ISSN 0253-2778

CN 34-1054/N

2018 Vol. 48, No. 8

Display Method:
Original Paper
On total {k}-domatic number of Cartesian and direct product of graphs
LIANG Yong, PEI Lidan, HU Futao, HOU Xinmin
2018, 48(8): 605-611. doi: 10.3969/j.issn.0253-2778.2018.08.001
For a positive integer k, the total {k}-dominating function (T{k} DF) of a graph G without isolated vertices is a function f from the vertex set V(G) to
Sufficient conditions for digraphs to be maximally connected and super-connected
HONG Zhenmu, VOLKMANN Lutz, XU Junming
2018, 48(8): 612-617. doi: 10.3969/j.issn.0253-2778.2018.08.002
Let D be a finite and simple digraph with vertex set V(D). For a vertex v∈V(D), the degree d(v) of v is defined as the minimum value of its out-degree d+(v) and its in-degree d-(v). If D is a digraph with minimum degree δ and connectivity κ, then κ≤δ. A digraph is maximally connected if κ=δ. A maximally connected digraph D is said to be super-connected if for every minimum vertex-cut S, the digraph D-S is either non-strongly connected with at least one trivial strong component or trivial. Here some sufficient conditions for digraphs or bipartite digraphs with given minimum degree to be maximally connected or super-connected were presented in terms of the number of arcs, and some examples were given to demonstrate that the lower bound on these conditions are sharp.
A note on Frobenius functors
ZHAO Zhibing
2018, 48(8): 618-621. doi: 10.3969/j.issn.0253-2778.2018.08.003
Some new characterizations of Frobenius bimodules in terms of Frobenius functors were given. It was proved that a bimodule is Frobenius if and only if it is finitely generated projective on both sides, and that the restriction of the corresponding tensor functor to the categories of finitely generated projective modules is a Frobenius functor. The characterizations allow us to give a new proof of the endomorphism ring theorem by a functorial method.
Survival analysis of stochastic three-species food chain model with white noise and general Lévy jumps
ZENG Ting, TENG Zhidong
2018, 48(8): 622-630. doi: 10.3969/j.issn.0253-2778.2018.08.004
The survival of a stochastic three species food chain model with white noise and general Lévy jumps was analyzed, which includes existence and uniqueness of global positive solution as well as permanence in the mean of the highest species.Situations where some species are extinct while others are persistent in the mean were also clarified.The results show that Lévy jumps can obviously change the survival of population, which can make the persistent population become extinct, or vice versa.
Dynamics analysis of an impulsive stochastic SIS epidemic model with standard incidence
YU Jiajia, LING Lin, DONG Jinhua, JIANG Guirong
2018, 48(8): 631-636. doi: 10.3969/j.issn.0253-2778.2018.08.005
Random disturbance, birth pulse and pulse treatments were simultaneously considered to build a class of SIS epidemic model with standard incidence.By applying the theory of stochastic differential equation, the sufficient conditions for the stochastic stability of the trivial solution were obtained.The sufficient conditions for the existence of the disease free solution were obtained by using a discrete map. The stochastic extinction of the disease was investigated by using the It formula.Moreover, numerical simulation was conducted to verify the theoretical analysis.
Complete convergence of weighted sums for extended ND random variables sequence under sub-linear expectation
LIANG Haiye, WU Qunying
2018, 48(8): 637-642. doi: 10.3969/j.issn.0253-2778.2018.08.006
The complete convergence of weighted sums for extended ND under sub-linear expectation was studied. With the condition of the p order Choquet integrals of the random variable being finite, the complete convergence of weighted sums for extended ND random variables sequence in the probability space was extended to the sub-linear expectations space.
Poisson bracket method for obtaining normal coordinates of quadratic Hamiltonian
LIN Quan, FAN Hongyi
2018, 48(8): 643-648. doi: 10.3969/j.issn.0253-2778.2018.08.007
It was found that the problem of searching for normal coordinates W of quadratic Hamiltonian H can be ascribed to solving the newly established secular equation with two consecutive Poisson bracket operations. Solving W would simultaneously lead to the normal frequency. Some examples about quadratic Hamiltonian were presented to demonstrate the effectiveness of the presented method.
Entangled state representation for two particles with unequal masses and the squeezed state generation
YANG Yang, FAN Hongyi
2018, 48(8): 649-654. doi: 10.3969/j.issn.0253-2778.2018.08.008
It was found that the entangled state representation of two particles with unequal masses can be directly derived by the Weyl correspondence and the technique of integration within an ordered product of operators. The entanglement properties can be achieved through its Schmidt decomposition. With this representation, a kind of new one- and two- combination squeezed state and corresponding squeezing operator was obtained.
Financial contagion and stability test of BRIC countries based on R-vine copula change-point model
YE Wuyi, GUO Renzhen, MIAO Baiqi
2018, 48(8): 655-666. doi: 10.3969/j.issn.0253-2778.2018.08.009
The BRIC countries (Brazil, Russia, India and China) are representations of the emerging markets. Financial contagion and stability from the perspective of the dependence of the analyzed countries on the global systemic risk was characterized, with the MSCI Global Index representing the global systemic risk factor. The dependency structure of the BRIC’s major indexes and the MSCI global index was analyzed, and an empirical analysis of the financial stability of the BRIC countries was performed. To analyze the structural changes of systemic risk impact on the BRIC countries, R-vine copula was used to test the change point and analyze the financial contagion and stability of the BRIC countries affected by the financial crisis and BRICs events. The financial stability among BRIC countries was measured using the correlation coefficient based on the MSCI index. The empirical results show that after the control of systemic risk, the independence of the BRIC countries’ stock markets has been strengthened. The BRIC countries have been hit harder by systemic risks after the financial crisis. Strengthening BRIC countries’ cooperation will help to reduce the risk of the affection between BRIC countries.
On the relationship between stock liquidity and corporate bond credit spreads
ZHAO Jing, FANG Zhaoben
2018, 48(8): 667-682. doi: 10.3969/j.issn.0253-2778.2018.08.010
Based on the spillover effects between stock and bond markets in China, an endogenous default credit model which includes both outside and inside liquidity shocks to stock and bond markets was presented. The effects of outside and inside liquidity shocks on corporate bonds spreads were analyzed. An empirical analysis of corporate bonds traded in Shanghai and Shenzhen stock exchanges during 2008-01-01~2016-12-31 was presented, and the effects of liquidity shocks on corporate bonds spreads predicted by the model were confirmed. For debts with shorter maturities and higher risks, the effects are even more significant.
Selection of tender evaluation methods based on product differentiation
ZHAO Yajuan, LI Shaobo
2018, 48(8): 683-690. doi: 10.3969/j.issn.0253-2778.2018.08.011
Lowest bid and multi-criteria tender evaluation are the two main tender evaluation methods, and their misuse will affect the fairness and impartiality of the evaluation result. Based on the perspective of product difference, a correlation analysis of the essential characteristics of homogeneous, heterogeneous products and two tender evaluation methods was presented, and the effectiveness of cross elasticity as the quantitative standard for selecting a tender evaluation method was discussed. Considering that the cross elasticity was determined by the shape of the demand curve, the Logit demand model based on the choice of consumers’ random utility was adopted as the theoretical basis. Finally, three types of project cases were selected for the application analysis, which verified the feasibility of the method and provides a novel and effective way for the selection of evaluation methods in practice.