期刊：
Finite Fields and Their Applications,2023年89:102223 ISSN：1071-5797
通讯作者：
Miao, Shujing(sjmiao2020@sina.com)
作者机构：
[Miao, Shujing; Wang, Junming; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Shujing Miao] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
关键词：
Cospectral graphs;Determined by generalized skew spectrum;Skew-adjacency matrix;Smith Normal Form
摘要：
Spectral characterization of graphs is an important topic in spectral graph theory. An oriented graph G(sigma) is obtained from a simple undirected graph G by assigning to every edge of G a direction so that G(sigma) becomes a directed graph. The skew-adjacency matrix of an oriented graph G(sigma) is a real skew-symmetric matrix S(G(sigma)) = (s(ij)), where s(ij) = -s(ji) = 1 if (i, j) is an arc; s(ij) = s(ji) = 0 otherwise. Let G(sigma) and H-tau be two oriented graphs whose skew-adjacency matrices are S(G(sigma)) and S(H-tau), respectively. We say G(sigma) is R-cospectral to H-tau if tJ - S(G(sigma)) and tJ - S(H-tau) have the same spectrum for any t is an element of R, where J is the all-ones matrix. An oriented graph G(sigma) is said to be determined by the generalized skew spectrum (DGSS for short), if any oriented graph which is R-cospectral to G(sigma) is isomorphic to G(sigma). Let W(G(sigma)) = [e, S(G(sigma))e, S-2(G(sigma))e, . . . , Sn-1(G(sigma))e] be the skew-walk-matrix of G(sigma), where e is the all-ones vector. A theorem of Qiu, Wang and Wang [9] states that if G(sigma) is a self-converse oriented graph and 2(-(sic)n/2(sic)) det W(G(sigma)) is odd and square-free, then G(sigma) is DGSS. In this paper, based on the Smith Normal Form of the skew-walk-matrix of G(sigma) we obtain our main result: Let q be a prime and G(sigma) be a self-converse oriented graph on n vertices with det W(G(sigma)) not equal 0. Assume that rank(q)(W(G(sigma))) = n - 1 if q is an odd prime, and rank(q)(W(G(sigma))) = (sic)n/2(sic) if q = 2. If Q is a regular rational orthogonal matrix satisfying Q(T)S(G(sigma))Q = S(H-tau) for some oriented graph H-tau, then the level of Q divides d(n)(W(G(sigma)))/q, where d(n)(W(G(sigma))) is the n-th invariant factor of q W(G(sigma)). Consequently, it leads to an easier way to prove Qiu, Wang and Wang's theorem above. (c) 2023 Elsevier Inc. All rights reserved.
作者机构：
[Qi, Yingfan; Cao, Rongjun; Chen, Minghua; Shi, Jiankang] Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China.;[Yin, Xiaobo] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Chen, MH ] L;Lanzhou Univ, Sch Math & Stat, Lanzhou 730000, Peoples R China.
关键词：
Asymptotically compatible scheme;Nonlocal model;Shifted-symmetric collocation;Stability and convergence analysis
摘要：
The piecewise quadratic polynomial collocation is used to approximate the nonlocal model, which generally leads to a nonsymmetric indefinite system (Chen et al. (2021) [5]). In this case, the discrete maximum principle is not satisfied, which might be trickier for the stability analysis of the high-order numerical schemes (D'Elia et al. (2020) [10]; Leng et al. (2021) [26]). Here, we present a modified (shifted-symmetric) piecewise quadratic polynomial collocation for solving the linear nonlocal diffusion model, which leads to a symmetric positive definite system and satisfies the discrete maximum principle. Using Faulhaber's formula and Riemann zeta function, the perturbation error for symmetric positive definite system and nonsymmetric indefinite system are given. Then rigorous convergence analysis for the nonlocal models are provided under the general horizon parameter delta = O (h beta), with beta >= 0. More concretely, the global error is O (hmin{2,1+beta}) if delta is not set as a grid point, while it recovers O (hmax{2,4-2 beta}) when delta is set as a grid point. We also prove that the shifted-symmetric scheme is asymptotically compatible, which has the global error O (hmin{2,2 beta}) as delta, h -> 0. The numerical experiments (including two-dimensional case) are performed to verify the convergence.(c) 2022 IMACS. Published by Elsevier B.V. All rights reserved.
作者机构：
[Yuan, Ganghua] Northeast Normal Univ, Sch Math & Stat, KLAS, Changchun 130024, Jilin, Peoples R China.;[Zhao, Yue; Zhao, Y] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Zhao, Y ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
作者：
Prasangika, K. D.;Tang, Wan;Yao, Zeng;Zuo, Guoxin
期刊：
Communications in Statistics - Theory and Methods,2023年52(5):1385-1399 ISSN：0361-0926
通讯作者：
Zuo, Guoxin(zuogx@mail.ccnu.edu.cn)
作者机构：
[Prasangika, K. D.] Univ Ruhuna, Dept Math, Matara, Sri Lanka.;[Tang, Wan] Tulane Univ, Dept Biostat & Data Sci, New Orleans, LA 70118 USA.;[Yao, Zeng; Zuo, Guoxin] Cent China Normal Univ, Sch Math & Stat, Wuhan, Peoples R China.
通讯机构：
[Guoxin Zuo] S;School of Mathematics and Statistics, Central China Normal University, Wuhan, P.R. China
关键词：
Non parametric regression;local linear regression;double smoothing local linear regression;time series;asymptotic properties
期刊：
Applied Mathematics and Computation,2023年438:127556 ISSN：0096-3003
通讯作者：
Sun, Wanting(wtsun2018@sina.com)
作者机构：
[Li, Shuchao; Liu, Xin; Sun, Wanting] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Yan, Lixia] Wuhan Business Univ, Sch Informat & Engn, Wuhan 430070, Peoples R China.
通讯机构：
[Wanting Sun] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
摘要：
The Steiner k-eccentricity of a vertex in a graph G is the maximum Steiner distance over all k-subsets containing the vertex. The average Steiner k-eccentricity of G is the mean value of all vertices' Steiner k-eccentricities in G. Let T-n be the set of all n-vertex trees, T-n,T-Delta be the set of n-vertex trees with maximum degree Delta, T-n,Delta(k) be the set of n-vertex trees with exactly k vertices of a given maximum degree Delta, and let MTnk be the set of n-vertex trees with exactly k vertices of maximum degree. In this paper, we first determine the sharp upper bound on the average Steiner 3-eccentricity of n-vertex trees with a given degree sequence. The corresponding extremal graphs are characterized. Consequently, together with majorization theory, all graphs among T-n,Delta(k) (resp. T-n,T-Delta, MTnk, T-n) having the maximum average Steiner 3-eccentricity are identified. Then we characterize the unique n-vertex tree with a given segment sequence having the minimum average Steiner 3-eccentricity. Finally, we determine all n-vertex trees with a given number of segments having the minimum average Steiner 3-eccentricity. (C) 2022 Elsevier Inc. All rights reserved.
作者机构：
[Liu, Nannan; Li, Shuchao] Cent China Normal Univ, Fac Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Huihui] Luoyang Normal Univ, Dept Math, Luoyang 471934, Peoples R China.
通讯机构：
[Shuchao Li] F;Faculty of Mathematics and Statistics, Central China Normal University, Wuhan 430079, PR China
关键词：
Diameter;Matching number;Normality;Tree
摘要：
Given a connected graph G, the eccentricity epsilon G(v) of a vertex v in G is the maximum distance from v to any other vertex, in which the vertex v satisfying epsilon G(v) = max{epsilon G(u) : u E VG} is called a peripheral vertex. The normality of a vertex v is the minimum distance from v to all peripheral vertices in G. The sum of normalities of G is denoted by Norm(G). The difference between the eccentricity and normality at a vertex v is denoted by lambda G(v). Let Lambda(G) = n-ary sumation vEV(G)lambda G(v). Very recently, Chen, Wang and Zhang (Chen et al., 2020) started a new research on the two novel parameters Norm(middot) and Lambda(middot) of trees. As a continuance of it, we obtain some relationship between Norm(T) (resp. Lambda(T)) with the matching number and the order of the tree T. We characterize all the n-vertex trees with given matching number having the largest (resp. smallest) sum of normalities. As well we establish sharp upper and lower bounds on Lambda(middot) of an n-vertex tree T with given matching number. Some further research problems are proposed.(c) 2022 Elsevier B.V. All rights reserved.
作者机构：
[Hua, Hongbo] Huaiyin Inst Technol, Fac Math & Phys, Huaian 223003, Jiangsu, Peoples R China.;[Hu, Xiaolan] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.
通讯机构：
[Hongbo Hua] F;Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huai’an, Jiangsu 223003, PR China
关键词：
Bounds;Forgotten index;Independence number;Lanzhou index;The second Zagreb index
期刊：
Applied Mathematics and Computation,2023年445:127842 ISSN：0096-3003
通讯作者：
Zhang, Shunzhe(shunzhezhang@hubu.edu.cn)
作者机构：
[Chen, Guantao] Georgia State Univ, Dept Math & Stat, Atlanta, GA 30303 USA.;[Chen, Yuan] Wuhan Text Univ, Res Ctr Nonlinear Sci, Sch Math & Phys Sci, Wuhan 430073, Peoples R China.;[Hu, Zhiquan] Cent China Normal Univ, Sch Math & Stat, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.;[Zhang, Shunzhe] Hubei Univ, Fac Math & Stat, Hubei Key Lab Appl Math, Wuhan 430062, Peoples R China.
通讯机构：
[Shunzhe Zhang] H;Hubei Key Laboratory of Applied Mathematics, Faculty of Mathematics and Statistics, Hubei University, Wuhan 430062, PR China
期刊：
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY,2023年31(05):2350037 ISSN：0218-348X
通讯作者：
Yi, SF
作者机构：
[Pan, Yuewei] GuiZhou Normal Univ, Sch Math Sci, Guiyang 550001, Guizhou, Peoples R China.;[Yi, Shanfeng; Yi, SF] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
通讯机构：
[Yi, SF ] C;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.
摘要：
Let Sigma(infinity)(i=1) c(i)R(i)(x) be the Rademacher series, where {R-i(x)}(i=1)(infinity) is the classical Rademacher function system and {c(i)}(i=1)(infinity) is an arbitrary real number sequence. In this paper, we first show that the value range of the Rademacher series at any subinterval of [0, 1] is R boolean OR {+/- 8} when {c(i)}(1)(infinity) is an element of l(2)\l(1). This result provides us with the basic facts that when {c(i)}(1)(infinity) is an element of l(2)\l(1), the Rademacher series cannot converge to an approximate continuous function, and there is no approximate limit at any point of [0,1]. Further, when {c(i)}(1)(infinity) is an element of l(2)\l(1), we show various dimensions of the level set of Rademacher series on any subinterval of [0, 1]. Finally, we give the relationship between the box dimension and the coefficient of Rademacher series when {ci}(1)(infinity) is an element of l(1), and the exact values of box dimension, packing dimension and Hausdorff dimension are obtained in some special cases.
摘要：
Let G be a graph and let k 2 be an integer. A {K1,j : 1 S j S k}-factor of G is a spanning subgraph of G, in which each component is isomorphic to a member in {K1,j : 1 S j S k}. In this paper, we first establish a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {K1,j : 1 S j S k}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {K1,j : 1 S j S k}-factor. Furthermore, we construct some extremal graphs to show all the bounds obtained in this contribution are best possible.(c) 2022 Elsevier B.V. All rights reserved.
作者机构：
[Wang, Jiajia] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Wang, Jiajia; Tu, Xinhui; Zhao, Weizhong; He, Tingting] Cent China Normal Univ, Hubei Prov Key Lab Artificial Intelligence & Smar, Wuhan 430079, Peoples R China.;[Wang, Jiajia; Tu, Xinhui; Zhao, Weizhong; He, Tingting] Cent China Normal Univ, Natl Language Resources Monitoring & Res Ctr Netw, Wuhan 430079, Peoples R China.
通讯机构：
[Xinhui Tu; Tingting He] H;Hubei Provincial Key Laboratory of Artificial Intelligence and Smart Learning, Central China Normal University, Wuhan, China<&wdkj&>National Language Resources Monitoring &Research Center for Network Media, Central China Normal University, Wuhan, China<&wdkj&>Hubei Provincial Key Laboratory of Artificial Intelligence and Smart Learning, Central China Normal University, Wuhan, China<&wdkj&>National Language Resources Monitoring &Research Center for Network Media, Central China Normal University, Wuhan, China
关键词：
PASSAGE;RETRIEVAL;TOKEN
摘要：
1 Introduction.Inspired by the impressive success of BERT[1]in various NLP applications,researchers have attem...展开更多 1 Introduction.Inspired by the impressive success of BERT[1]in various NLP applications,researchers have attempted to apply pretrained language models to information retrieval,and existing BERT-based retrieval models obtain improved performance on passage retrieval[2-4].Since BERT has the limitation that the maximum length of tokens is only 512,however,simply applying those models to the task of long document retrieval derives suboptimal results.收起
期刊：
Finite Fields and Their Applications,2023年85:102127 ISSN：1071-5797
通讯作者：
Fan, Yun(yfan@mail.ccnu.edu.cn)
作者机构：
[Fan, Yun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Yuchang] Hubei Normal Univ, Coll Math & Stat, Huangshi 435002, Peoples R China.
通讯机构：
[Yun Fan] S;School of Mathematics and Statistics, Central China Normal University, Wuhan 430079, China
关键词：
2-quasi-cyclic codes;Consta-dihedral codes;Dihedral group codes;Double circulant codes;Finite fields;Self-dual codes
期刊：
Communications in Nonlinear Science and Numerical Simulation,2023年118:106996 ISSN：1007-5704
通讯作者：
Huang, JC;Ruan, SG
作者机构：
[Shi, Shujing] Hangzhou Dianzi Univ, Sch Sci, Hangzhou 310018, Zhejiang, Peoples R China.;[Shi, Shujing; Huang, Jicai] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;[Kuang, Yang] Arizona State Univ, Sch Math & Stat Sci, Tempe, AZ 85287 USA.;[Ruan, Shigui] Univ Miami, Dept Math, Coral Gables, FL 33146 USA.
通讯机构：
[Huang, JC ] C;[Ruan, SG ] U;Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Hubei, Peoples R China.;Univ Miami, Dept Math, Coral Gables, FL 33146 USA.
关键词：
Anti-PD-1;Hopf bifurcation;Immunotherapy;Periodic orbit;Stability;Tumor–immune system interaction model
摘要：
In this paper we study a three-dimensional tumor-immune system interaction model consisted of tumor cells, activated T cells, and immune checkpoint inhibitor anti-PD-1. Based on the uncontrollable character of tumor cells in the absence of immune response and treatment, the growth of tumor cells is assumed to be exponential. We discuss the distribution of equilibria qualitatively and study the stability of all possible equilibria with and without anti-PD-1 drug. When no drug is applied, the model has a tumor-free equilibrium and at most one tumorous equilibrium. Biologically, there exists a threshold dT 1 for the death rate dT of T cells: when dT >= dT 1 tumor cells will keep growing; when dT < dT 1 tumor cells may be eradicated for some positive initial values and keep growing for some other positive initial values. For the case with anti-PD-1 treatment, the model has at most five tumor-free equilibria and two interior equilibria. Our analysis indicates that there exists a threshold gamma A1 for the intravenous continuous injection gamma A: when gamma A <= gamma A1 the fate of tumor cells is the same as the case with no drug applied; when gamma A > gamma A1 the model may exhibit bistable phenomena and periodic orbits. Furthermore, we establish the existence of local Hopf bifurcation around the interior equilibrium and determine the stability of the bifurcating periodic orbits. Our simulations show that the model exhibits a stable periodic orbit which implies the long term coexistence and balance of the tumor and immune system.(c) 2022 Elsevier B.V. All rights reserved.
作者：
Song, Guang-Jing;Ng, Michael K.;Zhang, Xiongjun
期刊：
Applied and Computational Harmonic Analysis,2023年65:348-373 ISSN：1063-5203
通讯作者：
Zhang, Xiongjun(xjzhang@mail.ccnu.edu.cn)
作者机构：
[Song, Guang-Jing] Weifang Univ, Sch Math & Informat Sci, Weifang 261061, Peoples R China.;[Ng, Michael K.] Univ Hong Kong, Dept Math, Hong Kong, Peoples R China.;[Zhang, Xiongjun] Cent China Normal Univ, Sch Math & Stat, Wuhan 430079, Peoples R China.;[Zhang, Xiongjun] Cent China Normal Univ, Hubei Key Lab Math Sci, Wuhan 430079, Peoples R China.
通讯机构：
[Xiongjun Zhang] S;School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Wuhan 430079, China
