Capacities with Values in Compact Hausdorff Lattices

For a compact Hausdorff topological lattice L the set M _L X of L-valued normed regular capacities on a compact Hausdorff topological space X is investigated. It is shown that the set M _L X carries a compact Hausdorff topology, and M _L extends to a weakly τ-normal functor in the category of compacta. If L is an upper and lower Lawson semilattice, then M _L is the functorial part of two semimonads. These semimonads coincide and are a monad if and only if L is distributive, i.e., is a Lawson lattice. The obtained results have a natural interpretation if capacities are regarded as subjective estimates of likelihood of realization of events in conditions of uncertainty.      

Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices

In the paper, the analog of Vahlen's theorem for Minkowski bases of three-dimensional lattices is sharpened.     

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.     

Lattices of subgroup and subsystem functors

Lattices of subgroup and subsystem functors are investigated. In particular, it is proved that for the case where X is a formation of finite groups and width of the lattice F₀(X) is at most |π(X)|, the formation X is metanilpotent and |π(X)| ⩽ 3. __________ Translated from Algebra i Logika, Vol. 45, No. 6, pp. 710–730, November–December, 2006.     

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.     

格子Boltzmann方法模拟微尺度流动和传热

本文采用格子Boltzmann方法(LBM)对微尺度Couette流的流动及传热进行了模拟.为了获得壁面边界的速度滑移和温度阶跃,在含有粘性热耗散的热格子模型的基础上,提出了一种新的直接基于宏观量的边界处理格式.模拟得到的速度场和温度分布与解析解吻合得相当好,充分说明了本文采用的模型和边界处理的合理性同时在模拟中还发现:对于不同的Kn数,均存在使得其上壁面的温度阶跃为零的临界Ec数,并且其临界值均在3.0附近.     

Fuzzy Horn logic II

The paper studies closure properties of classes of fuzzy structures defined by fuzzy implicational theories, i.e. theories whose formulas are implications between fuzzy identities. We present generalizations of results from the bivalent case. Namely, we characterize model classes of general implicational theories, finitary implicational theories, and Horn theories by means of closedness under suitable algebraic constructions.