关键词：
Self-Similar Sets;Symmetric Expansion;Set of Uniqueness
摘要：
Recently there are several works devoted to the study of self-similar subsets of a given self-similar set, which turns out to be a difficult problem. Let L >= 2 be an integer and let alpha is an element of (0,1/L). Let C alpha,L be the uniform Cantor set defined by the following set equation: C-alpha,(L) = boolean OR(L-1)(j=0)alpha(C-alpha,C-L + j). We show that for any alpha, beta is an element of (0,1/L-2), C-alpha,C-L and C-beta,C-L essentially have the same self-similar subsets. Precisely, E is a self-similar subset of C-alpha,C-L if and only if pi(beta) o pi(-1)(alpha)(E) is a self-similar subset of C-beta,C-L, where pi(alpha) (similarly pi(beta)) is the coding map from the symbolic space {0, 1,..., L - 1}(N) to C-alpha,C-L.
期刊：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE,2020年37(2):457-488 ISSN：0294-1449
通讯作者：
Zi, Ruizhao
作者机构：
[Zhang, Zhifei] Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China.;[Zi, Ruizhao] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Zi, Ruizhao] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Zi, Ruizhao] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Hubei, Peoples R China.
关键词：
Convergence to equilibrium;Global smooth solutions;Full compressible Navier-Stokes equations
作者机构：
[Zhang, Minjie; Wang, Chengyong] Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China.;[Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
摘要：
A path P is a segment of a tree if the endpoints of P are of degree 1 or at least 3, and each of the rest vertices are of degree 2 in the tree. The lengths of all the segments of this tree form its segment sequence. Denote by T-l the set of all trees on n vertices with the segment sequence l = (l(1),l(2), ..., l(m)), where l(1) >= l(2) ... >= l(m). In this paper, the extremal structures of trees among T-l which minimize or maximize the first (resp. second) Zagreb eccentricity index, the eccentric connectivity index, and the eccentric distance sum, are characterized. Furthermore, we consider similar extremal problems for trees with fixed number of segments. (C) 2020 Elsevier B.V. All rights reserved.
摘要：
DP-coloring (also known as correspondence coloring) is a generalization of list coloring introduced recently by Dvorak and Postle (2017). Kim and Ozeki proved that planar graphs without k-cycles where k = 3,4,5, or 6 are DP-4-colorable. In this paper, we prove that every planar graph G without k-cycles adjacent to triangles is DP-4-colorable for k = 5,6, which implies that every planar graph G without k-cycles adjacent to triangles is 4-choosable for k = 5,6. This extends the result of Kim and Ozeki on 3-, 5-, and 6-cycles. (C) 2019 Published by Elsevier B.V.
期刊：
Communications in Statistics - Simulation and Computation,2020年49(12):3367-3379 ISSN：0361-0918
通讯作者：
Ning, Jianhui(thq80@163.com)
作者机构：
[Ning, Jianhui; Tao, Huiqiang] School of Mathematics and Statistics, Central China Normal University, Wuhan, China;School of Mathematics and Statistics, Huanghuai University, Zhumadian, China;[Tao, Huiqiang] ;[Tao, Huiqiang] School of Mathematics and Statistics, Huanghuai University, Zhumadian, China
通讯机构：
[Jianhui Ning] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, China
关键词：
Mean square error;Randomized Quasi Monte Carlo;Sampling/importance resampling
作者机构：
[Liu, Runrun] Cent China Normal Univ, Sch Math & Stat, Wuhan, Hubei, Peoples R China.;[Liu, Xujun] Univ Illinois, Dept Math, Urbana, IL 61801 USA.;[Yu, Gexin; Rolek, Martin] William & Mary, Dept Math, Williamsburg, VA 23185 USA.
通讯机构：
[Liu, Xujun] U;Univ Illinois, Dept Math, Urbana, IL 61801 USA.
关键词：
Packing coloring;Subcubic graphs;Independent sets;Maximum average degree
摘要：
For a sequence of non-decreasing positive integers S = (s(1),..., s(k)), a packing S-coloring is a partition of V(G) into sets V-1,...,V-k such that for each 1 <= i <= k the distance between any two distinct x, y is an element of V-i is at least s(i) + 1. The smallest k such that G has a packing (1, 2,..., k)-coloring is called the packing chromatic number of G and is denoted by chi(p)(G). For a graph G, let D(G) denote the graph obtained from G by subdividing every edge. The question whether chi(p)(D(G)) <= 5 for all subcubic graphs G was first asked by Gastineau and Togni and later conjectured by Bresar, Klavzar, Rall and Wash. Gastineau and Togni observed that if one can prove every subcubic graph except the Petersen graph is packing (1, 1, 2, 2)-colorable then the conjecture holds. The maximum average degree, mad(G), is defined to be max{2 vertical bar E(H)vertical bar/vertical bar V(H)vertical bar : H subset of G}. In this paper, we prove that subcubic graphs with mad(G) < 30/11 are packing (1, 1, 2, 2)-colorable. As a corollary, the conjecture of Bresar et al holds for every subcubic graph G with mad(G) < 30/11. (C) 2020 Elsevier B.V. All rights reserved.
作者机构：
[Chen, Yan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zheng, Chengli; Cai, Ya] Cent China Normal Univ, Financial Engn Res Ctr, Sch Econ & Business Adm, Wuhan 430079, Peoples R China.
通讯机构：
[Zheng, Chengli] C;Cent China Normal Univ, Financial Engn Res Ctr, Sch Econ & Business Adm, Wuhan 430079, Peoples R China.
期刊：
Applied Mathematics and Computation,2020年377:125149 ISSN：0096-3003
通讯作者：
Zou, Yan
作者机构：
[Zou, Yan; Hu, Zhiquan] Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Zou, Yan] C;Cent China Normal Univ, Fac Math & Stat, Wuhan, Peoples R China.
关键词：
Edge prorating number;Path two bipancyclic;Bipanconnected;Bipartite graph
摘要：
Given a bipartite graph G = (A(1), A(2), E) with m := min {vertical bar A(1)vertical bar, |vertical bar A(2)vertical bar} >= 2, the edge prorating number for x is an element of A(i) is defined as rho(G)(x) = (d(x) - 1)/vertical bar A(3-i)vertical bar, i = 1, 2. Set.(G) := min {rho(G)(x): x is an element of A(1) boolean OR A(2)} and call it the minimum edge prorating number of G. We call G path two bipancyclic if for every path P of length two in G, and for every integer k is an element of [2, m], G has a 2k-cycle passing through P. In this article, it is shown that the minimum edge prorating number condition rho(G) >= 1/2 implies that a bipartite graph G is either path two bipancyclic or isomorphic to G(2n,4), where n >= 3 and G(2n,4) is a 2n by 4 bipartite graph. As an application, we proved that the minimum edge prorating number condition rho(G) = 1/2 also implies the bipanconnectivity of a bipartite graph G: for every pair u, v of distinct vertices, and for every appropriate integer l is an element of [2, 2m], G has a u, v-path of length l. This unifies the known results in Tian and Zang (1989) and Du et al. (2018). Examples show that the minimum edge prorating number condition rho(G) = 1/2 in both of our results are sharp. (C) 2020 Published by Elsevier Inc.
期刊：
Applied Mathematics and Computation,2019年361:232-245 ISSN：0096-3003
通讯作者：
Wang, Shujing
作者机构：
[Wang, Shujing; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Wang, Hua] Georgia Southern Univ, Dept Math Sci, Statesboro, GA 30460 USA.
通讯机构：
[Wang, Shujing] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
Tree;Subtree;Wiener index;Ratio
摘要：
Among many topological indices of trees the sum of distances sigma (T) and the number of subtrees F(T) have been a long standing pair of graph invariants that are well known for their negative correlation. That is, among various given classes of trees, the extremal structures maximizing one usually minimize the other, and vice versa. By introducing the "local" versions of these invariants, sigma(T) (nu) for the sum of distance from nu to all other vertices and sigma(T) (nu) for the number of subtrees containing nu, extremal problems can be raised and studied for vertices within a tree. This leads to the concept of "middle parts" of a tree with respect to different indices. A challenging problem is to find extremal values of the ratios between graph indices and corresponding local functions at middle parts or leaves. This problem also provides new opportunities to further verify the the correlation between different indices such as sigma(T) and F(T). Such extremal ratios, along with the extremal structures, were studied and compared for the distance and subtree problems for general trees (Barefoot, 1997; Szekely and Wang, 2013, 2014). In this paper, this study is extended to binary trees, a class of trees with numerous practical applications in which the extremal ratio problems appear to be even more complicated. After justifying some basic properties on the distance and subtree problems in trees and binary trees, characterizations are provided for the extremal structures achieving two extremal ratios in binary trees of given order. The generalization of this work to k-ary trees is also briefly discussed. The findings are compared with the previous established extremal structures in general trees. Lastly some potential future work is mentioned. (C) 2019 Elsevier Inc. All rights reserved.
期刊：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY,2019年27(8):1950136 ISSN：0218-348X
通讯作者：
Yin, Feng-Li
作者机构：
[Wang, Cong] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Yin, Feng-Li] Zhoukou Normal Univ, Sch Math & Stat, Zhoukou 466001, Peoples R China.
通讯机构：
[Yin, Feng-Li] Z;Zhoukou Normal Univ, Sch Math & Stat, Zhoukou 466001, Peoples R China.
摘要：
Let mu({pn, dn}) be a Cantor-Moran measure given by the infinite convolution of finite measures with equal probability mu({pn,) (dn}) = delta(p1-1{0, d1}) * delta((p1p2)-1 {0, d2})* ..., where {p(n), d(n)} subset of Z and 0 < d(n) < p(n) for n >= 1. In this paper, we present a complete characterization for maximal orthogonal sets of exponentials of L-2 (mu({pn, dn})) in terms of maximal mappings. As its application, we give a sufficient condition for a maximal orthogonal set to be a basis.
作者机构：
[Lu, Dengfeng] Hubei Engn Univ, Sch Math & Stat, Xiaogan 432000, Peoples R China.;[Lu, Zongze] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Lu, Zongze] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
Kirchhoff-type equation;Least energy solution;Perturbation method;Pohozaev type identity
期刊：
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE,2019年36(1):1-25 ISSN：0294-1449
通讯作者：
Ruan, Lizhi
作者机构：
[Fan, Lili] Wuhan Polytech Univ, Sch Math & Comp Sci, Wuhan 430023, Hubei, Peoples R China.;[Ruan, Lizhi] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Hubei, Peoples R China.;[Xiang, Wei] City Univ Hong Kong, Dept Math, Kowloon, Tat Chee Ave, Hong Kong, Peoples R China.
通讯机构：
[Ruan, Lizhi] C;Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Phys, Wuhan 430079, Hubei, Peoples R China.
期刊：
Applied Mathematics and Computation,2019年340:156-163 ISSN：0096-3003
通讯作者：
Yu, Rong
作者机构：
[Xu, Baogen] East China Jiaotong Univ, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China.;[Yu, Rong; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Zhao, Qin] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.
通讯机构：
[Yu, Rong] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
Weighted adjacency matrix;Weighted spectral radius;Weighted energy
摘要：
Let G be a graph of order n and let d(i) be the degree of the vertex v(i) in G for i = 1, 2, ..., n. The weighted adjacency matrix A(db) of G is defined so that its (i, j) entry is equal to d(i)+d(j)/d(i)d(j) if the vertices v(i) and v(j )are adjacent, and 0 otherwise. The spectral radius rho(1) and the energy epsilon(db) of the A(db) -matrix are examined. Lower and upper bounds on rho(1) and epsilon(db) are obtained, and the respective extremal graphs are characterized. (C) 2018 Elsevier Inc. All rights reserved.
作者机构：
[Zhang, Minjie] Hubei Univ Arts & Sci, Sch Math & Stat, Xiangyang 441053, Peoples R China.;[Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Wang, Guangfu; Xu, Baogen] East China Jiaotong Univ, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.
期刊：
Applied Mathematics and Computation,2019年354:411-421 ISSN：0096-3003
通讯作者：
Li, Shuchao
作者机构：
[Feng, Zhimin] Xinyang Normal Univ, Sch Math & Stat, Xinyang 464000, Peoples R China.;[Huang, Jing; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Luo, Xiaobing] Wuhan Polytech, Sch Comp Technol & Software Engn, Wuhan 430074, Hubei, Peoples R China.
通讯机构：
[Li, Shuchao] C;Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Hubei, Peoples R China.
关键词：
Rank;Nullity;Matching number
摘要：
cGiven a simple graph G, let A(G) be its adjacency matrix and alpha'(G) be its matching number. The rank of G, written as r(G), refers to the rank of A(G). In this paper, some relations between the rank and the matching number of a graph are studied. Firstly, it is proved that -2d(G) <= r(G) - 2 alpha'(G) <= N-0, where d(G) and N-0 are, respectively, the dimension of cycle space and the number of odd cycles of G. Secondly, sharp lower bounds on both r(G) - alpha'(G) and r (G)/alpha'(G) are determined. All the corresponding extremal graphs are characterized, respectively. (C) 2019 Elsevier Inc. All rights reserved.
