Multiple values and uniqueness problem of meromorphic mappings sharing hypersurfaces

The purpose of this article is to deal with the multiple values and uniqueness problem of meromorphic mappings from $\mathbb{C}^{m}$ into the complex projective space $\mathbb{P}^{n}(\mathbb{C})$ sharing fixed and moving hypersurfaces. We obtain several uniqueness theorems which improve and extend some known results.Comment: 14 pages. This is the final versio

Remarks on Quantum Modular Exponentiation and Some Experimental Demonstrations of Shor's Algorithm

An efficient quantum modular exponentiation method is indispensible for Shor's factoring algorithm. But we find that all descriptions presented by Shor, Nielsen and Chuang, Markov and Saeedi, et al., are flawed. We also remark that some experimental demonstrations of Shor's algorithm are misleading, because they violate the necessary condition that the selected number $q=2^s$, where $s$ is the number of qubits used in the first register, must satisfy $n^2 \leq q < 2n^2$, where $n$ is the large number to be factored.Comment: 12 pages,5 figures. The original version has 6 pages. It did not point out the reason that some researchers took for granted that quantum modlar exponentiation is in polynomial time. In the new version, we indicate the reason and analyze some experimental demonstrations of Shor's algorithm. Besides, the author Zhenfu Cao is added to the version for his contribution. arXiv admin note: text overlap with arXiv:1409.735

Phase Transition in Evolutionary Games

The evolution of cooperative behaviour is studied in the deterministic version of the Prisoners' Dilemma on a two-dimensional lattice. The payoff parameter is set at the critical region $1.8 < b < 2.0$ , where clusters of cooperators are formed in all spatial sizes. Using the factorial moments developed in particle and nuclear physics for the study of phase transition, the distribution of cooperators is studied as a function of the bin size covering varying numbers of lattice cells. From the scaling behaviour of the moments a scaling exponent is determined and is found to lie in the range where phase transitions are known to take place in physical systems. It is therefore inferred that when the payoff parameter is increased through the critical region the biological system of cooperators undergoes a phase transition to defectors. The universality of the critical behaviour is thus extended to include also this particular model of evolution dynamics.Comment: 12 pages + 3 figures, latex, submitted to Natur

Disentangle the nature of resonances in coupled-channel models

We present several possible hadronic states found in coupled-channel models within the on-shell approximation. The interaction potential is constructed as a sum of the tree-level Feynman diagrams calculated with the effective Lagrangians. Based on the recent empirical data, we illustrate the possible existence of several baryonic and mesonic states with definite quantum numbers in the model. We give their properties for the purpose of further study and discuss the potential of finding them in future experiments.Comment: values in table update