• Journal for History of Mathematics
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• v.14 no.1
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• pp.101-108
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• 2001

There are two uses of zero which are both important but are different. One use of zero is as a number itself. The number zero is an abstract concept measuring the size of set with no elements in it. The second use of it is as an empty place indicator in our place-value number system. It is the notation. In this paper, we study a history of zero and the mistakes from a few earlier works in connection with some arithmetical operations involving the number zero.

• Kyungpook Mathematical Journal
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• v.55 no.3
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• pp.515-530
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• 2015

We say that (R, f, g) is an additive (m, n)-semihyperring if R is a non-empty set, f is an m-ary associative hyperoperation, g is an n-ary associative operation and g is distributive with respect to f. In this paper, we describe a number of characterizations of additive (m, n)-semihyperrings which generalize well-known results. Also, we consider distinguished elements, hyperideals, Rees factors and regular relations. Later, we give a natural method to derive the quotient (m, n)-semihyperring.

• Journal of the Korean Mathematical Society
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• v.35 no.1
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• pp.23-76
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• 1998

We prove that a non-empty separable metrizable space X admits a totally bounded metric for which the metric dimension of X in Assouad's sense equals the topological dimension of X, which leads to a characterization for the latter. We also give a characterization based on this Assouad dimension for the demension (embedding dimension) of a compact set in a Euclidean space. We discuss Assouad dimension and these results in connection with porous sets and measures with the doubling property. The elementary properties of Assouad dimension are proved in an appendix.

• Journal of the Korea Society of Computer and Information
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• v.19 no.10
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• pp.197-205
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• 2014

This study set out to develop a logistics rationalization model to reduce logistics costs including return route costs by using open information systems that overcame the limitations of the old closed logistics systems by the corporations and applying the principle of freight car sharing among them. In recent years, information infrastructure that can be easily shared by many such as information networks, however, One of the causes of rising logistics costs is high empty transfer rates on return routes after goods are transported from the distribution center of each company to consumption sites, It is propose to promote logistic efficiency and innovation. The study especially identified a logistics rationalization plan by examining and analyzing the stages of transportation on the circulation route of a distribution system from the distribution center of a corporation to consumption sites and the empty transfer rates and their current state.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.12
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• pp.1992-2007
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• 1997

A new algorithm for planning a collision-free path is developed based on linear prametric curve. In this paper robot is assumed to a point, and two linear parametric curve is used to construct a path connecting start and goal point, in which single intermediate connection point between start and goal point is considered. The intermediate connection point is set in polar coordinate(${\theta}{\delta}$) , and the interference between path and obstacle is mapped into CPS(connection point space), which is defined a CWS GM(circular work space geometry mapping). GM of all obstacles in workspace creates overlapping images of obstacle in CPS(Connection Point Space). The GM for all obstacles produces overlapping images of obstacle in CPS. The empty area of CPS that is not occupied by obstacle images represents collision-free paths in Euclidian Space. A GM based on connection point in elliptic coordinate(${\theta}{\delta}$) is also developed in that the total length of path is depend only on the variable .delta.. Hence in EWS GM(elliptic work space geometry mapping), increasing .delta. and finding the value of .delta. for collision-free path, the shortest path can be searched without carring out whole GM. The GM of obstacles expersses all possible collision-free path as empty spaces in CPS. If there is no empty space available in CPS, it indicates that path planning is not possible with given number of connection points, i.e. path planning is failed, and it is necessary to increase the number of connection point. A general case collision-free path planning is possible by appling GM to configuration space obstacles. Simulation of GM of obstacles in Euclidian space is carried out to measure performance of algorithm and the resulting obstacle images are reported.

• Journal of Korea Society of Digital Industry and Information Management
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• v.10 no.3
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• pp.273-283
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• 2014

Imported and exported agricultural products are facing a very difficult time due to the rising distribution costs spurred by the increasing labor and oil prices. High empty transfer rates, which take place on a return route after the regular transportation of imported and exported agricultural products, are especially a major cause of the rising distribution costs. In an effort to overcome those limitations, this study set out to examine the transportation stages connecting harbor warehouses, processing plants, and central distribution centers on the circulation route of such imported grains as wheat, barley, corn, and soybean and the transportation route from the warehouses devoted to exported agricultural products to harbors for such exported agricultural products as apple, pear, and persimmon in order to develop a model on the creation of a compound logistics complex for processing plants and transshipment of imported and exported agricultural products. The study also promoted the logistic rationalization of imported and exported agricultural products by creating a compound logistics complex that would combine processing plants for imported agricultural products and transshipment functions for exported agricultural products.

• Steel and Composite Structures
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• v.23 no.2
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• pp.217-228
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• 2017

Braces are one of the retrofitting systems of structure under earthquake loading. Buckling restrained braces (BRBs) are one of the very efficient braces for lateral loads. One of the key needs for a desirable and acceptable behavior of buckling-restraining brace members under intensive loading is that it prevents total buckling until the bracing member tolerates enough plastic deformation and ductility. This paper presents the results of a set of analysis by finite element method on buckling restrained braces in which the filler materials within the restraining member have been removed. These braces contain core as the conventional BRBs, but they have a different buckling restrained system. The purpose of this analysis is conducting a parametric study on various empty spaces between core and restraining member, the effect of friction between core and restraining member and applying initial deformation to brace system to investigate the global buckling behavior of these braces. The results of analysis indicate that the flexural stiffness of restraining member, regardless of the amount of empty space, can influence the global buckling behavior of brace significantly.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.25-36
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• 2013

By using some existence theorems of maximal elements for a family of set-valued mappings involving a better admissible set-valued mapping under noncompact setting of FC-spaces, we present some non-empty intersection theorems for a family $\{G_i\}_{i{\in}I}$ in product FC-spaces. Then, as applications, some new existence theorems of equilibrium for a system of generalized vector equilibrium problems are proved in product FC-spaces. Our results improve and generalize some recent results.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.573-582
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• 2009

This paper is indented to explain a dynamics on homotopies on the compact metric space, by the envelopes of homotopies. It generalizes the notion of not only the envelopes of maps in discrete geometry ([3]), but the envelopes of flows in continuous geometry ([5]). Certain distinctions among the homotopy geometry, the ow geometry and the discrete geometry will be illustrated. In particular, it is shown that any ${\omega}$-limit set, as well as any attractor, for an envelope of homotopies is an empty set (provided the homotopies that we treat are not trivial), whereas it is nonempty in general in discrete case.

• Journal of the Korean Mathematical Society
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• v.41 no.3
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• pp.479-487
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• 2004

Let G be a finite group and N be a normal subgroup of G. We denote by ncc(N) the number of conjugacy classes of N in G and N is called n-decomposable, if ncc(N) = n. Set $K_{G}\;=\;\{ncc(N)$\mid$N{\lhd}G\}$. Let X be a non-empty subset of positive integers. A group G is called X-decomposable, if KG = X. In this paper we characterise the {1, 3, 4}-decomposable finite non-perfect groups. We prove that such a group is isomorphic to Small Group (36, 9), the $9^{th}$ group of order 36 in the small group library of GAP, a metabelian group of order $2^n{2{\frac{n-1}{2}}\;-\;1)$, in which n is odd positive integer and $2{\frac{n-1}{2}}\;-\;1$ is a Mersenne prime or a metabelian group of order $2^n(2{\frac{n}{3}}\;-\;1)$, where 3$\mid$n and $2\frac{n}{3}\;-\;1$ is a Mersenne prime. Moreover, we calculate the set $K_{G}$, for some finite group G.