• Korean Journal of Mathematics
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• v.27 no.3
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• pp.613-627
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• 2019

Consider a connected molecular graph G = (V, E) where V is the set of vertices and E is the set of edges. In G, vertices represent the atoms and edges represent the covalent bonds between atoms. In graph G, every edge (say) e = uv will be connected by two atoms u and v. The edge Szeged index is a topological index which has been introduced by Ivan Gutman. In this paper, we have computed edge Szeged indices of a hydrocarbon family called Benzene ring and is denoted by $(BR)_{n{\times}n}$.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.1
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• pp.53-59
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• 2009

As a special type of Wireless Ad Hoc Networks, Wireless Mesh Networks (WMNs) have become the comer stone of research issues. Due to the limited operational environment of WMNs, an efficient connected dominating set (CDS) construction scheme is an important concern since it has been found extremely useful in broadcasting, routing and virtual backbone construction. In this paper, we propose a distributed Bandwidth-Interference aware CDS construction scheme to improve the network performance via two parameters such as node's number of neighbor and link bandwidth. Our CDS construction scheme selects the node that has more neighbors and enough bandwidth to support more end-devices in order to enhance overall network throughput and reliability. We confirm through simulations and show that our scheme constructs the CDS with the small subset of DS and the link that has better bandwidth.

• The Transactions of the Korea Information Processing Society
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• v.4 no.2
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• pp.596-605
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• 1997

The synamic systrm emplohing the self-squared function, , $f(Z)=z^2+c$, provides the Mandelbrot set which classifies constants c using the divergence of the sequence starting from the origin.To speed-up the generation of Mandelbrot set images, two approaches , called as the divide-and-conquer technique and the triangular boundary tracing technique, have been developed.However , the divede-and-conquer technique genrates sequences of some pixels that so not affect graphical representations of the Mandelbrot set.The triangular boundary tracing tech-mique does noot represent some 8-connected components of the Mandelbrost set.In this paper, we prorose a new ;method which solves the 8-connectivity problem of triangular boundary tracing technique.This algorithm considers the divergence for only pixels which are essential to the graphical repressentation of the Mandelbrot set.It also foves good representations for 8-connected components like hairly structures.

• Journal of the Korean Mathematical Society
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• v.46 no.4
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• pp.813-826
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• 2009

In this paper, we generalize the notions of preserving and strongly preserving maps to arbitrary set based topological categories. Further, we obtain characterizations of each of these concepts as well as interprete analogues and generalizations of theorems of Gerlits at al [20] in the categories of filter and local filter convergence spaces.

• Bulletin of the Korean Mathematical Society
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• v.34 no.2
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• pp.225-231
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• 1997

In 1970's Goodykoontz gave characterizations of connectedness imkleinen and locally arcwise connectedness of $2^X$ only at singleton set {x} ${\epsilon} 2^X$ [5,6,7]. In [7], we gave necessary conditions for C(X) to be arcwise connected im kileinen at any point $A {\epsilon} C(X)$.

• Bulletin of the Korean Mathematical Society
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• v.54 no.5
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• pp.1851-1857
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• 2017

We study relations between two descriptions of closed orientable 3-manifolds: as branched coverings and as Heegaard splittings. An explicit relation is presented for a class of 3-manifolds which are branched cyclic coverings of connected sums of lens spaces, where the branching set is an axis of a hyperelliptic involution of a Heegaard surface.

• Korean Journal of Mathematics
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• v.14 no.1
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• pp.65-70
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• 2006

In this article, we mention some subsequent developments of the theory of cluster sets, and present a new boundary cluster set for a simply connected domain in the complex plane and its applications.

• Proceedings of the KIPE Conference
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• 2000.07a
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• pp.493-497
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• 2000

A battery is the device that transforms the chemical energy into the direct-current electrical energy without a mechanical process. Unit cells are connected in series to obtain the required voltage while being connected in parallel to organize capacity for load current. Because the voltage drop down in one set of battery is faster than in two one it may result in the low efficiency of power converter with the voltage drop and cause the system shutdown. However when the system being shutdown. However when the system being driven in parallel a circular-current can be generated,. It is shown that as a result the new batteries are heated by over-charge and over-discharge and the over charge current increases rust of the positive grid and consequently shortens the lifetime of the new batteries. The difference between the new batteries and old ones is the amount of internal resistance. In this paper we can detect the unbalance current using the microprocessor and achieve the balance current by adjusting resistance of each set, The internal resistance of each set becomes constant and the current of charge and discharge comes to be balanced by inserting the external resistance into the system and calculating the change of internal resistance.

• Journal of the Korean Operations Research and Management Science Society
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• v.24 no.3
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• pp.93-107
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• 1999

We consider the development of an integer programming model and algorithm for the ATM switching node location problem. There are two kinds of facilities, hub facilities and remote facilities, with different capacities and installation costs. Each customer needs to be connected to one or more hub facilities via remote facilities, where the hub(remote) facilities need to be installed at the same candidate installation site of hub(remote) facility. We are given a set of customers with each demand requirements, a set of candidate installation sites of facilities, and connection costs between facilities, We need to determine the locations to place facilities, the number of facilities for each selected location, the set of customers who are connected to each installed hub facilities via installed remote facilities with minimum costs, while satisfying demand requirements of each customer. We formulate this problem as a general integer programming problem and solve it to optimality. In this paper, we develop a branch-and-cut algorithm with path variables. In the algorithm, we consider the integer knapsack polytope and derive valid inequalities. Computational experiments show that the algorithm works well in the real world situation. The results of this research can be used to develop optimization algorithms to solve capacitated facility location problems.

• Journal of the Korean Mathematical Society
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• v.37 no.1
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• pp.31-44
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• 2000

We study a free boundary problem satisfying Bernoulli type boundary condition along which the gradient of a piecewise harmonic solution jumps zero to a given constant value. In such problem, the free boundary splits the domain into two regions, the zero set and the harmonic region. Our main interest is to identify the global shape and the location of the zero set. In this paper, we find the lower and the upper bound of the zero set. In a convex domain, easier estimation of the upper bound and faster disk test technique are given to find a rough shape of the zero set. Also a simple proof on the convexity of zero set is given for a connected zero set in a convex domain.