Abstract:
Interpreting the number of ramified covering of a Riemann surface by Riemann surfaces as the relative Gromov-Witten invariants and applying a gluing formula, we derive a recursive formula for the number of ramified covering of a Riemann surface by Riemann surface with elementary branch points and prescribed ramification type over a special point.

Abstract:
In this paper, we study the symplectic geometry of singular conifolds of the finite group quotient $$ W_r=\{(x,y,z,t)|xy-z^{2r}+t^2=0 \}/\mu_r(a,-a,1,0), r\geq 1, $$ which we call orbi-conifolds. The related orbifold symplectic conifold transition and orbifold symplectic flops are constructed. Let $X$ and $Y$ be two symplectic orbifolds connected by such a flop. We study orbifold Gromov-Witten invariants of exceptional classes on $X$ and $Y$ and show that they have isomorphic Ruan cohomologies. Hence, we verify a conjecture of Ruan.

Abstract:
We study the multiple existence of periodic solutions for a second-order non-autonomous dynamical systems (1). Using the method of invariant sets of descending flow and chain of rings theorem, we obtain the existence of seven -periodic solutions.

Abstract:
Tracking fusion with dissimilar sensors, which is a challenge work in multisensor fusion, is studied. Under the condition of general correlated measurement noises, the centralized and distributed tracking fusion question is investigated based on linear unbiased minimum variance estimation theory. The basic algorithms of measurement fusion and state vector fusion are presented in linear system with dissimilar sensors by the way of sequential filtering. These algorithms involve with not only the correlated measurement noises but also the configuration difference in local sensors, so information about multi-sensors fusion is increased. Through a simulation example it is indicated that the results of proposed algorithm is better than that classic ones where the measurement noises and processing noises are assumed to be uncorrelated.

Abstract:
Based on the controlled order rearrange encryption (CORE) for quantum key distribution using EPR pairs[Fu.G.Deng and G.L.Long Phys.Rev.A68 (2003) 042315], we propose the generalized controlled order rearrangement encryption (GCORE) protocols of $N$ qubits and $N$ qutrits, concretely display them in the cases using 3-qubit, 2-qutrit maximally entangled basis states. We further indicate that our protocols will become safer with the increase of number of particles and dimensions. Moreover, we carry out the security analysis using quantum covariant cloning machine for the protocol using qutrits. Although the applications of the generalized scheme need to be further studied, the GCORE has many distinct features such as great capacity and high efficiency.

Abstract:
The relations among the occupation number of the lowest natural orbital (ONLNO), momentum distributions (MD) and off-diagonal long-range element (ODLRE) of the reduced single-particle density matrix (RSPDM) are studied while Tonks-Girardeau gas in one dimensional periodic potential is in the ground state. For $N$-body systems of large enough, RSPDM and its lowest natural orbital do not vary with $N$ in overlapped areas in commensurate and incommensurate cases correspondingly. In commensurate case, the ODLRE is exponential attenuation with $N$, which results in that the ONLNO and MD are invariant with $N$. While in contrast, in incommensurate case, the off-diagonal elements are inversely proportional to $\sqrt{N}$, which results in the different behavior of the ONLNO and MD.