A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted.In this paper,for a connected graph G with sufficiently large order,we pres...A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted.In this paper,for a connected graph G with sufficiently large order,we present a tight sufficient condition for G with fixed minimum degree to be k-connected based on the Q-index.Our result can be viewed as a spectral counterpart of the corresponding Dirac-type condition.展开更多
MgAl-LDH（layered double hydroxides） were prepared with CO（NH2）2, NH4 Cl and NH3·H2O by the coprecipitation method, respectively. Corresponding composite membranes were prepared by the coating method. LDHs wer...MgAl-LDH（layered double hydroxides） were prepared with CO（NH2）2, NH4 Cl and NH3·H2O by the coprecipitation method, respectively. Corresponding composite membranes were prepared by the coating method. LDHs were characterized by WAXS, CO2-TPD and SEM. The morphology of the PVC/LDHs composite membranes were characterized by means of SEM. The thermal stability of the membranes was analyzed by air aging box and TGA-FTIR. The SEM results show that nano-particles can be compatible with poly（vinyl chloride）（PVC） matrix homogeneously by the stirring-ultrasound blend method with two steps. Furthermore, the air aging box results proved that MgAl-CO（NH2）2-LDH has the best effect on thermal stability of PVC. TGA-FTIR results show that MgAl-CO（NH2）2-LDH could adsorb more HCl that resulted from the degradation of PVC and improve the pyrolysis temperature of the first degradation stage by 15 K compared with PVC.展开更多
Let D = （V, E） be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD（v）, is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu,...Let D = （V, E） be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD（v）, is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD（V1） ≤ exPD（V2） …≤ exPD（Vn）. Then exPD（Vk） is called the k- point exponent of D and is denoted by exPD （k）, 1≤ k ≤ n. In this paper we define e（n, k） ：= max{expD （k） ｜ D ∈ PD（n, 2）} and E（n, k） ：= {exPD（k）｜ D ∈ PD（n, 2）}, where PD（n, 2） is the set of all primitive digraphs of order n with girth 2. We completely determine e（n, k） and E（n, k） for all n, k with n ≥ 3 and 1 ≤ k ≤ n.展开更多
基金the National Natural Science Foundation of China(Nos.11971311,12161141003,and 12026230)Science and Technology Commission of Shanghai Municipality(No.22JC1403600)+1 种基金Li-Hua Feng and Wei-Jun Liu are partly supported by the National Natural Science Foundation of China(Nos.11871479,12071484)Hunan Provincial Natural Science Foundation(Nos.2020JJ4675,2018JJ2479).
文摘A connected graph G is said to be k-connected if it has more than k vertices and remains connected whenever fewer than k vertices are deleted.In this paper,for a connected graph G with sufficiently large order,we present a tight sufficient condition for G with fixed minimum degree to be k-connected based on the Q-index.Our result can be viewed as a spectral counterpart of the corresponding Dirac-type condition.
基金supported by the Shanghai Municipal Education Commission with“Twelfth Five”scientific connotation construction project(No.nhky-2012-05)foreign visiting scholar fellowship program(No.B-8938-12-0406)Opening Project of Shanghai Key Laboratory of Multiphase Flow and Heat Transfer in Power Engineering
文摘MgAl-LDH（layered double hydroxides） were prepared with CO（NH2）2, NH4 Cl and NH3·H2O by the coprecipitation method, respectively. Corresponding composite membranes were prepared by the coating method. LDHs were characterized by WAXS, CO2-TPD and SEM. The morphology of the PVC/LDHs composite membranes were characterized by means of SEM. The thermal stability of the membranes was analyzed by air aging box and TGA-FTIR. The SEM results show that nano-particles can be compatible with poly（vinyl chloride）（PVC） matrix homogeneously by the stirring-ultrasound blend method with two steps. Furthermore, the air aging box results proved that MgAl-CO（NH2）2-LDH has the best effect on thermal stability of PVC. TGA-FTIR results show that MgAl-CO（NH2）2-LDH could adsorb more HCl that resulted from the degradation of PVC and improve the pyrolysis temperature of the first degradation stage by 15 K compared with PVC.
基金Supported by the National Natural Science Foundation of China(No.10771061,No.10771058)SRF of Hunan Provincial Education Department(No.07C267).
文摘Let D = （V, E） be a primitive digraph. The vertex exponent of D at a vertex v∈ V, denoted by expD（v）, is the least integer p such that there is a v →u walk of length p for each u ∈ V. Following Brualdi and Liu, we order the vertices of D so that exPD（V1） ≤ exPD（V2） …≤ exPD（Vn）. Then exPD（Vk） is called the k- point exponent of D and is denoted by exPD （k）, 1≤ k ≤ n. In this paper we define e（n, k） ：= max{expD （k） ｜ D ∈ PD（n, 2）} and E（n, k） ：= {exPD（k）｜ D ∈ PD（n, 2）}, where PD（n, 2） is the set of all primitive digraphs of order n with girth 2. We completely determine e（n, k） and E（n, k） for all n, k with n ≥ 3 and 1 ≤ k ≤ n.
