Abstract:
BES Collaboration measured the $R$ values at 3.650, 3.6648 and 3.773 GeV, the $R$ values at 68 energy points in the energy region between 3.650 and 3.872 GeV, the resonance parameters of $\psi(3686)$ and $\psi(3770)$, the branching fractions for $\psi(3770)\to D^0\bar D^0, D^+D^-, D\bar D$ and non-$D\bar D$, and the observed cross sections for some exclusive light hadron final states at 3.773 and 3.650 GeV. These measurements are made by analyzing the data sets collected with the BESII detector at the BEPC collider.

Abstract:
We discuss the Monte Carlo studies of searching for the rare and forbidden pure-leptonic and semi-leptonic decays of D+,0 and D+s mesons, based on a full Monte Carlo simulation for the BES-III detector, with the BES-III Offline Software System. The experimental sensitivities of searching for 36 rare and forbidden charm meson decays are estimated.

Abstract:
The $CP$ violation in the $D$ system is predicted to be an unobserved level in the Standard Model. In this paper, we describe the method of searching for $CP$ violation decay processes with the coherently produced $D^0\bar D^0$ mesons from the $\psi(3770)$ decay. The $CP$ violation decay processes can be searched for at the BES-III experiment. The experimental sensitivity for searching for the $CP$ violation can reach about a $10^{-4}$ level with a $\psi(3770)$ data sample of about $20$ fb$^{-1}$.

Abstract:
We suggest a Lorentz-covariant theory of gravity that is equivalent to general relativity in weak gravitational field. We first derive the mass variation of a body falling freely in static gravitational field based on the principle of equivalence and the mass-energy relation. We then modify the standards of space-time in local gravitational field to keep them consistent with the standards in inertial frame of reference at infinity based on the influence of gravitational field on the light. The metric thus obtained agrees with Schwarzschild metric at first order approximation. The gravitational vector potential produced by a moving gravitational source can be obtained by applying Lorentz transformations in local gravitational field. Although inertial and non-inertial frames are equally valid in describing the motion of bodies in gravitational field, we still regard inertial frame, i.e. center of mass of the system, as the preferred frame of reference. This is because Newton's laws of motion only hold for inertial frames. The apsidal motion of binary system and the expansion of the universe can be explained more reasonably when observed from their respective centers of mass than that from relative motions. The expression of static metric in our theory does not contain gravitational radius, thus black hole and singularity do not exist. In our theory, the gravity in the presence of matter is the same as that in the vacuum, i.e. TOV equation does not hold. The maximum mass of a neutron star is about five times of solar mass based on our computation.

Abstract:
In the derivation of Bell's inequalities, probability distribution is supposed to be a function of only hidden variable. We point out that the true implication of the probability distribution of Bell's correlation function is the distribution of the joint measurement outcomes on the two sides. So it is a function of both hidden variable and settings. In this case, Bell's inequalities fail. Our further analysis shows that Bell's locality holds neither for dependent events nor for independent events. We think that the measurements of EPR pairs are dependent events, thus violation of Bell's inequalities cannot rule out the existence of local hidden variable. In order to explain the results of EPR-type experiments, we suppose that polarization entangled photon pair can be composed of two circularly or linearly polarized photons with correlated hidden variables, and a couple of experiments of quantum measurement are proposed. The first uses delayed measurement on one photon of the EPR pair to demonstrate directly whether measurement on the other could have any non-local influence on it. Then several experiments are suggested to reveal the components of polarization entangled photon pair. The last one uses successive polarization measurements on a pair of EPR photons to show that two photons with a same quantum state will behave in the same way under the same measuring condition.

Abstract:
We suggest an explanation for superluminal phenomena based on wave-particle duality of photons. A single photon may be regarded as a wave packet, whose spatial extension is its coherence volume. As photon propagates as a wave train, its velocity is just the speed of light in vacuum. When it tunnels through a barrier as a particle, its wave function collapses and it travels faster than light. But superluminal propagation can only occur within the coherence length, and the duration is constrained by uncertainty principle. On the other hand, a particle with non-vanishing mass cannot travel faster than light. So superluminal phenomena do not violate causality. We explain the principles of existing superluminal experiments and propose three types of experiments to further verify superluminal phenomena. The first is to show that a single photon is equivalent to a wave packet, which occupies certain spatial volume. The second demonstrates that superluminal phenomena can only occur within the coherence length. The third indicates that negative and superluminal group velocity in anomalous dispersion medium is merely a reshaping phenomenon of the pulse, and it will become subluminal at large distances.

Abstract:
In order for different kinds of neutrino to transform into each other, the eigenvalues of energy of neutrino must be different. In the present theory of neutrino oscillations, this is guaranteed by the mass differences between the different eigenstates of neutrino. Thus neutrino cannot oscillate if it is massless. We suggest an explanation for neutrino oscillations by analogy with the oscillation of quantum two-state system, where the flipping of one state into the other may be regarded as a process of quantum tunneling and the required energy difference between the two eigenstates comes from the barrier potential energy. So neutrino with vanishing mass can also oscillate. One of the advantages of the explanation is that neutrino can still be described with Weyl equation within the framework of standard model.

Abstract:
Let M be a compact symplectic manifold, and L be a closed Lagrangian submanifold which can be lifted to a Legendrian submanifold in the contactization of M. For any Legendrian deformation of L satisfying some given conditions, we get a new Lagrangian submanifold L'. We prove that the number of intersection of L and L' can be estimated from below by the sum of $Z_2$-Betti numbers of L, provided they intersect transversally.

Abstract:
Let (M,\omega) be a compact symplectic manifold, and \phi be a symplectic diffeomorphism on M, we define a Floer-type homology FH_*(\phi) which is a gen- eralization of Floer homology for symplectic fixed points defined by Dostoglou and Salamon for monotone symplectic manifolds. These homology groups are modules over a suitable Novikov ring and depend only on \phi up to a Hamiltonian isotopy.