Detecting the neutral top-pion at future muon colliders
The signals of the neutral top-pion $\pi^{0}_{t}$ at the first muon collider (FMC) are discussed by calculating its contributions to the processes $\mu^{+}\mu^{-}\longrightarrow b\bar{b}$ and $\mu^{+}\mu^{-}\longrightarrow \bar{t}c$. We find that the contributions to the process $\mu^{+}\mu^{-}\longrightarrow b\bar{b}$ are very small and the ratio of signal over square root of the background ($S/\sqrt{B})$ is smaller than 0.2. However, in most of the parameter space, the $\pi^{0}_{t}$ can generate 36 and up to 649 observable $\bar{t}c$ events at the FMC. The signals of the neutral top-pion $\pi^{0}_{t}$ may be detected via the process $\mu^{+}\mu^{-}\longrightarrow \bar{t}c$ at the FMC.

title: Single Production of Charged Top-Pions at High Energy Linear e+e- Colliders*
abstract: The dominant decay modes of charged top-pions are or . We consider the single production of charged top-pions in association with a top quark via e+e- annihilation and calculate the production cross section of the processes at the leading order. We find that it can reach 1.2 fb with reasonable parameter values. The charged top-pions may be detected via the channel in the future high energy e+e- colliders.

title: Wormhole solution in Bergmann-Wagoner scalar-tensor gravitational theory
abstract: We give a Euclidean wormhole solution in the vacuum Bergmann-Wagoner scalar-tensor gravitational theory. We show that this wormhole, unlike others, has complex charge and is a baby universe (half a wormhole).

title: The Statistic thermodynamical entropy of de Sitter space and its one loop correction
abstract: From the partition function of canonical ensemble we derive the entropy of the de Sitter space by anti-Wick rotation. And then from the one-loop bubble $S^2\times S^2$ created from vacuum fluctuation in de Sitter background space, we obtain the one-loop quantum correction to the entropy of de Sitter space.

title: Neutrino mixing in matter
abstract: Three-neutrino mixing in matter is studied through a set of evolution equations which are based on a rephasing invariant parametrization. Making use of the known properties of measured neutrino parameters, analytic, approximate solutions are obtained. Their accuracy is confirmed by comparison with numerical integration of these equations. The results, when expressed in the elements squared of the mixing matrix, exhibit striking patterns as the matter density varies.

title: GRAVITATIONAL THERMODYNAMICS OF SPACETIME FOAM IN ONE-LOOP APPROXIMATION
abstract: We show from one-loop quantum gravity and statistical thermodynamics that the thermodynamics of quantum foam in flat spacetime and Schwarzschild spacetime is exactly the same as that of Hawking–Unruh radiation in thermal equilibrium. This means we show unambiguously that Hawking–Unruh thermal radiation should contain thermal gravitons or the contribution of quantum spacetime foam. As a by-product, we give also the quantum gravity correction in one-loop approximation to the classical black hole thermodynamics.

title: Relics Theory of Dark Matter in quantum evaporating Black Hole
abstract: We introduce first a new road to quantize the Schwarzschild black hole. Then we find that the ground state or relic of the quantum evaporating black hole can be identified as dark matter.