A NEW APPROXIMATE INERTIAL MANIFOLD AND ASSOCIATED ALGORITHM

In this article the authors propose a new approximate inertial manifold(AIM) to the Navier-Stokes equations. The solutions are in the neighborhoods of this AIM with thickness δ=o(h2k 1-ε). The article aims to investigate a two grids finite element approximation based on it and give error estimates of the approximate solution where (h, h*) and (k, m) are coarse and fine meshes and degree of finite element subspaces, respectively. These results are much better than Standard Galerkin(SG) and nonlinear Galerkin (NG) methods. For example, for 2D NS eqs and linear element, let uh,uh,u* be the SG, NG and their approximate solutions respectively, then and h*≈h2 for NG, h*≈h3/2 for theirs.     

Efficiently packing unequal disks in a circle

Placing non-overlapping circles in a smallest container is a hard task. In this paper we present our strategy for optimally placing circles in a smallest circle which led us to win an international competition by properly mixing local and global optimization strategies with random search and local moves.     

Overview of some new results concerning the theory and applications of the Rayleigh special function

The author’s previous work provided a detailed overview of the results concerning the theory and applications of the Rayleigh special function starting from its appearance in science until recent years. Its numerous applications in various areas of mathematics, physics, and other fields were described, and an extensive bibliography was presented. This work overviews the studies not covered in the previous one and addresses new results published in many monographs and journals. Additionally, results concerning the estimation of zeros of some special polynomials and functions closely related to the Rayleigh function are described. The overview embraces the issues addressed in the scientific literature up to the last years. Dedicated to the memory of Academician A.A. Samarskii, my teacher and friend. The text was submitted by the author in English.     

Study of the aggregation of 1-alkanoylperylenes in 1,4-dioxane-H_2O binary solvents-Derivation of a new empirical equation relating CAgC to both chain-length and solvent aggregating power

Aggregation behaviors of 1-alkanoylperylenes (Pe-n, n = 4, 8,12) driven by hydrophobic-lipophilic interaction (HLI) have been investigated in dioxane (DX )-H2O binary aquiorgano solvents by means of fluorescence spectroscopy. A novel empirical equation, which rationalizes CAgC (critical aggregate concentration) dependence of the aggregates both on the chain-length of the substituent alkyl group and on the solvent aggregating power (SAgP) for Pe-n, has been derived.     

Quantization of constrained systems: A comparative look at three methods

Constrained Hamiltonian systems are investigated using three different methods: Hamilton-Jacobi, Batalin-Fradkin-Tyutin and gauge unfixing methods. The abelian Proca model is analyzed and the involutive Hamiltonian is obtained by the three methods.     

A new Leray formula for smooth functions on bounded domains in Cn

By means of a new technique of integral representations in Cn given by the authors, we establish a new abstract formula with a vector function W for smooth functions on bounded domains in Cn, which is different from the well-known Leray formula, This new formula eliminates the term that contains the parameter λ from the classical Leray formula, and especially on some domains the uniform estimates for the -equation are very simple. From the new Leray formula, we can obtain correspondingly many new formulas for smooth functions on many domains in Cn, which are different from the classical ones, when we properly select the vector function W.     

Static and Dynamic Analysis of Non-Linear Uncertain Structures

The procedures usually adopted in the evaluation of the stochastic response of structures with uncertain parameters, the so-called stochastic structures, are affected by some limits. Namely, the major drawbacks are: the conspicuous computational time required for the analysis of many degree of freedom systems and the loss of accuracy in the case of large uncertainty in the parameters. A method able to reduce the previous inconveniences was recently introduced in the study of statically loaded linear structures. The method, named improved perturbation method, was also extended to the field of linear dynamics. In both cases, the improved perturbation method provides a good approximation, even in the case of moderately large deviation of the uncertain parameters, and the computational time required is comparable to conventional first order perturbation. The present paper intends to apply the improved perturbation method in the second order analysis of geometrically non-linear uncertain systems subjected to static and dynamic deterministic forces.     

一个包含新的F．Smarandache函数的方程

定义一个新的F.Smarandache函数(?)(n),并研究一个包含该函数的方程.利用初等方法.给出了一个包含函数(?)(n)的方程的正整数解.该方程只有两个正整数解.     

Fundamental problems of sonochemistry and cavitation

This paper discusses the problems of cavitation which are associated with sonochemistry. It is concluded that the hot-spot theory is not sufficient to accommodate all experimental data and the alternative is a new electrical theory of cavitation phenomena.