ISSN 0253-2778

CN 34-1054/N

2015 Vol. 45, No. 3

Display Method:
Original Paper
Invariant graphs of rational maps
CAI Hongjian
2015, 45(3): 173-185. doi: 10.3969/j.issn.0253-2778.2015.03.001
The problem of invariant graphs for rational maps was studied. It was mainly proved that if f is a post-critically finite rational map, whose post-critical set consists of one superattracting fixed point and two points in the Julia set, and whose Julia set is a Sierpinski curve, then an fk-invariant graph containing the post-critical set of f for each sufficiently large k could be found.
Optimal t-pebbling on paths and cycles
XIA Zhengjiang, PAN Yongliang, XU Junming
2015, 45(3): 186-192. doi: 10.3969/j.issn.0253-2778.2015.03.002
A pebbling move removes two pebbles from a vertex and places one pebble on one of its neighbours. For t≥1, the optimal t-pebbling number of a graph G, f′t(G), is the minimum number of pebbles necessary so that from some initial distribution of them it is possible to move t pebbles to any target vertex by a sequence of pebbling moves. f′(G)=f′1(G) be the optimal pebbling number of G. Here the optimal t-pebbling numbers of the path Pn and the cycle C5 were given, respectively. In the final section, it was obtained that f′9t(P2×P3)=20t, f′9t+1(P2×P3)=20t+3, and 20t+2r+1≤f′9t+r(P2×P3)≤20t+2r+2, for 2≤r≤8, the last equality holds for r=5,6,7,8.
On GI-flat and GF-torsion modules
WANG Xiujian, ZHAO Yu'e, DU Xianneng
2015, 45(3): 193-198. doi: 10.3969/j.issn.0253-2778.2015.03.003
Two classes of modules were studied: GI-flat and GF-torsion modules, where GI stands for Gorenstein injective modules and GF for Gorenstein flat modules. Two homological dimensions for a ring were investigated, the supremum of the flat dimension of Gorenstein injective modules and the supremum of the GF-torsion dimension of all modules. The relation between these classes of modules and the homological dimensions was also studied.
Quantum codes from cyclic codes over ring Fq+uFq
LI Jin
2015, 45(3): 199-204. doi: 10.3969/j.issn.0253-2778.2015.03.004
A method for constructing quantum codes from cyclic codes over the ring Fq+uFq was given, where q is a prime power and u2=0. First, symplectic self-orthogonal codes over Fq were obtained as images of cyclic codes over Fq+uFq. Then, these codes were used to construct quantum codes. Examples including quantum MDS codes were given.
Poisson approximation variable threshold method in rare variants association study
FANG Hongyan
2015, 45(3): 205-209. doi: 10.3969/j.issn.0253-2778.2015.03.005
The association study of rare genetic variants and disease traits as a supplement of genome-wide association study (GWAS) has achieved remarkable development and application. But the traditional association testing methods are not suitable for the rare variants association problem. Many new testing methods designed specifically for the rare variants have been proposed and applied. The variable-threshold (VT) method is one of them, which has achieved more power than the traditional association test methods. Here the occurrence of the mutation of rare variants was treated as a rare event. Poisson distribution was taken instead of binomial distribution and a new test statistic was proposed. Base on the VT method, a new test method was proposed, namely, the Poisson approximation variable threshold method (PAVT). Simulation results show that the new method has more power than VT method uniformly, and variant selection is more efficient.
Convergence rate of location parameter change-point estimator
TAN Changchun, YU Xiangxiang, DONG Cuiling
2015, 45(3): 210-219. doi: 10.3969/j.issn.0253-2778.2015.03.006
For the location parameter change point model allowing at most one change, an antisymmetric kernel function was constructed and a change point estimator was proposed with the help of the CUSUM method. The consistency and convergence rate of the change point estimator were studied under normal conditions and its consistency was given under the condition of local alternative hypothesis. Finally, simulation was performed under different sample sizes and parameter settings. From the histograms, the closer the change-point location gets to the middle, the more accurate the estimate is. The results show that our methods are effective.
Experimental demonstration of indirect Hamiltonian tomography for 3-spin XY chain
GUO Xueyi, JIANG Min, ZHENG Wenqiang, LI Jun, PENG Xinhua
2015, 45(3): 220-223. doi: 10.3969/j.issn.0253-2778.2015.03.007
To realize quantum control and quantum computation on a quantum system, its Hamiltonian parameters must be determined first. However, in many cases a quantum system is access-limited. In our experiment, the dynamic evolution of a 3-spin XY chain was simulated with an NMR quantum simulator. The Hamiltonian parameters of the 3-spin XY chain were determined by measuring only the first spin and processing the data obtained.
Realization of quantum gates in rotating single crystal
YAN Benjun, CUI Jiangyu, LIU Xiaomei
2015, 45(3): 224-230. doi: 10.3969/j.issn.0253-2778.2015.03.008
Quantum gates in solid-state nuclear magnetic resonance (NMR) under magic-angle spinning (MAS) was realized. First, all anisotrope interactions of the sample were averaged out under the MAS. Then, the special pulse sequences or conditions were used to recover the interactions used to realize controlled operations. The advantage of this method for them in liquid NMR is that the pulse sequences of controlled operations are simplified, because they do not need complicated decoupling sequences, and the evolution time of the pulse sequences is shorter. Finally, the quantum operations were simulated, and the results are in complete agreement with the theoretical predictions.
Influencing factors of the foreign exchange risk exposure of the manufacturing industry in China
WANG Xiangning, HU Bingqing
2015, 45(3): 231-237. doi: 10.3969/j.issn.0253-2778.2015.03.009
324 A-share listed companies from 10 subsectors of the manufacturing industry were taken as samples. First each companys foreign exchange risk exposure coefficient was calculated with the traditional two-factor model. Then the influencing factors were obtained through cross-sectional regression, and finally the relationship between foreign exchange risk exposure of subsectors of the manufacturing industry and the influencing factors was analyzed. It was found that 117% of the companies have significant foreign exchange risk exposure under the significance level of 10%, and that foreign exchange risk exposure has a positive correlation with export ratio, quick ratio, net cash flow of operating activities, and a negative correlation with total market value, net profit margin. The further finding is that for companies negatively affected by the appreciation of RMB, foreign exchange risk exposure has a positive correlation with total asset turnover ratio, the growth rate of basic per share earnings, and a negative correlation with research and development costs, and that for companies positively affected by the appreciation of RMB, foreign exchange risk exposure has a negative correlation with the rate of assets and liabilities, the growth rate of basic per share earnings.
Analyzing and measuring loan-to-value ratios of the stock repurchase agreement
WANG Xiangning, FAN Qing
2015, 45(3): 238-245. doi: 10.3969/j.issn.0253-2778.2015.03.010
Establishing the loan-to-value (LTV) ratios of the stock repurchase agreement is important for securities traders to resist risks and get new revenue streams.In order to calculate the LTV ratios of this kind of agreements, an LTV model was employed. In addition, simulated loans on SHSE-SZSE300 index yield were tested using different discount rates with two methods, the historical simulation method and the generalized Pareto distribution (GPD) method, to compare corresponding LTV ratios.The study shows that the LTV ratios using the LTV model and the two calculation methods are basically reasonable, and limiting LTV up to 60% is meaningful,but the impacts of the two VaR methods on LTV ratios are not comparable.The backtesting which used historical data can determine the performance of simulated loans, thus improving the quality of loans under different terms.
Analysis of the influencing factors of Chinas international capital flow
BA Shusong, GU Lei, YAN Min
2015, 45(3): 246-253. doi: 10.3969/j.issn.0253-2778.2015.03.011
Through principle component analysis, the general factors affecting international capital flows were obtained. Then by dividing the international capital flows into long-term and short-term capital flows, further analysis of the factors was conducted. The results of empirical study show that increased level of openness, increasing economic output, increased labor compensation and moderate inflation may bring in FDI, which can be inhibited by an appreciation of an RMB; increasing expectation of RMB appreciation and a boom of Chinese real estate and security markets are driving short-term capital into China; increased level of openness and interest rate differentials have no influence on short-term capital inflows.
Building the term structure of interest rates with splines based on Q-SCAD
GUO Jianhong, CHENG Xijun, LIU Feng
2015, 45(3): 254-258. doi: 10.3969/j.issn.0253-2778.2015.03.012
Penalized quantile regression with the SCAD was introduced into the spline function to build the term structure of interest rates of treasure bills. This method can automatically select the optimal quantile and complete the models knot selection and parameter estimation at the same time. The out-of-sample forecasting results show that, compared with the traditional methods, the new method can select the appropriate model effectively, increase the robustness of parameter estimation, improve forecast accuracy and enhance the pricing precision of the term structure of interest rates.