Abstract:
An unmanned mining technology for the fully mechanized longwall face automation production is proposed and studied. The essential technology will bring the longwall face production into visualization through the VR (Virtual Reality) and AR (Augmented Reality) combination. Based on the visual theoretical model of the longwall face, the combination of virtual and reality, the real-time interactive and the 3D registration function were realized. The 3D image of the longwall face may be scaled and viewed from free angles. Using the overall affine coordinate system, the stereoscopic impression for the longwall face was enhanced; the video image is matched to 3D characteristics; the occlusion issue is resolved with the depth information solution; and the simplification visualization interactive method is proposed. The Key technology and Alpha channel are used to the combination of the real longwall face and the virtual user.

Abstract:
The direct boundary integral equation in Neumann problem of two-dimension Laplace equation Δu(x)=0 is discussed. It is deduced from Green's formula and fundamental solution -(1/2)ln|x-y|. The Galerkin method with constant boundary elements is applied to solve the variational equation of second kind Fredholm integral equation. In computation of stiffness matrix, the exactly integral formula are used in the first order integral expression , the numerical integral formula are used in the second order integral expression. Thus the precision of the scheme is improved. The numerical results of example illustrate that the scheme presented is effective and practical.

Abstract:
The boundary elementlinear complementarities method for solving the Poisson Signorini problem is presented in this paper. Both Green’s formula and the fundamental solution of the Laplace equation have been used to 〖JP+3〗solve the boundary integral equation. By imposing the Signorini constraints of the potential and its normal derivative on the boundary, the discrete integral equation can be written into a standard linear complementarities problem in the form of U1≥0,AIIU1+N≥0 and UT1(AU1+N)=0, which is affected by the Signorini boundary constraints with the boundary potential variable only. 〖JP〗A projected successive overrelaxation iterative method is employed to solve the problem, and numerical results are presented to illustrate the efficiency of this method.

Abstract:
Based on variable transformation method, this paper deduces the linear ordinary differential equations with constant coefficients for some kinds of second order Euler equation x2y″+pxy′+qy=f(x). The particular solutions of special shape non-homogeneous terms f(x)=Axαcos(βln* are obtained by complex number algorithm, and the general formulas of scheme are given by *. The results of some examples illustrate the correctness of conclusion and practicality of the scheme presented．(* Indicates a formula, please see the full text)

Abstract:
We show that the complex phase diagram of high $T_c$ superconductors can be deduced from a simple symmetry principle, a $SO(5)$ symmetry which unifies antiferromagnetism with $d$ wave superconductivity. We derive the approximate $SO(5)$ symmetry from the microscopic Hamiltonian and show furthermore that this symmetry becomes exact under the renormalization group flow towards a bicritical point. With the help of this symmetry, we construct a $SO(5)$ quantum nonlinear $\sigma$ model to describe the effective low energy degrees of freedom of the high $T_c$ superconductors, and use it to deduce the phase diagram and the nature of the low lying collective excitations of the system. We argue that this model naturally explains the basic phenomenology of the high $T_c$ superconductors from the insulating to the underdoped and the optimally doped region.

Abstract:
In this talk I outline the general strategy behind the SO(5) theory of high $T_c$ superconductivity. Progress in the direction of exact SO(5) models, numerical exact diagonalization and possible experimental tests are reviewed. I also address the criticisms raised recently against the SO(5) theory and point out directions for future exploration.

Abstract:
In this talk I give a brief update on the recent progress in the SO(5) theory of high T_c superconductivity (Science, 275: 1089,1997). Reviewed topics include SO(5) ladders, the unification of BCS and SDW quasi-particles in the SO(5) theory and the microscopic origin of the condensation energy.

Abstract:
This paper gives a simple introduction to the SO(5) theory of high T_c superconductivity. Current status and relation to experiments are summarized.

Abstract:
Throughout John Wheeler's career, he wrestled with big issues like the fundamental length, the black hole and the unification of quantum mechanics and relativity. In this essay, I argue that solid state physics -- historically the study of silicon, semiconductors and sand grains -- can give surprisingly deep insights into the big questions of the world.

Abstract:
The higher dimensional quantum Hall liquid constructed recently supports stable topological membrane excitations. Here we introduce a microscopic interacting Hamiltonian and present its exact ground state wave function. We show that this microscopic ground state wave function describes a topological quantum membrane. We also construct variational wave functions for excited states using the non-commutative algebra on the four sphere. Our approach introduces a non-perturbative method to quantize topological membranes.