed convex optimization solution can be applied for such relative interference cases.

• The Journal of the Acoustical Society of Korea
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• v.18 no.3E
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• pp.37-43
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• 1999

In this paper, we present a new technique for the optimal local decomposition of convex structuring elements on a hexagonal grid, which are used as templates for morphological image processing. Each basis structuring element in a local decomposition is a local convex structuring element, which can be contained in hexagonal window centered at the origin. Generally, local decomposition of a structuring element results in great savings in the processing time for computing morphological operations. First, we define a convex structuring element on a hexagonal grid and formulate the necessary and sufficient conditions to decompose a convex structuring element into the set of basis convex structuring elements. Further, a cost function was defined to represent the amount of computation or execution time required for performing dilations on different computing environments and by different implementation methods. Then the decomposition condition and the cost function are applied to find the optimal local decomposition of convex structuring elements, which guarantees the minimal amount of computation for morphological operation. Simulation shows that optimal local decomposition results in great reduction in the amount of computation for morphological operations. Our technique is general and flexible since different cost functions could be used to achieve optimal local decomposition for different computing environments and implementation methods.

• KIPS Transactions on Computer and Communication Systems
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• v.3 no.1
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• pp.1-6
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• 2014

Most of the previous algorithms focus on computing the convex hull for a set of points. In this paper, we present a method for approximating the convex hull for a set of spheres with various radii in discrete space. Computing the convex hull for a set of spheres is a base technology for many applications that study structural properties of molecules. We present a voxel map data structures, where the molecule is represented as a set of spheres, and corresponding algorithms. Based on CUDA programming for using the parallel architecture of GPU, our algorithm takes less than 40ms for computing the convex hull of 6,400 spheres in average.

• The Pure and Applied Mathematics
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• v.25 no.1
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• pp.49-57
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• 2018

We have introduced two new notions of convexity and closedness in functional analysis. Let X be a real normed space, then $C({\subseteq}X)$ is functionally convex (briefly, F-convex), if $T(C){\subseteq}{\mathbb{R}}$ is convex for all bounded linear transformations $T{\in}B$(X, R); and $K({\subseteq}X)$ is functionally closed (briefly, F-closed), if $T(K){\subseteq}{\mathbb{R}}$ is closed for all bounded linear transformations $T{\in}B$(X, R). By using these new notions, the Alaoglu-Bourbaki-Eberlein-${\check{S}}muljan$ theorem has been generalized. Moreover, we show that X is reflexive if and only if the closed unit ball of X is F-closed. James showed that for every closed convex subset C of a Banach space X, C is weakly compact if and only if every $f{\in}X^{\ast}$ attains its supremum over C at some point of C. Now, we show that if A is an F-convex subset of a Banach space X, then A is bounded and F-closed if and only if every element of $X^{\ast}$ attains its supremum over A at some point of A.