• Bulletin of the Korean Mathematical Society
• /
• v.38 no.2
• /
• pp.317-324
• /
• 2001

A Cayley graph of a finite group G is called normal edge-transitive if its automorphism group has a subgroup which both normalized G and acts transitively on edges. In this paper, we consider Cayley graphs of finite cyclic groups, namely, finite circulant graphs. We characterize the normal edge-transitive circulant graphs and determine the normal edge-transitive circulant graphs of prime power order in terms of lexicographic products.

• Journal of the Chungcheong Mathematical Society
• /
• v.23 no.3
• /
• pp.487-494
• /
• 2010

In [9], M. Green introduced the partial elimination ideals defining the multiple loci of the projection image of a closed subscheme in ${\mathbb{P}}^n$. In this paper, we give some geometric consequences obtained from partial elimination ideals.

• The Journal of the Institute of Internet, Broadcasting and Communication
• /
• v.17 no.5
• /
• pp.51-59
• /
• 2017

In this paper, we propose a gray code order of antenna index permutations for differential spatial modulation (DSM). To facilitate the implementation, the well-known Trotter-Johnson ranking and unranking algorithms are adopted, which result in similar computational complexity to the existing DSM that uses the lexicographic order. The signal-to-noise ratio gain achieved by the proposed gray code order over the lexicographic order is also analyzed and verified via simulations. Based on the gray coding framework, we further propose a diversity-enhancing scheme named intersected gray (I-gray) code order, where the permutations of active antenna indices are selected directly from the odd (or even) positions of the full permutations in the gray code order. From analysis and simulations, it is shown that the I-gray code order can harvest an additional transmit diversity order with respect to the gray code order.

• Journal of Korean Society of Transportation
• /
• v.26 no.5
• /
• pp.175-184
• /
• 2008

Uncertainties are unavoidable in engineering applications. In this paper we propose an alpha reliable multi-variable network design problem under demand uncertainty. In order to decide the optimal capacity enhancement, three performance measures based on 3E(Efficiency, Equity, and Environmental) are considered. The objective is to minimize the total budget required to satisfy alpha reliability constraint of total travel time, equity ratio, and total emission, while considering the route choice behavior of network users. The problem is formulated as the chance-constrained model for application of alpha confidence level and solved as a lexicographic optimization problem to consider the multi-variable. A simulation-based genetic algorithm procedure is developed to solve this complex network design problem(NDP). A simple numerical example ispresented to illustrate the features of the proposed NDP model.

• Journal of the Korean Mathematical Society
• /
• v.46 no.4
• /
• pp.701-711
• /
• 2009

We prove that every non-separable connected metric space can be endowed with a total preorder that is order-isomorphic to a nonrepresentable subset of the lexicographic plane and semicontinuous with respect to the metric topology.

• Journal of Korean Society for Quality Management
• /
• v.26 no.4
• /
• pp.79-87
• /
• 1998

This paper considers the problem of testing a one-sided hypothesis under the generalized sampling plan which is defined by a sequence of independent Bernoulli trials. A certain lexicographic order is defined for the boundary points of the sampling plan. It is shown that the family of probability mass function defined on the boundary points has monotone likelihood ratio, and that the test function is uniformly most powerful.

• Honam Mathematical Journal
• /
• v.36 no.3
• /
• pp.493-503
• /
• 2014

We consider the simple antisymmetrized algebra $N(e^{A_P},n,t)_1^-$. The simple non-associative algebra and its simple subalgebras are defined in the papers [1], [3], [4], [5], [6], [8], [13]. Some authors found all the derivations of an associative algebra, a Lie algebra, and a non-associative algebra in their papers [2], [3], [5], [7], [9], [10], [13], [15], [16]. We find all the derivations of the Lie subalgebra $N(e^{{\pm}x_1x_2x_3},0,3)_{[1]}{^-}$ of $N(e^{A_p},n,t)_k{^-}$ in this paper.

• Journal for History of Mathematics
• /
• v.32 no.3
• /
• pp.97-108
• /
• 2019

This paper is an outgrowth of a study on recent papers and presentations of Hong Sung Sa, Hong Young Hee and/or Lee Seung On on Gugo Wonlyu which is believed to be written by the famous Joseon scholar Jeong Yag-yong. Most of what is discussed here is already explained in these papers and presentations but due to brevity of the papers it is not understood by most of us. Here we present them in more explicit and mathematical ways which, we hope, will make them more accessible to those who have little background in history of classical Joseon mathematics. We also explain them using elementary projective geometry which allow us to visualize Pythagorean polynomials geometrically.

• Journal for History of Mathematics
• /
• v.28 no.6
• /
• pp.301-310
• /
• 2015

Since Jiuzhang Suanshu, the main tools in the theory of right triangles, known as Gougushu in East Asia were algebraic identities about three sides of a right triangle derived from the Pythagorean theorem. Using tianyuanshu up to siyuanshu, Song-Yuan mathematicians could skip over those identities in the theory. Chinese Mathematics in the 17-18th centuries were mainly concerned with the identities along with the western geometrical proofs. Jeong Yag-yong (1762-1836), a well known Joseon scholar and writer of the school of Silhak, noticed that those identities can be derived through algebra and then wrote Gugo Wonlyu (勾股源流) in the early 19th century. We show that Jeong reveals the algebraic structure of polynomials with the three indeterminates in the book along with their order structure. Although the title refers to right triangles, it is the first pure algebra book in Joseon mathematics, if not in East Asia.

• Journal of Korean Society of Transportation
• /
• v.11 no.2
• /
• pp.5-26
• /
• 1993

In order to analyze travel mode choice behavior, behavioral models including logit model, based on revealed preference theory, have been using easily measurable variables such as individual socioeconomic characteristics and physical attributes of travel modes. But some recent attitudinal models of travel choice behavior have implied that the negligence of individual psychological variables and individual choice constraints in travel mode choice might preclude better prediction of individual travel mode choice behavior. In this context, this study was attempted to reconstruct an attitudinal model(AM), especially focused on the decision rules in travel mode choice decision making process, consistent with the conceptual framework relating individual attitude and choice constraints to choice behavior. And to evaluate the strengths of the AM to other comparative models(logit, linear-additive, conjunctive, lexicographic model) in predicting travel mode choice bebavior, an empirical study of the mode choice in work-trip to CBD in Seoul was performed. According to the results the percent of correct prediction(PCP) derived from the AM was higher than those derived from comparative models by at least 7 to 20% in predicting travel mode choice. But each model produced a different prediction accuracy depending on market segmentation by travel modal users, individual socioeconomic characteristics, transportation system characteristics, and satisfaction levels. The finding that different groups divided by a certain criterion employ different decision rules supports the necessity of developing a choice model such as the AM combining compensatory and noncompensatory decision rules, and suggests that a proposed transportation system management plan or policy may have different effects on each group.