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学者姓名：陈爱莲
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Abstract ：
A graph H has Hamiltonicity if it contains a cycle which covers each vertex of H. In graph theory, Hamiltonicity is a classical and worth studying problem. In 1952, Dirac proved that any n-vertex graph H with minimum degree at least inverted right perpendicular n/2 inverted left perpendicular has Hamiltonicity. In 2012, Lee and Sudakov proved that if p >> log n/n, then asympotically almost surely each n-vertex subgraph of random graph G(n, p) with minimum degree at least (1/2 + o(1))np has Hamiltonicity. In this paper, we exend Dirac's theorem to random 3-uniform hypergraphs. The random 3-uniform hypergraph model H-3(n, p) consists of all 3-uniform hypergraphs on n vertices and every possible edge appears with probability p randomly and independently. We prove that if p >> log n/n(2), then asympotically almost surely every n-vertex subgraph of H-3(n, p) with minimum degree at least (1/4 + o(1))(n/2) p has Berge Hamiltonicity. The value log n/n(2) and constant 1/4 both are best possible.
Keyword ：
Berge cycle Berge cycle Dirac's theorem Dirac's theorem Hamilton cycle Hamilton cycle Random hypergraph Random hypergraph
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| GB/T 7714 | Chen, Ailian , Zhang, Liping . Minimum degree condition of Berge Hamiltonicity in random 3-uniform hypergraphs [J]. | FILOMAT , 2023 , 37 (26) : 9039-9050 . |
| MLA | Chen, Ailian 等. "Minimum degree condition of Berge Hamiltonicity in random 3-uniform hypergraphs" . | FILOMAT 37 . 26 (2023) : 9039-9050 . |
| APA | Chen, Ailian , Zhang, Liping . Minimum degree condition of Berge Hamiltonicity in random 3-uniform hypergraphs . | FILOMAT , 2023 , 37 (26) , 9039-9050 . |
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For a conditional density function (CDF) in the right-censored model, the local linear (LL) estimator has superior bias properties compared with the Nadaraya-Watson (NW) one, but it may have negative values and thus give rise to unsuitable inference. In order to alleviate the possible negativity of the LL estimator, we define a reweighted NW (RNW) estimator of the CDF in the right-censored model by employing the empirical likelihood (EL) method. The RNW estimator is constructed by modifying the NW estimator slightly, so it naturally inherits the nonnegativity of the NW one. It is assumed that the censoring time is independent of the survival time with the associated covariate. Under stationary alpha-mixing observations, the weak consistency and asymptotic normality of the RNW estimator are developed. The asymptotic normality shows that the RNW estimator possesses the bias and variance of the LL estimator. Finally, we conduct simulations to evaluate the finite sample performance of the estimator. (C) 2020 Elsevier B.V. All rights reserved.
Keyword ：
Asymptotic normality Asymptotic normality CDF CDF Nonnegativity Nonnegativity Right-censored model Right-censored model RNW estimator RNW estimator
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| GB/T 7714 | Xiong, Xianzhu , Ou, Meijuan , Chen, Ailian . Reweighted Nadaraya-Watson estimation of conditional density function in the right-censored model [J]. | STATISTICS & PROBABILITY LETTERS , 2021 , 168 . |
| MLA | Xiong, Xianzhu 等. "Reweighted Nadaraya-Watson estimation of conditional density function in the right-censored model" . | STATISTICS & PROBABILITY LETTERS 168 (2021) . |
| APA | Xiong, Xianzhu , Ou, Meijuan , Chen, Ailian . Reweighted Nadaraya-Watson estimation of conditional density function in the right-censored model . | STATISTICS & PROBABILITY LETTERS , 2021 , 168 . |
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A complex square matrix is a ray pattern matrix if each of its nonzero entries has modulus 1. A ray pattern matrix naturally corresponds to a weighted-digraph. A ray pattern matrix A is ray nonsingular if for each entry-wise positive matrix K, A omicron K is nonsingular. A random model of ray pattern matrices with order n is introduced, where a uniformly random ray pattern matrix B is defined to be the adjacency matrix of a simple random digraph D-n,D- p whose arcs are weighted with i.i.d. random variables uniformly distributed over the unit circle in the complex plane. It is shown that p* (n) = 1/n is a threshold function for the random matrix M = I-B to be ray nonsingular, which is the same as the threshold function of the appearance of giant strong components in D-n,D-p.
Keyword ：
random digraph random digraph ray nonsingular ray nonsingular ray pattern matrix ray pattern matrix Threshold function Threshold function uniformly random uniformly random
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| GB/T 7714 | Liu, Yue , Chen, Ailian , Lin, Fenggen . Threshold function of ray nonsingularity for uniformly random ray pattern matrices [J]. | LINEAR & MULTILINEAR ALGEBRA , 2021 . |
| MLA | Liu, Yue 等. "Threshold function of ray nonsingularity for uniformly random ray pattern matrices" . | LINEAR & MULTILINEAR ALGEBRA (2021) . |
| APA | Liu, Yue , Chen, Ailian , Lin, Fenggen . Threshold function of ray nonsingularity for uniformly random ray pattern matrices . | LINEAR & MULTILINEAR ALGEBRA , 2021 . |
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This article focuses on the conditional density of a scalar response variable given a random variable taking values in a semimetric space. The local linear estimators of the conditional density and its derivative are considered. It is assumed that the observations form a stationary -mixing sequence. Under some regularity conditions, the joint asymptotic normality of the estimators of the conditional density and its derivative is established. The result confirms the prospect in Rachdi etal. (2014) and can be applied in time-series analysis to make predictions and build confidence intervals. The finite-sample behavior of the estimator is investigated by simulations as well.
Keyword ：
alpha-mixing dependence alpha-mixing dependence Conditional density Conditional density Functional data Functional data Joint asymptotic normality Joint asymptotic normality Local linear estimator Local linear estimator
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| GB/T 7714 | Xiong, Xianzhu , Zhou, Peiqin , Ailian, Chen . Asymptotic normality of the local linear estimation of the conditional density for functional time-series data [J]. | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2018 , 47 (14) : 3418-3440 . |
| MLA | Xiong, Xianzhu 等. "Asymptotic normality of the local linear estimation of the conditional density for functional time-series data" . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS 47 . 14 (2018) : 3418-3440 . |
| APA | Xiong, Xianzhu , Zhou, Peiqin , Ailian, Chen . Asymptotic normality of the local linear estimation of the conditional density for functional time-series data . | COMMUNICATIONS IN STATISTICS-THEORY AND METHODS , 2018 , 47 (14) , 3418-3440 . |
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In this paper we consider the random r-uniform r-partite hypergraph model H(Thi,r12, " " ",Thr; ri,P) which consists of all the r-uniform r-partite hypergraphs with vertex partition {171, V2, " " ",17,-} where 1Vil = n(i) = n(i)(n) (1 < i < r) are positive integer-valued functions on n with m1 +n2 + " " " +n, = n, and each r-subset containing exactly one element in V-i (1 < i < r) is chosen to be a hyperedge of H E (n,1,Th2, " " ",Thr; ri,P) with probability p = p(m), all choices being independent. Let,A.vi =,"v1 (H) and (5v1 = Spi (H) be the maximum and minimum degree of vertices in 171 of H, respectively; Xd,v, = Xd,vi (H), Yd,Vi = Yd,Vi (H), Z d Vi = Z d Vi (H) and Ze,d,vi = ZC,d, Vi (H) be the number of vertices in 171 of H with degree d, at least d, at most d, and between c and d, respectively. In this paper we obtain that in the space 7-i(Thi,Th2, " " ", rir; Xdyi Yd,Vi Zd,Vi, and Ze,d,vi all have asymptotically Poisson distributions. We also answer the following two questions. What is the range of p that there exists a function D(n) such that in the space H(Thi, ri2, " " ", mr; n, p), lira P(.171 = D(m)) = 1? What is the range of p such that a.e., Hp E 7i(Thi,n2, " " ",Thriri,p) has a unique vertex in 171 with degree,,v1 (Hp)? Both answers are p = o (log ni N), where N = nni. The corresponding i=2 problems on (5 (Hp) also are considered, and we obtained the answers are p < (1 o(1))(log ni/N) and p = o (log ThilN), respectively.
Keyword ：
degree distribution degree distribution maximum degree maximum degree minimum degree minimum degree random uniform hypergraphs random uniform hypergraphs
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| GB/T 7714 | Chen, Ai-lian , Li, Hao , Zhang, Fu-ji . The Maximum and Minimum Degree of the Random r-uniform r-partite Hypergraphs [J]. | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES , 2016 , 32 (4) : 867-874 . |
| MLA | Chen, Ai-lian 等. "The Maximum and Minimum Degree of the Random r-uniform r-partite Hypergraphs" . | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES 32 . 4 (2016) : 867-874 . |
| APA | Chen, Ai-lian , Li, Hao , Zhang, Fu-ji . The Maximum and Minimum Degree of the Random r-uniform r-partite Hypergraphs . | ACTA MATHEMATICAE APPLICATAE SINICA-ENGLISH SERIES , 2016 , 32 (4) , 867-874 . |
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Topological indices based on the distances between vertices(atoms) of a molecular graph are widely used for characterizing molecular graphs and their fragments, establishing relationships between structures and properties of molecules, predicting biological activity of chemical compounds, and making other chemical applications. Polyphenyls are a kind of macrocyclic aromatic hydrocarbons and their derivatives are very important organic chemicals, which can be used in organic synthesis, drug synthesis, heat exchanger, etc. In this paper we investigate the relationships between the Wiener index and other distance-based topological indices in the tree-like polyphenyl systems and obtain some exactly formulae on the relationships. (C) 2016 Elsevier Inc. All rights reserved.
Keyword ：
Degree distance Degree distance Polyphenyl chain Polyphenyl chain Szeged index Szeged index Topological index Topological index Wiener index Wiener index
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| GB/T 7714 | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Distance-based topological indices of the tree-like polyphenyl systems [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 281 : 233-242 . |
| MLA | Chen, Ailian 等. "Distance-based topological indices of the tree-like polyphenyl systems" . | APPLIED MATHEMATICS AND COMPUTATION 281 (2016) : 233-242 . |
| APA | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Distance-based topological indices of the tree-like polyphenyl systems . | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 281 , 233-242 . |
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The Wiener index W(G) and the edge-Wiener index W-e(G) of a graph G are defined as the sum of all distances between pairs of vertices in a graph G and the sum of all distances between pairs of edges in G, respectively. The Wiener index, due to its correlation with a large number of physico-chemical properties of organic molecules and its interesting and non-trivial mathematical properties, has been extensively studied in both theoretical and chemical literature. The edge-Wiener index of G is nothing but the Wiener index of the line graph of G. The concept of line graph has been found various applications in chemical research. In this paper, we show that if G is a catacondensed hexagonal system with h hexagons and has t linear segments S-1, S-2, ,S-t of lengths l(S-i) = l(i)(1 <= i <= t), then W-e(G) = 25/16W(G) + 1/16(120h(2) + 94h + 29) - 1/4 Sigma(t)(i=1)(l(i) - 1)(2). Our main result reduces the problems on the edge-Wiener index to those on the Wiener index in the catacondensed hexagonal systems, which makes the former ones easier. (C) 2015 Elsevier Inc. All rights reserved.
Keyword ：
Catacondensed hexagonal system Catacondensed hexagonal system Edge-Wiener index Edge-Wiener index Line graph Line graph Wiener index Wiener index
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| GB/T 7714 | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems [J]. | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 273 : 1100-1106 . |
| MLA | Chen, Ailian 等. "Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems" . | APPLIED MATHEMATICS AND COMPUTATION 273 (2016) : 1100-1106 . |
| APA | Chen, Ailian , Xiong, Xianzhu , Lin, Fenggen . Explicit relation between the Wiener index and the edge-Wiener index of the catacondensed hexagonal systems . | APPLIED MATHEMATICS AND COMPUTATION , 2016 , 273 , 1100-1106 . |
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Dimer problem for three dimensional lattice is an unsolved problem in statistical mechanics and solid-state chemistry. In this paper, we obtain asymptotical expressions of the number of close-packed dimers (perfect matchings) for two types of three dimensional lattice graphs. Let M(G) denote the number of perfect matchings of G. Then log(M(K-2 X C-4 X P-n)) approximate to (-1.171. n(-1.1223) + 3.146)n, and log(M(K-2 X P-4 X P-n)) approximate to (-1.164. n(-1.196) + 2.804)n, where log() denotes the natural logarithm. Furthermore, we obtain a sufficient condition under which the lattices with multiple cylindrical and multiple toroidal boundary conditions have the same entropy. (C) 2015 Elsevier B.V. All rights reserved.
Keyword ：
Dimer Dimer Entropy Entropy Three dimensional lattice Three dimensional lattice
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| GB/T 7714 | Lin, Fenggen , Chen, Ailian , Lai, Jiangzhou . Dimer problem for some three dimensional lattice graphs [J]. | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS , 2016 , 443 : 347-354 . |
| MLA | Lin, Fenggen 等. "Dimer problem for some three dimensional lattice graphs" . | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 443 (2016) : 347-354 . |
| APA | Lin, Fenggen , Chen, Ailian , Lai, Jiangzhou . Dimer problem for some three dimensional lattice graphs . | PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS , 2016 , 443 , 347-354 . |
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The author obtains explicit expressions for the expected value of the Merrifield-Simmons index of a random phenylene chain and a random hexagon chain, respectively. The author also computes the corresponding entropy constants and obtains the maximum and minimum values in both random systems, respectively.
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| GB/T 7714 | Chen, Ailian . Merrifield-Simmons Index in Random Phenylene Chains and Random Hexagon Chains [J]. | DISCRETE DYNAMICS IN NATURE AND SOCIETY , 2015 . |
| MLA | Chen, Ailian . "Merrifield-Simmons Index in Random Phenylene Chains and Random Hexagon Chains" . | DISCRETE DYNAMICS IN NATURE AND SOCIETY (2015) . |
| APA | Chen, Ailian . Merrifield-Simmons Index in Random Phenylene Chains and Random Hexagon Chains . | DISCRETE DYNAMICS IN NATURE AND SOCIETY , 2015 . |
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In this paper, as a generalization of the binomial random graph model, we define the model of multigraphs as follows: let G( n; {p(k)}) be the probability space of all the labelled loopless multigraphs with vertex set V = {v(1), v(2), ..., v(n)}, in which the distribution of t(vi), v(j), the number of the edges between any two vertices v(i) and v(j) is P{t(vi), v(j) = k} = p(k), k = 0, 1, 2, ... and they are independent of each other. Denote by X-d = X-d(G), Y-d = Y-d(G), Z(d) = Z(d)(G) and Z(cd) = Z(cd)(G) the number of vertices of G with degree d, at least d, at most d and between c and d. In this paper, we discuss the distribution of X-d, Y-d, Z(d) and Z(cd) in the probability space G(n; {p(k)}).
Keyword ：
Degree distribution Degree distribution degree sequence degree sequence random multigraph random multigraph
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| GB/T 7714 | Chen, Ai Lian , Zhang, Fu Ji , Li, Hao . The degree distribution of the random multigraphs [J]. | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2012 , 28 (5) : 941-956 . |
| MLA | Chen, Ai Lian 等. "The degree distribution of the random multigraphs" . | ACTA MATHEMATICA SINICA-ENGLISH SERIES 28 . 5 (2012) : 941-956 . |
| APA | Chen, Ai Lian , Zhang, Fu Ji , Li, Hao . The degree distribution of the random multigraphs . | ACTA MATHEMATICA SINICA-ENGLISH SERIES , 2012 , 28 (5) , 941-956 . |
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