SEMIGROUPS CHARACTERIZED BY THEIR FUZZY IDEALS

ＳＥＭＩＧＲＯＵＰＳＣＨＡＲＡＣＴＥＲＩＺＥＤＢＹＴＨＥＩＲＦＵＺＺＹＩＤＥＡＬＳＪ．ＡｈｓａｎａｎｄＫ．Ｓａｉｆｕｌｌａｈ（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅｓＫｉｎｇＦａｈｄＵｎｉｖｅｒｓｉｔｙｏｆＰｅｔｒｏｌｅｕｍａ...     

Comparative study of lattice‐Boltzmann and finite volume methods for the simulation of laminar flow through a 4:1 planar contraction

In the present paper, a comparative study of numerical solutions for Newtonian fluids based on the lattice‐Boltzmann method (LBM) and the classical finite volume method (FVM) is presented for the laminar flow through a 4:1 planar contraction at a Reynolds number of value one, Re=1. In this study, the stress field for LBM is directly obtained from the distribution function. The calculations of the stress based on the FVM‐data use the evaluations of velocity gradients with finite differences. The stress field for both LBM and FVM is expressed in the present study in terms of the shear stress and the first normal stress difference. The lateral and axial profiles of the velocity, the shear stress and the first normal stress difference for both methods are investigated. It is shown that the LBM results for the velocity and the stresses are in excellent agreement with the FVM results. Copyright © 2004 John Wiley & Sons, Ltd.     

Platonic solids symmetry in particle physics

Non-linearity of the Yang-Mills fields caused by the commutator in the Lagrangian calls attention to symmetries helping to reveal important features of the system, while obviating the need of actual solutions. To this end, a charge fixing procedure is carried out by means of counting photon oscillations between test particles moving along trajectories that form Platonic solids shaped patterns. With the infinite-range electromagnetic interaction as its origin, the procedure defines a class of interactions allowed for particle physics. Besides the familiar electromagnetic, weak and strong interactions, the scheme suggests an unusual force that cannot be detected with conventional means though possibly contributes to gravitation.     

Covers in the Lattice of Varieties of m-Groups

We consider some questions on covers in the lattice of varieties of m-groups. We prove the existence of a nonabelian cover of the smallest nontrivial variety of m-groups. We show that there exists an uncountable set of o-approximable varieties of m-groups each of which has continuum many o-approximable covers. In the lattice of o-approximable varieties of m-groups we find a variety that has no covers in this variety and no independent basis of identities.     

Index of lattices and Hilbert polynomials

An upper bound for the index of a sublattice, which arises in relation to various versions of zero lemmas in the theory of linear forms in logarithms of algebraic numbers, in terms of the Hilbert polynomial is found. Simultaneously, a lower bound for the values of this polynomial is obtained.     

Investigation of Raman spectrum for nano-SnO2

The dependence of the microstructural change and lattice space symmetry of nano-SnO₂ on the annealing temperature has been studied systematically using Raman spectroscopy and X-ray diffraction. Comparing the results of nano-SnO₂ with the results of amorphous film and single crystal of SnO₂, it is found that the new Raman peaks N₁ and N₂ are in accordance with Matossi’s force constant model completely. When the annealing temperature is near 673K, the local lattice disorders and the density of vacant lattice decrease rapidly in the nano-SnO₂ grains. The lattice distortion and the new Raman peaks disappear almost at the same time. The possible mechanisms of the microstructural change and the new Raman peaks N₁ and N₂ are discussed. Project supported by the Foundation of State Science and Technology Commission and the Natural Science Foundation of Anhui Province.     

格上TL理想的性质及生成

本文利用完备Ｂｒｏｕｗｅｒ格Ｌ及Ｌ上的无穷Ｖ－分配ｔ－模定义分配格Ｍ上的ＴＬ理想，讨论一些基本性质，并给出由Ｌ子集生成的ＴＬ理想的计算公式．     

Evolution systems on a lattice

In the framework of the algebraic geometric approach to differential-difference equations, we study symmetries and conservation laws of evolutionary systems on multidimensional lattices. We describe conservation laws in terms of their characteristics. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 391–405, December, 2008.     

模糊幂格

本文研究了格向其模糊幂集上提升的问题.利用模糊集理论,引入了模糊幂格的概念,获得了模糊幂格及其模糊理想的若干基本性质,推广了格的结果.