Abstract:
In this article, we give some important theorems of forward difference, backward difference, central difference and difference quotient and forward difference, backward difference, central difference and difference quotient formulas of some special functions.

Abstract:
Due to the presence of a large orbital angular momentum of the parton system produced at the early stage of non-central heavy-ion collisions, quarks and anti-quarks are shown to be polarized in the direction opposite to the reaction plane which is determined by the impact-parameter and the beam momentum. The global quark polarization via elastic scattering was first calculated in an effective static potential model, then using QCD at finite temperature with the hard-thermal-loop re-summed gluon propagator. The measurable consequences are discussed. Global hyperon polarization from the hadronization of polarized quarks are predicted independent of the hadronization scenarios. It has also been shown that the global polarization of quarks and anti-quarks leads also to spin alignment of vector mesons. Dedicated measurements at RHIC are underway and some of the preliminary results are obtained. In this presentation, the basic idea and main results of global quark polarization are presented. The direct consequences such as global hyperon polarization and spin alignment are summarized.

Abstract:
Characteristics of the available data are briefly summarized. Different theoretical approaches are reviewed with special attention to a non-perturbative model which explicitly takes the orbital motion of the valence quarks into account. The connection between such asymmetries and hyperon polarization in unpolarized reactions is discussed.

Abstract:
We show that the polarization of hyperons observed in high energy collisions using unpolarized hadron beams and unpolarized nucleon or nuclear targets is closely related to the left-right asymmetries observed in single spin inclusive hadron production processes. The relationship is most obvious for the production of the hyperons which have only one common valence quark with the projectile. Further implications of the existence of large polarization for hyperon which has two valence quarks in common with the projectile and their consequences are discussed. A comparison with the available data is made. Further tests are suggested.

Abstract:
We suggested that longitudinal polarization of Lambda produced in e+e- annihilation at LEP energies can provide useful information on hadronization mechanism in general and on testing the validity of different pictures for the spin content of baryon in describing the fragmentation process in particular. We present the results obtained from the calculations based on two very much different pictures.We compare the results with the recent ALEPH data and make suggestions for future measurements.

Abstract:
Topological crystalline insulators in IV-VI compounds host novel topological surface states consisting of multi-valley massless Dirac fermions at low energy. Here we show that strain generically acts as an effective gauge field on these Dirac fermions and creates pseudo-Landau orbitals without breaking time-reversal symmetry. We predict the realization of this phenomenon in IV-VI semiconductor heterostructures, due to a naturally occurring misfit dislocation array at the interface that produces a periodically varying strain field. Remarkably, the zero-energy Landau orbitals form a flat band in the vicinity of the Dirac point, and coexist with a network of snake states at higher energy. We propose that the high density of states of this flat band gives rise to interface superconductivity observed in IV-VI semiconductor multilayers at unusually high temperatures, with non-BCS behavior. Our work demonstrates a new route to altering macroscopic electronic properties to achieve a partially flat band, and paves the way for realizing novel correlated states of matter.

Abstract:
Spin effects in high energy fragmentation processes can provide us with important information on hadronization mechanisms and spin structure of hadrons. It can in particular give new tests to the hadronization models. In this talk, we make a brief introduction to the different topics studied in this connection and a short summary of the available data. After that, we present a short summary of the main theoretical results we obtained in studying these different topics. The talk was mainly based on the publications [4-8] which have been finished in collaboration with C.Boros, Liu Chun-xiu and Xu Qing-hua.

Abstract:
We study the right regular representation on the space $L^2(N_0\setminus G;\psi)$ where $G$ is a quasi-split $p$-adic group and $\psi$ a non-degenerate unitary character of the unipotent subgroup $N_0$ of a minimal parabolic subgroup of $G$. We obtain the direct integral decomposition of this space into its constituent representations. In particular, we deduce that the discrete spectrum of $L^2(N_0\setminus G;\psi)$ consists precisely of $\psi$ generic discrete series representations and derive the Plancherel formula for $L^2(N_0\setminus G;\psi)$.

Abstract:
Theoretical research and specific surface area analysis of nitrogen adsorption indicated that a lot of structural micropores exist in sepiolite minerals fibers. However, the microporous size, existing form, and the distribution relationship between microporous structures were not proved yet. In this paper, the section TEM samples of nanofibers were prepared on the basis of the metal embedding and cutting technique, and the inner structure of sepiolite nanofibers was observed by TEM. The results showed that sepiolite fibers have multiplayer structure similar to concentric circles, and many micropores with the size of about 2–5？nm are normal and parallel to the -axis. The reason for the previously mentioned phenomenon was explained by using BET analysis and X-ray diffraction analysis results. 1. Introduction Sepiolite is a kind of fibrous silicate clay mineral rich of magnesium with a structure of layer and chain. The study on structure of sepiolite could be dated back from 1930s, and Longchanbon studied the structure of sepiolite. Until 1955, Nagy and Bradley [1] proposed the first structural model and theoretical structure: Si12Mg9O30(OH)6(OH2)4·6H2O. Nagy believed that sepiolite crystal was amphibole chain composed of two pyroxene chains, with silicon-oxy tetrahedron on each side in standard spacing. Two layers of silicon-oxy tetrahedron parallel to axis had six silicon-oxy tetrahedron, separately. Structure units are connected to each other by four oxygen atoms on the apex angle, which formed channels with a sectional area of 0.38 × 0.94？nm parallel to the chain. Brauner and Preisinger [2] proposed the structural model of two amphibole chains composed by three pyroxene chains, as shown in Figure 1. According to Brauner’s model, the theoretical structure of sepiolite was Si12Mg8O30(OH)4(OH2)4·8H2O, whose fibrous structures were composed of two layers of silicon-oxy tetrahedron units connected by oxygen atoms and central magnesium octahedron layers. Silicon-oxy tetrahedron layers were continuous, and were inverted at intervals of six tetrahedron units, leading to the existence of channels of dimensions of 0.37？nm × 1.06？nm running parallel to the length of the fibers. The two models mentioned previously were not different obviously in terms of the sizes of crystal, but they had eight and nine of octahedron cations in Brauner’s and Nagy’s model, separately. Moreover, they had four hydroxyl groups, eight zeolite water, and sectional area of 0.3572？nm2 in Brauner’s model; six hydroxyl groups, six zeolite water, and sectional area of 0.3816？nm2 in Nagy’s