• The Bulletin of The Korean Astronomical Society
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• v.38 no.2
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• pp.57.2-57.2
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• 2013

Cosmology is entering an era of percent precision with large surveys, demanding accurate simulations. In this paper, we aim to study the effects of initial conditions on the results of cosmological simulations, which will help us to make percent-level accuracy simulations. For this purpose, we use a series of cosmological N-body simulations with varying initial conditions. We test the influence of the initial conditions, namely the pre-initial configuration (preIC), the order of the perturbation theory, and the initial redshift, on the statistics associated with the large scale structures of the universe such as the halo mass function, the density power spectrum, and the maximal extent of the large scale structures. We find that glass or grid pre-initial conditions give similar results. However, the order of the Lagrangian perturbation theory used to generate the initial conditions and the starting epoch of the simulations play a crucial role, especially at high redshift (z ~ 2-4). The initial conditions have to be chosen with care, taking into account the specificity of the simulation.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.1159-1174
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• 1996

The spectrum of the Laplacian matrix of a graph gives an information of the structure of the graph. For example, the product of non-zero eigenvalues of the characteristic polynomial of the Laplacian matrix of a graph with n vertices is n times of the number of spanning trees of that graph. The characteristic polynomial of the Laplacian matrix of a graph tells us the number of spanning trees and the connectivity of given graph. in this paper, we compute the characteristic polynomial of the Laplacian matrix of a graph bundle when its voltage lie in an abelian subgroup of the full automorphism group of the fibre; in particular, the automorphism group of the fibre is abelian. Also we study a relation between the characteristic polynomial of the Laplacian matrix of a graph G and that of the Laplacian matrix of a graph bundle over G. Some applications are also discussed.

• Proceedings of the Korean Society for Bioinformatics Conference
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• 2005.09a
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• pp.357-360
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• 2005

In this paper we consider the well-known semiparametric proportional hazards (PH) models for survival analysis. These models are usually used with few covariates and many observations (subjects). But, for a typical setting of gene expression data from DNA microarray, we need to consider the case where the number of covariates p exceeds the number of samples n. For a given vector of response values which are times to event (death or censored times) and p gene expressions (covariates), we address the issue of how to reduce the dimension by selecting the significant genes. This approach enable us to estimate the survival curve when n < < p. In our approach, rather than fixing the number of selected genes, we will assign a prior distribution to this number. The approach creates additional flexibility by allowing the imposition of constraints, such as bounding the dimension via a prior, which in effect works as a penalty. To implement our methodology, we use a Markov Chain Monte Carlo (MCMC) method. We demonstrate the use of the methodology to diffuse large B-cell lymphoma (DLBCL) complementary DNA(cDNA) data.

• Korean Management Science Review
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• v.15 no.2
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• pp.229-237
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• 1998

This paper presents a new algorithm for the K Shortest Paths Problem which is developed with a Double Shortest Arborescence and an inward arc breaking method. A Double Shortest Arborescence is made from merging a forward shortest arborescence and a backward one with Dijkstra algorithm. and shows us information about each shorter path to traverse each arc. Then K shorter paths are selected in ascending order of the length of each short path to traverse each arc, and some paths of the K shorter paths need to be replaced with some hidden shorter paths in order to get the optimal paths. And if the cross nodes which have more than 2 inward arcs are found at least three times in K shorter path, the first inward arc of the shorter than the Kth shorter path, the exposed path replaces the Kth shorter path. This procedure is repeated until cross nodes are not found in K shorter paths, and then the K shortest paths problem is solved exactly. This algorithm are computed with complexity o($n^3$) and especially O($n^2$) in the case K=3.

• Structural Engineering and Mechanics
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• v.25 no.1
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• pp.91-106
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• 2007

A new class of finite elements is described for dealing with mesh gradation. The approach employs the moving least square (MLS) scheme to devise a class of elements with an arbitrary number of nodal points on the parental domain. This approach generally leads to elements with rational shape functions, which significantly extends the function space of the conventional finite element method. With a special choice of the nodal points and the base functions, the method results in useful elements with polynomial shape functions for which the $C^1$ continuity breaks down across the boundaries between the subdomains comprising one element. Among those, (4 + n)-noded MLS based finite elements possess the generality to be connected with an arbitrary number of linear elements at a side of a given element. It enables us to connect one finite element with a few finite elements without complex remeshing. The effectiveness of the new elements is demonstrated via appropriate numerical examples.

• Bulletin of the Korean Mathematical Society
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• v.25 no.2
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• pp.185-194
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• 1988

In [2], we have shown that the optimal boundary controls for hyperbolic systems in L$^{2}$-spaces can be attained in a feedback form via Riccati operators. A number of authors [1, 5, 7 and 10] have investigated approximations of Riccati operators arising in distributed parameter systems. They assumed bounded controls for parabolic systems. However, we in this paper study Galerkin approximations of Riccati operators and feedback controls for hyperbolic systems with unbounded control actions. Let us briefly introduce some results of [2]. Let .ohm. be an open bounded region in R$^{n}$ with smooth boundary .GAMMA. where n is a fixed positive integer. We consider a strictly hyperbolic differential operator H(x) of order 1 on .ohm. with noncharacteristic boundary on .GAMMA.

• Journal of the Korean Mathematical Society
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• v.52 no.5
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• pp.1003-1021
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• 2015

A matrix completion problem has been exploited amply because of its abundant applications and the analysis of contractions enables us to have insight into structure and space of operators. In this article, we focus on a specific completion problem related to Hankel partial contractions. We provide concrete necessary and sufficient conditions for the existence of completion of Hankel partial contractions for both extremal and non-extremal types with lower dimensional matrices. Moreover, we give a negative answer for the conjecture presented in [8]. For our results, we use several tools such as the Nested Determinants Test (or Choleski's Algorithm), the Moore-Penrose inverse, the Schur product techniques, and a congruence of two positive semi-definite matrices; all these suggest an algorithmic approach to solve the contractive completion problem for general Hankel matrices of size $n{\times}n$ in both types.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1711-1723
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• 2013

P. V$\acute{a}$mos called a ring R 2-good if every element is the sum of two units. The ring of all $n{\times}n$ matrices over an elementary divisor ring is 2-good. A (right) self-injective von Neumann regular ring is 2-good provided it has no 2-torsion. Some of the earlier results known to us about 2-good rings (although nobody so called at those times) were due to Ehrlich, Henriksen, Fisher, Snider, Rapharl and Badawi. We continue in this paper the study of 2-good rings by several authors. We give some examples of 2-good rings and their related properties. In particular, it is shown that if R is an exchange ring with Artinian primitive factors and 2 is a unit in R, then R is 2-good. We also investigate various kinds of extensions of 2-good rings, including the polynomial extension, Nagata extension and Dorroh extension.

• Communications for Statistical Applications and Methods
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• v.6 no.1
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• pp.275-283
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• 1999

In order to estimate a parameter $(\alpha,\beta^r), r\epsilonN$, in a distribution belonging to a location-scale family we usually use best invariant estimator (BIE) and best unbiased estimator (BUE). But in some conditions Ryu (1996) showed that BIE is better than BUE. In this paper we calculate risks of BIE and BUE in a normal and an exponential distribution respectively and calculate a percentage risk improvement exponential distribution respectively and calculate a percentage risk improvement (PRI). We find the sample size n which make no significant differences between BIE and BUE in a normal distribution. And we show that BIE is always significantly better than BUE in an exponential distribution. Also simulation in a normal distribution is given to convince us of our result.

• Journal of the Korean Chemical Society
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• v.18 no.3
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• pp.175-179
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• 1974

EHT calculation have been carried out on phenyl chloro-thiol, phenyl chloro-thiono and phenyl dithioformates to explain the conformations and reactivity of the compounds. Results of calculation lead us to conclude that the mechanism of SN reaction of these compounds are likely to be the $S_N2$ type and trans form is more stable than cis form for all molecules.