ISSN 0253-2778

CN 34-1054/N

2017 Vol. 47, No. 11

Research Articles:Mathematics
A uniform asymptotic estimate for ruin probability of a discrete-time risk model with subexponential innovations
SHEN Linchuan, CHEN Yu
2017, 47(11): 885-893. doi: 10.3969/j.issn.0253-2778.2017.11.001
The recursive equation Tn=Xn+Tn-1Yn was considered, in which Xn and Yn are two independent random variables, and Tn-1 on the right-hand side is independent of (Xn,Yn). Under the assumption that Xn follows a subexponential distribution with a nonzero lower Karamata index, and that (Xn,Yn) fulfills a certain dependence structure, some asymptotic formulas were obtained for the tail probabilities of Tn in this equation.
n-color1-2-3 compositions of positive integers
GUO Yuhong
2017, 47(11): 894-898. doi: 10.3969/j.issn.0253-2778.2017.11.002
An n-color 1-2-3 composition of positive integers is defined as an n-color composition with only parts of size 1, 2 or 3. An n-color 1-2-3 palindromic composition is an n-color 1-2-3 composition that reads the same forward as backward. Here the generating function, explicit formulas and recurrence relations for the number of n-color 1-2-3 compositions and the n-color 1-2-3 palindromic compositions of positive integers were obtained. In addition, a relation between the number of 1-2-3 compositions of a positive integer and the number of compositions of a positive integer with parts omitting all multiples of size 3 was given. Furthermore, the generalized relation was obtained.
Linear codes and their weight enumerators over the ring Fp+uFp+vFp+uvFp
CHEN Yanna, WU Huazhang, SHI Minjia
2017, 47(11): 899-905. doi: 10.3969/j.issn.0253-2778.2017.11.003
The linear codes over the ring Fp+uFp+vFp+uvFp were studied, where p is a prime and u2=u, v2=v, uv=vu. A kind of Gray map and some weight enumerators and their relationships of linear codes over R were discussed. Moreover, an example was given to show the validity of the above weight enumerators formulas.
A special class of near-perfect numbers
LI Jian, LIAO Qunying
2017, 47(11): 906-911. doi: 10.3969/j.issn.0253-2778.2017.11.004
Let α≥2 be an integer, p1 and p2 be odd prime numbers with p12. By using elementary methods and techniques, it was proved that there are no near-perfect numbers of the form 2α-1p12p22 with the redundant divisor d∈{1,p12,p22,p1p2,p1p22,p12p2}, and then an equivalent condition for near-perfect numbers of the form 2α-1p12p22 with the redundant divisor d∈{p1,p2} was obtained. Furthermore, for a fixed positive integer k≥ 2, by generalizing the definition of nearperfect numbers to be k-weakly-near-perfect numbers, it was proved that there are no k-weakly-near-perfect numbers of the form n=2α-1p12p22 when k≥ 3.
A class of new binary 6-point subdivision scheme
XING Yan, GUO Benyun, TAN Jieqing
2017, 47(11): 912-918. doi: 10.3969/j.issn.0253-2778.2017.11.005
A class of interpolation and approximation blending binary 6-point subdivision scheme was presented. The smoothness of the scheme was analyzed by the Laurent polynomial method. The limit curve can reach C4 continuous. The Holder exponent of the limit curves was also calculated. Compared with the existing binary 6-point subdivision schemes, the proposed scheme achieves higher continuity and better approximating results. Furthermore, the uniform subdivision scheme is extended to the non-uniform subdivision scheme. Experimental results illustrate the effectiveness of the subdivision scheme and the role of the shape parameters.
Research Articles:Physics
Defocus image restoration by an accurate optical transfer function of Fresnel zone plate in soft X-ray microscopy
LI Fahu, GUAN Yong, XIONG Ying, ZHANG Xiaobo, LIU Gang, TIAN Yangchao
2017, 47(11): 918-923. doi: 10.3969/j.issn.0253-2778.2017.11.006
High-resolution soft X-ray microscopy has been widely adopted for obtaining the three-dimensional structure of physical objects. However, the limited depth of focus may cause sample defocusing and, subsequently, lead to blurring of images. A defocused image restoration method was proposed based on an optical transfer function (OTF) of a Fresnel zone plate (FZP). Using this restoration method the defocused image of Siemens star was restored. The results show that the restoration method based on OTF is capable of suppressing the blurring effect and restore defocus images caused by defocusing of the object. Furthermore, related simulations have been carried out to demonstrate the effectiveness of this method in overcoming the limitations to focal depth and accomplishing three dimensional imaging of samples.
Research Reviews: Physics
Non-destructive grating-based phase contrast X-ray imaging of crucian carp
FENG Damin, HU Renfang, WANG Shenghao, GAO Kun, PAN Zhiyun
2017, 47(11): 924-928. doi: 10.3969/j.issn.0253-2778.2017.11.007
Recently, grating-based phase contrast X-ray imaging has become a hot spot, and it is considered the key technology for future clinical medical nondestructive diagnosis due its high compatibility with the conventional X-ray source. Compared with the existing X-ray absorption contrast imaging technology, phase-contrast imaging has the unique ability to distinguish soft tissues. Here the grating-based phase contrast X-ray imaging was used to nondestructively detect the structure of local crucian carp treated by formalin. The structure of the intestine tissues are shown clearly, the very first time using such imaging technology.
Research Articles:Management Science and Engineering
Evolutionary game analysis between local governments and power generation enterprises based on carbon trading mechanism
XU Jingzhi, DONG Yu
2017, 47(11): 929-939. doi: 10.3969/j.issn.0253-2778.2017.11.008
Based on evolutionary game theory, a game model between local governments and power generation enterprises was constructed, and then the dynamic stability and evolution trend were analyzed. The analysis result suggests that there exist some different equilibria in the evolution of the game system when the expected profits of enterprises are changing. Accordingly, local governments need to take some measures, for example, strengthening incentives to enterprises who actively abide by emission reduction polices, increasing carbon trading prices appropriately, reducing the variance of cost when local governments choose strict regulation or loose regulation, and strengthening public supervision of the governments, so as to urge the power generation enterprises to consciously reduce carbon emissions, thus achieving control over the overall carbon emissions.
The impact of consumer confusion on the product rollover strategy
ZHA Yong, HU Zhangchen, XU Chuanyong
2017, 47(11): 940-950. doi: 10.3969/j.issn.0253-2778.2017.11.009
With frequent product upgrades, consumers have substantive difficulty in differentiating products from various generations, which leads to consumer confusion. This brings great challenges for the firms when choosing product upgrading strategies. To address the impact of consumer confusion on firm's rollover strategy, a joint quality and pricing optimization model was constructed, incorporating the effect of consumer confusion. It was found that, under the single rollover strategy, wherein only one upgraded product is offered, the price and quality of the upgraded product decrease with the increase in consumer confusion, and so will the demand and profits of the firm. Under the dual rollover strategy, wherein both an upgraded product and the base product are offered, if the level of consumer confusion is lower than a threshold, the price and quality of the new product increase with the increase in consumer confusion, and so will the demand and profits of the firm. However, when the level of consumer confusion is higher than the threshold, the price and quality of the new product remain unchanged, and so will the demand and profit. When consumer confusion is at a high level, the price and quality of the new product under the dual rollover strategy are greater than those under the single rollover strategy. If consumer confusion is at a low level, the firm chooses a single rollover strategy and otherwise dual rollover strategy is profitable.
The price strategy of information asymmetry platform with partly multi-homing
GAO Jiping
2017, 47(11): 951-959. doi: 10.3969/j.issn.0253-2778.2017.11.010
In real life, it is a rare occurrence that all customers are multi-homing or single-homing to platforms. The more prevalent case is that a part of the customers are multi-homing to platforms, while others are single-homing. Based on the Hotelling model, a two-sided platform competition model with asymmetric information was built. A research of the platform price strategies with different market structures under customer partly multi-homing was conducted. The research show: ①platforms charge a low price to customers who join in first and the price is closely related to the customers’ affiliated situation; ②platforms will set a low price for those who arrive later if they are multi-homing to platforms and it is more beneficial for those who join in first if they single-home when the network effect is high enough;③it is important for the development of the platform to set appropriate price strategies for guiding customers’ affiliation under various market structures.
Smart device product pricing based on operating system performance
2017, 47(11): 960-970. doi: 10.3969/j.issn.0253-2778.2017.11.011
Smart devices are a typical two-layer platform system, whose performance depends on both hardware quality and operating system performance. Manufactures usually release smart device products to the market sequentially due to quality improvement, and the performance of a lower version product is lower than that of a high version one. Here the pricing problem of smart device products was modeled under two scenarios: one-side market and two-side market. To explore the optimal product prices of two versions of products on a monopoly platform, the impacts of operating system performance and network externalities on the optimal prices, market shares and profits was investigated. The results show that total market share and profit of two version products increase with the enhancement of operating system performance, and platform network externalities have significant impacts on the market shares and optimal prices of the two version products. According to the model calculation results, it is obtained that how the performance of the operating system specifically influences the optimal product pricing decision of smart devices while network externality intensities are in five different areas.