ISSN 0253-2778

CN 34-1054/N

2019 Vol. 49, No. 9

Display Method:
On the Sparre-Andersen dual model perturbed by diffusion
2019, 49(9): 689-698. doi: 10.3969/j.issn.0253-2778.2019.09.001
A diffusion perturbed Sparre-Andersen dual risk model was studied, in which the times between gains are independent and identically distributed random variables with a generalized Erlang(n) distribution. An integro-differential equation with certain boundary for the Laplace transform of the ruin time was derived and then its explicit expression was obtained. In particular, an explicit form of the Laplace transform of the time to ruin were studied when jump sizes were exponential. Finally, by studying the expected discounted dividends with the threshold-dividend strategy in the diffusion perturbed Sparre-Andersen dual risk model, an integro-differential equation with certain boundary for the expected discounted dividends was derived.
Log-concavity of compound Poisson distributions
XIA Wanwan
2019, 49(9): 699-703. doi: 10.3969/j.issn.0253-2778.2019.09.002
Log-concavity and total positivity of order 2 (TP2)properties of two-parameter compound Poisson distributions Q(x|θ,ν) with respect to x, θ and ν was studied by exploiting the interrelationships between log-concavity, TP2 and reproductive property developed by the existing literatures. One application was also presented.
On near-imperfect numbers with two distinct prime divisors
TAO Tiantian, SUN Cuifang
2019, 49(9): 704-710. doi: 10.3969/j.issn.0253-2778.2019.09.003
Let ρ be a multiplicative arithmetic function defined by ρ(pα)=pα-pα-1+pα-2-…+(-1)α for every prime power pα. For a positive integer n, n is called a near-imperfect number if 2ρ(n)=n+d where d is a proper divisor of n. Here all near-imperfect numbers with two distinct prime divisors were obtained.
Complexiton solutions to a negative order four-potential Ablowitz-Ladik equation
CHEN Shouting, XUE Yimin
2019, 49(9): 711-722. doi: 10.3969/j.issn.0253-2778.2019.09.004
Searching for the exact solutions to the differential-difference integrable equations has always been a very important topic in the soliton theory and the extending teaching contents of partial differential equation.
Three-dimensional static linear elasticity crack path prediction
CHEN Chong, YANG Dapeng
2019, 49(9): 723-730. doi: 10.3969/j.issn.0253-2778.2019.09.005
Three-dimensional static stress intensity factors were analyzed for a curved crack by using a second order perturbation method. The method was extended to obtain an approximate representation of a three-dimensional static stress intensity factors at the tip of a curved crack. The criterion of elastic bending crack propagation the three-dimensional body was summarized. The shape parameters of three-dimensional linear elastic bending crack propagation were figured out. A static energy release rate due to three-dimensional curved crack growth could be calculated by using Irwin’s formula. Considerations were made for a three-dimensional static curved crack in materials with inhomogeneous fracture toughness. As far as homogeneous matter was concerned, in the framework of the second-order perturbation analysis theory, the two criteria indicated the same three-dimensional static load bending crack propagation path. However, the energy criterion was superior to the stress criterion in materials with non-uniform fracture toughness. Three-dimensional static curved crack path destabilizing factors were compared and analyzed. Critical relations between the material degradation and the static applied stress or the outer static stress for various initial three-dimensional crack lengths have been studied.
Quasi-static axial compression properties of circular tube with periodic holes
LI Delong, ZHANG Ke, CUI Shitang, TANG Zhiping
2019, 49(9): 731-739. doi: 10.3969/j.issn.0253-2778.2019.09.006
By combining the compressibility of the multi-cell material and the axisymmetry of the circular tube, a new energy absorption structure of circular tube with periodic holes was proposed. The mechanical properties of the structure under axial quasi-static loading were studied by numerical simulation. The specimens of typical dimensions were processed and quasi-static experiments were carried out. The experiment proved the reliability of the numerical simulation. The numerical simulation and the experiment show that under the quasi-static axial compression, the main deformation mode of the structure is the overall axial uniform compression, the load displacement curve is smooth, the load force is stable and the amplitude is large, the specific energy absorption and stroke efficiency are moderate, and the cushioning energy absorption performance is good. The influence of geometric parameters on the energy absorption performance of the structure was discussed. It is found that the thickness of the circular tube decides the magnitude of the mean force, and the relationship between them is linear; with the increase of the number of periodic openings or cell wall thickness, the mean force increases gradually, the stroke efficiency decreases gradually, and the specific energy absorption changes little.
Optimal copyright protection and pricing decision of digital content products in monopoly enterprise
YANG Dong, LING Liuyi
2019, 49(9): 740-750. doi: 10.3969/j.issn.0253-2778.2019.09.007
With the development of technology and the increasing market demand for digital products, there are more and more pirated products. The optimal decision (intensity of copyright protection and product pricing) of a monopoly enterprise for the copyright of digital content products was studied under different market conditions and the existence of copyright protection cost. A cost function of copyright protection was given, which specifically depicts the relationship between copyright protection cost, copyright protection intensity and product price.According to the situation of consumers, the market was divided into two types: non-piracy market and piracy market. The results show that the copyright protection intensity is not as high as possible. In addition, when consumer piracy aversion is low, the profit of the piracy market is almost the same as that of the non-piracy market; when consumer piracy aversion is high, it is more beneficial not to take copyright protection measures for the monopoly enterprise.
An optimal combination forecasting model based on maximum closeness of TOPSIS and its properties
WANG Zicheng, CHEN Huayou, HAN Bing, ZHU Jiaming
2019, 49(9): 751-761. doi: 10.3969/j.issn.0253-2778.2019.09.008
Technique for order preference by similarity to ideal solution (TOPSIS) is a common decision-making method. Here it was used as a new criterion for forecasting accuracy. Based on the concepts of positive ideal point sequence and negative ideal point sequence, the optimal combination forecasting model was constructed based on the criterion of maximizing closeness degree in the TOPSIS model. Based on this model, some new concepts were defined, such as the non-inferior combination forecasting, superior combination forecasting, redundant forecasting method and dominant forecasting method. Mathematical properties of this model were studied, in which the advantages of optimal combination forecasting were expounded theoretically. Finally, an example was given and was compared with other combined forecasting models. The results show that the combined forecasting model is feasible and effective.
Evolution game between government and port enterprises under mandatory emission reduction
XU Yan, MENG Yanping
2019, 49(9): 762-772. doi: 10.3969/j.issn.0253-2778.2019.09.009
In recent years, port environmental pollution has become increasingly serious. As a core enterprise in the port supply chain, port enterprises play an important role in promoting the construction of green harbors. Based on mandatory emission reductions, economic performance and environmental performance have been taken into account to build an evolutionary game model of a local government with port companies’ emission reductions. The model introduces carbon tax as a penalty factor and considers the government’s regulatory costs and corporate rent-seeking costs. By analyzing different equilibrium states, the effects of government regulation and punishment on both parties’ strategies were discussed. The results show that the optimal Nash equilibrium strategy is the government does not fully supervise and port companies reduce emissions. The government can decide whether to adopt full supervision by adjusting the relationship between the intensity of supervision and the unit carbon tax, which will affect the decision of port enterprises to reduce emissions. To a certain extent, it provides an effective reference for promoting the construction of green ports in the future.