ISSN 0253-2778

CN 34-1054/N

2015 Vol. 45, No. 6

Display Method:
Original Paper
The Lagrangian surfaces with constant curvature in Q2
LI Kang, HU Sen
2015, 45(6): 431-435. doi: 10.3969/j.issn.0253-2778.2015.06.001
A class of H-minimal Lagrangian surfaces with constant curvature in Q2 was described, and an example was given of minimal Lagrangian S2 with Gaussian curvature K=2.
Hamilton paths and cycles in fault-tolerant varietal hypercubes
HUANG Yanyun, XU Junming
2015, 45(6): 436-442. doi: 10.3969/j.issn.0253-2778.2015.06.002
The varietal hypercube VQn, a variant of the hypercube Qn, was studied. It was proved that VQn contains a fault-free Hamilton cycle provided faulty edges do not exceed n-2, and that for two distinct vertices, x and y, there is a fault-free xy-Hamilton path in VQn provided faulty edges do not exceed n-3 for n≥3. The proof is based on an inductive construction.
Solubility of finite groups
ZHANG Li, LI Baojun
2015, 45(6): 443-448. doi: 10.3969/j.issn.0253-2778.2015.06.003
Let H be a p-subgroup of G. Then: ① H satisfies Φ*-property in G if H is a Sylow subgroup of some subnormal subgroup of G and for any non-solubly-Frattini chief factor L/K of G, |G:NG(K(H∩L))| is a power of p; ② H is called Φ*-embedded in G if there exists a subnormal subgroup T of G such that HT is S-quasinormal in G and H∩T≤S, where S≤H satisfies Φ*-property in G. Here Φ*-embedded subgroups were used to study the structure of finite groups and, in particular, some new characterizations for a group G to be soluble are obtained.
Sequential shrinkage estimation in generalized linear models with measurement errors
LU Haibo, WANG Zhanfeng, WU Yaohua
2015, 45(6): 449-459. doi: 10.3969/j.issn.0253-2778.2015.06.004
A sequential shrinkage estimation method was developed to determine a minimum sample size under which both of the variable selection and the parameter estimation with a pre-specified accuracy were achieved for the generalized linear model with measurement errors. Asymptotic properties of the proposed sequential estimation method, such as the coverage probability of the sequential confidence set and the efficiency of the minimum sample size, were studied. Simulation studies were conducted and the results show that the proposed method can save a large number of samples compared to the traditional sequential sampling method. Finally a diabetes data set was used as an example.
Strong limit theorems for negatively associated random variables with general moment conditions
XIA Fengxi, DENG Xin, ZHENG Lulu, WANG Xuejun
2015, 45(6): 460-464. doi: 10.3969/j.issn.0253-2778.2015.06.005
Let {X,Xn,n≥1} be a sequence of negatively associated random variables with identical distribution, {an,n≥1} be a sequence of positive constants with an/n↑. The strong law of large numbers and complete convergence for {X,Xn,n≥1} were obtained. These results are equivalent to the general moment condition ∑∞[]n=1P(|X|>an)<∞. On the other hand, the results extend the corresponding ones for pairwise independent random variables with identical distribution.
Negacyclic codes over Fq+uFq+…+uk-1Fq
CHEN Xiaojing, ZHU Shixin
2015, 45(6): 465-469. doi: 10.3969/j.issn.0253-2778.2015.06.006
Negacyclic codes of arbitrary lengths over the polynomial residue ring Fq+uFq+…+uk-1Fq were studied. By means of the finite ring theory, the structure of negacyclic codes over the ring of arbitrary lengths was given. The Hamming distance of negacyclic codes of length ps over the ring was also studied.
Experimental research on the hydrodynamic processes of water exit and entry
SHI Honghui, GAO Jurui, JIA Huixia, CHEN Bo, ZHOU Yangjie
2015, 45(6): 470-475. doi: 10.3969/j.issn.0253-2778.2015.06.007
Using a pneumatic gun and a single stage light gas gun, the supercavitation phenomena during water entry and exit of high-speed bodies (slender bodies) were investigated experimentally. The flow fields were visualized by a high speed camera. The study shows that the trailing vortices consisting of small bubbles shed periodically behind a supercavity. During water exit, the bodies velocities decrease generally, but a short acceleration may occur when the water splash impacts on the bottom of the body. During water entry, the hydroballistics of the underwater body may change due to the asymmetric bubble shedding behind the body and the collision between the body and the cavitys wall. According to experimental results, the drag coefficient in water Cd was measured, and Cd≈07~12.
Research on longitudinal vibration and rock breaking characteristics of rotary cutting drill bits
TIAN Jialin, YANG Zhi, FU Chuanhong, YANG Lin, ZHU Yonghao, LI You, WU Chunming
2015, 45(6): 476-484. doi: 10.3969/j.issn.0253-2778.2015.06.008
Aiming at the rock-breaking problems of drill bits and characteristics of bottom hole model, a new type of drill bit that breaks rock with rotary-cutting motion was proposed. Based on the structure and the kinematics principles of rotary-cutting drill bit, its dynamics was analyzed, and the vibration displacement and speed of the cutter on different gear rings were obtained by establishing the vibration equation of the cutters. After that, rock-breaking properties of the rotary-cutting drill bit were researched. On the basis of an analysis model for the rock-breaking characteristics of the cutters on different gear rings, the cutters impact force, shear force and rock-breaking volume were obtained and compared. The results showed that compared with the existing drilling technology, the rotary-cutting drill bit breaks rock with shock and shear together and the largest gear ring through the center, which can improve the rock-breaking efficiency of the drill bit center effectively; the bottom hole model is tornado-like which can make all gear rings cut the wall and achieve bit gauge function in the rock-breaking process. At the same time, the analysis model can also be used for other types of bits like composite drill bits by changing corresponding parameters.
Heat transfer simulation for ground heat exchangers with varying heat fluxes
TANG Changfu, ZHANG Wenyong, ZHU Wenwei, YU Xianzhong, LIU Guijian
2015, 45(6): 485-489. doi: 10.3969/j.issn.0253-2778.2015.06.009
Based on the superposition principle and uniform inlet fluid temperature assumption, the semi-analytical solution to heat transferring of ground heat exchangers (GHEs) with varying heat fluxes was built and validated. The effects of load imbalance and heat interference were further examined. Results indicate that the heat transfer capacity for individual boreholes in GHE depends on the strength of heat interference. If the heat rejected into the ground is greater than the heat absorbed from the ground, the outlet fluid temperature of GHE increases gradually every year. Case study indicates that the outlet fluid temperature of GHE, compared with that in the first year, increases about 0.8 ℃ in the 10th year. The capacity of heat rejection for the GHE becomes smaller with stronger heat interference.
Calculation of solar radiation based on inhomogeneous atmosphere model
ZENG Li, CHENG Xiaofang
2015, 45(6): 490-496. doi: 10.3969/j.issn.0253-2778.2015.06.010
An inhomogeneous atmosphere model was proposed to derive formulas which can be used to calculate single-wavelength solar radiation and solar irradiance at any height, from the Earths surface to various levels of the atmosphere. Besides, the error from ignoring the curvature of the atmosphere was considered, and a correction method was given to reduce it. The validation results show that calculated values are closely consistent with measured data.
Supply chain optimization based on Shapley fair theory
ZHU Lili, SHI Yucheng, ZHU Jiaang, DU Shaofu
2015, 45(6): 497-506. doi: 10.3969/j.issn.0253-2778.2015.06.011
A supply chain system with one supplier and two homogeneous retailers was considered to investigate the influence of retailers fairness concern on the supply chain and its members decision by using the Shapley fair distribution theory. Through modeling and behavioral analysis, it was found that retailers fairness concern will reduce suppliers optimal wholesale price and improves retailers own optimal order quantity in equilibrium. Besides, retailers fairness concern also increases their profit shares as well as channel profits, which leads to a higher supply chain efficiency.
Optimal pricing based on customers perceived values of products
LEI Junfei, LIU Jie, JIANG Ning
2015, 45(6): 507-516. doi: 10.3969/j.issn.0253-2778.2015.06.012
Different customers attach different perceived values to the same products. And a customer chooses a firm based on such a difference in perceived values and his rational expectation of the firms product availability. In a monopoly market, a firms optimal quantity and product availability increase with its optimal price. Due to the non-monotonicity of distribution density from customers perceived values, a firms local optimal price is not necessarily equal to its global optimal price. In a competitive market with n firms, the pure Nash equilibrium result was solved and its uniqueness proved. When n is finite, firms may adopt different optimal prices, and all firms achieve the same optimal profit expect in two special conditions. However, when n is infinite, all firms share a same optimal profit in equilibrium.