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http://dspace.ewha.ac.kr/handle/2015.oak/171825
20190426T13:11:05Z

TWO CONJECTURES IN RAMSEYTURAN THEORY
http://dspace.ewha.ac.kr/handle/2015.oak/249607
Title: TWO CONJECTURES IN RAMSEYTURAN THEORY
Ewha Authors: 김연진
Abstract: Given graphs H1, ... , Hk, a graph G is (H1, ... , Hk)free if there is a kedgecoloring phi: E(G) > [k] with no monochromatic copy of Hi with edges of color i for each i is an element of [k]. Fix a function f(n); then the Ramsey Turan function RT(n, H1, ... , Hk, f(n)) is the maximum number of edges in an nvertex (H1, ... , Hk)free graph with independence number at most f (n). We determine RT(n, K3, Ks, delta n) for s is an element of {3, 4, 5} and sufficiently small (5, confirming a conjecture of Erdos and SOs [Stud. Sci. Math. Hung., 14 (1979), pp. 2736]. It is known that RT(n, K8, f (n)) has a phase transition at f (n) = Theta(root n log n). However, the value of RT(n, K8, o(root n log n)) was not known. We determined this value by proving RT(n, Kg, n, K8, o(root n log n)) = n(2)/4 + o(n(2)), answering a question of Balogh, Hu, and Simonovits [J. Combin. Theory Ser. B, 114 (2015), pp. 148169]. The proofs utilize, among others, dependent random choice and results from graph packings.
20190101T00:00:00Z

Energy stable compact scheme for CahnHilliard equation with periodic boundary condition
http://dspace.ewha.ac.kr/handle/2015.oak/248338
Title: Energy stable compact scheme for CahnHilliard equation with periodic boundary condition
Ewha Authors: 신재민
Abstract: We present a compact scheme to solve the CahnHilliard equation with a periodic boundary condition, which is fourthorder accurate in space. We introduce schemes for two and three dimensions, which are derived from the onedimensional compact stencil. The energy stability is completely proven for the proposed scheme based on the application of the compact method and wellknown convex splitting methods. Detailed proofs of the mass conservation and unique solvability are also established. Numerical experiments are presented to demonstrate the accuracy and stability of the proposed methods. (C) 2018 Elsevier Ltd. All rights reserved.
20190101T00:00:00Z

Sparse spanning κconnected subgraphs in tournaments
http://dspace.ewha.ac.kr/handle/2015.oak/247288
Title: Sparse spanning κconnected subgraphs in tournaments
Ewha Authors: 김연진
Abstract: In 2009, BangJensen asked whether there exists a function g(κ) such that every strongly κconnected nvertex tournament contains a strongly κconnected spanning subgraph with at most κn + g(κ) arcs. In this paper, we answer the question by showing that every strongly kconnected nvertex tournament contains a strongly κconnected spanning subgraph with at most κn+750κ2 log2(κ+1) arcs, and there is a polynomialtime algorithm to find the spanning subgraph. © 2017 Society for Industrial and Applied Mathematics.
20170101T00:00:00Z

Evaluation of the convolution sums al+bm=n lσ(l) σ(m) with ab ≤ 9
http://dspace.ewha.ac.kr/handle/2015.oak/247001
Title: Evaluation of the convolution sums al+bm=n lσ(l) σ(m) with ab ≤ 9
Ewha Authors: 박윤경
Abstract: The generating functions of divisor functions are quasimodular forms of weight 2 and their products belong to a space of quasimodular forms of higher weight. In this article, we evaluate the convolution sumsal+bm=nlσ(l)σ(m) sumal+bm=n σ(l)σ(m) for all positive integers a, b and n with ab ≤ 9 and gcd(a, b) = 1. © 2017 Park.
20170101T00:00:00Z