ASYMPTOTIC HOMOGENIZATION IN A PARABOLIC SEMILINEAR PROBLEM WITH PERIODIC COEFFICIENTS AND INTEGRABLE INITIAL DATA

In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.

The Insphere of a Tetrahedron

A contiguous derivation of radius and center of the insphere of a general tetrahedron is given. Therefore a linear system is derived. After a transformation of it the calculation of radius and center can be separated from each other. The remaining linear system for the center of the insphere can be solved after discovering the inverse of the corresponding coefficient matrix. This procedure can also be applied in the planar case to determine radius and center of the incircle of a triangle.

STUDY ON THE METHOD OF CONSTRUCTING RATIONAL CUBIC CURVES AND CURVED SURFACE INCLUDING CONTROLLING PARAMETERS

By adopting the method of controlling parameters this paper describes the construction of various kinds of cubic curve segment and curved surface fragment with rational and non rational parameters, and discusses the relationship between controlling parameters, weighted factors and types, kinds and characteristics of curve segments and curved surface fragments. A mathematical method is provided for CAGD with abundant connotations, broad covering region, convenience, flexibility and direct simplicity.

Simplified method for simulation of ergodic spatially correlated seismic ground motion

A simplified method for the simulation of the ergodic spatially correlated seismic ground motion is proposed based on the commonly used original spectral representation method. To represent the correlation in the ground motion, the phase angles are given by explicit terms with a clear physical meaning. By these explicit terms, the computational efficiency can be improved by converting the decomposition of the complex cross-spectral matrix into the decomposition of the real incoherence coefficient matrix. Double-indexing frequencies are introduced to simulate the ergodic seismic ground motion, and the ergodic feature of the improved method is demonstrated theoretically. Subsequently, an explicit solution of the elements of the lower triangular matrix under the Cholesky decomposition is given. With this explicit solution, the improved method is simplified, and the computational efficiency can be improved greatly by avoiding the repetitive Cholesky decomposition of the cross-spectral matrix in each frequency step. Finally, a numerical example shows the good characteristic of the improved method.

Time Series of Random Macro-price and Application

This paper tries to utilize the methods of stochastic analysis and matrix analysis to research the existential problem of price series. By using the means of time series analysis, the input-output, Markov processes and the modern matrix analysis, the limiting problem of price balance and vibration in stochastic economic environment has been researched, and surprising conclusions obtained are as following： the probability that the economic collapse time is equal ∞ is 0.

STUDY ON AUTOMATIC BALANCE TECHNOLOGY FOR THE RIGID ROTOR

The theory and application of automatic balance technology for the rigid rotor is re- searched. New analysis about the mechanical model of vibratory system is done in view of feature of automatic balance, and the result is that the accurate model of system can be gained by compensa- tion method and the traditional principle error of balance machines both for soft and hard bearing can be overcome. The automatic balance testing theory for sofi and hard bearing machines is pro- posed. The automatic balance system has been developed and the function and technical key is also introduced in detail.

Mechanical, electrical, and thermal expansion properties of carbon nanotube-based silver and silver–palladium alloy composites

The mechanical, electrical, and thermal expansion properties of carbon nanotube（CNT）-based silver and silver–palladium（10：1, w/w） alloy nanocomposites are reported. To tailor the properties of silver, CNTs were incorporated into a silver matrix by a modified molecular level-mixing process. CNTs interact weakly with silver because of their non-reactive nature and lack of mutual solubility. Therefore, palladium was utilized as an alloying element to improve interfacial adhesion. Comparative microstructural characterizations and property evaluations of the nanocomposites were performed. The structural characterizations revealed that decorated type-CNTs were dispersed, embedded, and anchored into the silver matrix. The experimental results indicated that the modification of the silver and silver–palladium nanocomposite with CNT resulted in increases in the hardness and Young＇s modulus along with concomitant decreases in the electrical conductivity and the coefficient of thermal expansion（CTE）. The hardness and Young＇s modulus of the nanocomposites were increased by 30%？40% whereas the CTE was decreased to 50%-60% of the CTE of silver. The significantly improved CTE and the mechanical properties of the CNT-reinforced silver and silver–palladium nanocomposites are correlated with the intriguing properties of CNTs and with good interfacial adhesion between the CNTs and silver as a result of the fabrication process and the contact action of palladium as an alloying element.

Thermal properties of diamond/Al composites by pressure infiltration:comparison between methods of coating Ti onto diamond surfaces and adding Si into Al matrix

This study was pertained to the effects of Ti coating on diamond surfaces and Si addition into Al matrix on the thermal conductivity（TC） and the coefficient of thermal expansion（CTE） of diamond/Al composites by pressure infiltration.The fracture surfaces,interface microstructures by metal electro-etching and interfacial thermal conductance of the composites prepared by two methods were compared.The results reveal that Ti coating on diamond surfaces and only12.2 wt% Si addition into Al matrix could both improve the interfacial bonding and increase the TCs of the composites.But the Ti coating layer introduces more interfacial thermal barrier at the diamond/Al interface compared to adding 12.2 wt% Si into Al matrix.The diamond/Al composite with 12.2 wt% Si addition exhibits maximum TC of 534 W·m^-1·K^-1and a very low CTE of 8.9×10^-6K^-1,while the coating Ti-diamond/Al composite has a TC of 514 W·m^-1·K^-1 and a CTE of 11.0×10^-6K^-1.

The Input-Output Model and the Analysis of Profit and Tax of Product

With the combination of modern quantitative analysis method and enterprise inputoutput model,in this paper we make a scientific analysis on the effect to product profit tax from the change of internal and external important factors of enterprise,and some important results hare been given.

A Dynamic Input- Output Model Solution

In this paper we research the homogeneous input output model of forward delay that lag is one production cycle. It is conformed that the necessary and sufficient conditions of economic balanced development are that the output vector GENG Xian\|min Xinjiang Petroleum Institute, Urumqi 830000, ChinaAbstract:\ In this paper we research the homogeneous input output model of forward delay that lag is one production cycle. It is conformed that the necessary and sufficient conditions of economic balanced development are that the output vector X(t) is the right positive characteristic vector of (I-A) -1 (A+B), and the input vector is AX(t). We also constitute the workable economic subset S-,when the output vector of the first production cycle is X(1), the economy will surely collapse.

Center-configuration selection technique for the reconfigurable modular robot

The reconfigurable modular robot has an enormous amount of configurations to adapt to various environments and tasks. It greatly increases the complexity of configuration research in that the possible configuration number of the reconfigurable modular robot grows exponentially with the increase of module number. Being the initial configuration or the basic configuration of the reconfigurable robot, the center-configuration plays a crucial role in system＇s actual applications. In this paper, a novel center-configuration selection technique has been proposed for re- configurable modular robots. Based on the similarities between configurations＇ transformation and graph theory, configuration network has been applied in the modeling and analyzing of these configurations. Configuration adjacency matrix, reconfirmation cost matrix, and center-configuration coefficient have been defined for the configuration network correspondingly. Being similar to the center-location problem, the center configuration has been selected according to the largest center-configuraUon coefficient. As an example of the reconfigurable robotic system, AMOEBA-I, a three-module reconfigurable robot with nine configurations which was developed in Shenyang Institute of Automation （SIA）, Chinese Academy of Sciences （CAS）, has been introduced briefly. According to the numerical simulation result, the center-configuration coefficients for these nine configurations have been calculated and compared to validate this technique. Lastly, a center-configuration selection example is provided with consideration of the adjacent configurations. The center-configuration selection technique proposed in this paper is also available to other reconfigurable modular robots.

On representations of real Jacobi groups

We consider a category of continuous Hilbert space representations and a category of smooth Fr'echet representations,of a real Jacobi group G.By Mackey's theory,they are respectively equivalent to certain categories of representations of a real reductive group L.Within these categories,we show that the two functors that take smooth vectors for G and for L are consistent with each other.By using Casselman-Wallach's theory of smooth representations of real reductive groups,we define matrix coefficients for distributional vectors of certain representations of G.We also formulate Gelfand-Kazhdan criteria for real Jacobi groups which could be used to prove multiplicity one theorems for Fourier-Jacobi models.

AN IMPROVED NON-TRADITIONAL FINITE ELEMENT FORMULATION FOR SOLVING THE ELLIPTIC INTERFACE PROBLEMS

We propose a non-traditional finite element method with non-body-fitting grids to solve the matrix coefficient elliptic equations with sharp-edged interfaces. All possible situations that the interface cuts the grid are considered. Both Diriehlet and Neumann boundary conditions are discussed. The coefficient matrix data can be given only on the grids, rather than an analytical function. Extensive numerical experiments show that this method is second order accurate in the L∞ norm.