LI-ideal Spaces of Lattice Implication Algebra

In this paper, a topological space based on LI-ideals of a lattice implication algebra is constructed, and its topological properties, such as separability, compactness and connectedness are discussed.

Lattice Im plication Homom orphism inIm plication Filter Spaces

In this paper,we investigate some special properties of lattice implication homomorphism in implication filter spaces. We show that lattice implication homomorphism is a continuous function with respect to implication filter topology. Moreover,we give a structural characterstic of left translation topology and right translation topology,which finally leads to the structural characteristics of product topology.

Lattices Associated with a Finite Vector Space

Let be a n-dimensional row vector space over a finite field For , let be a d-?dimensional subspace of . denotes the set of all the spaces which are the subspaces of and not the subspaces of except . We define the partial order on by ordinary inclusion (resp. reverse inclusion), and then is a poset, denoted by (resp. ). In this paper we show that both and are finite atomic lattices. Further, we discuss the geometricity of and , and obtain their characteristic polynomials.

A Euclidean-Like Discrete Spacetime from the Unification of a Multitude of Hypercubic Lattices

An autonomous discrete space is proposed consisting of a huge number of four dimensional hypercubic lattices, unified along one of the four axes. The unification is such that the properties of the individual lattice are preserved. All the unifying axes are parallel, and the other axes have indeterminate mutual relations. The two kinds of axes are non-interchangeable resembling time and space of reality. The unification constitutes a framework without spatial properties. In case the axes with indeterminate relations are present at regular intervals in the time and the space, a Euclidean-like metric and goniometry can be obtained. In thus defined space-like structure, differences in speed and relativistic relations are only possible within regions of space enclosed by aberrations of the structure.

Prime Space of Lattice Implication Algebras

In this paper,after discussing the prime implication filter of lattice implication algebra,we introduced the concept of prime space of lattice implication algebra,in which we analysised its topological property and discussed the relation between the category of topological space and the category of lattice implication algebras.

<i>L</i>-Topological Spaces Based on Residuated Lattices

In this paper, we introduce the notion of L-topological spaces based on a complete bounded integral residuated lattice and discuss some properties of interior and left (right) closure operators.

The Level Structures of the Kernel and Hull on Lattice—Valued Funcetions and Induced Spaces

It is studied systematically for the level strcture of the kernel and hull on continuous-lattice- calued function.In terms of these results,the level characterixations of induced space are odtained.

Physical Constants as Result of the Many Hypercubic Lattices of a Multidirectional Discrete Space

A multidirectional discrete space consists of numerous hypercubic lattices each of which contains one of the spatial directions. In such a space, several groups of lattices can be distinguished with a certain property. Each group is determined by the number of lattices it comprises, forming the characterizing numbers of the space. Using the specific properties of a multidirectional discrete space, it is shown that some of the characterizing numbers can be associated with a physical constant. The fine structure constant appears to be equal to the ratio of two of these numbers, which offers the possibility of calculating the series of smallest numerical values of these numbers. With these values, a reasoned estimate can be made of the upper limit of the smallest distance of the discrete space of approximately the Planck length.

并列双方柱绕流的Lattice Boltzmann模拟分析

采用Lattice Boltzmann方法对并列双方柱绕流问题进行数值模拟。对方柱间距比s/D=0.2、0.3、0.4、0.5、1.0、1.4、1.5、1.6、1.8、2.0、2.5共11种情况下的流场分别进行计算,给出了对应的流线图、方柱的升力图及阻力图,同时计算了方柱各边中点的压力,给出了压力与间距比的变化曲线,并对各个流线图、升力图、阻力图及压力图进行了分析讨论。结果表明:当s/D≤1.5时,流动呈偏流型,形成周期漩涡;当s/D>1.5时,流动呈对称型,形成对称漩涡;s/D=1.5为流动从偏流型向对称型转换的临界间距比。该结果对工程中建筑物位置的安排及其安全系数的提高有一定的参考价值。

GENERALIZATIONS AND CARTESIAN CLOSED SUBCATEGORIES OF SEMICONTINUOUS LATTICES

In this article, the authors mainly study how to obtain new semicontinuous lattices from the given semicontinuous lattices and discuss the conditions under which the image of a semicontinuous projection operator is also semicontinuous. Moreover, the authors investigate the relation between semicontinuous lattices and completely distributive lattices. Finally, it is proved that the strongly semicontinuous lattice category is a Cartesian closed category.

First Principle Self-Consistent Pseudopotential Calculation on the Electronic Structure of (InAs)_(1)(GaAs)_(1) Superlattice

The band structure of the(InAs)i(GaAs)i strained superlattice is calculated by the self-consistent pseudopotential method.The results show that the(InAs)_(1)(GaAs)_(1) is a direct-gap superlattice.With the local density approximation,the band gap calculated with the room-temperature lattice constants is 0.43eV,and the corrected value is 0.91 eV,in agreement with experimental results.Because of the lattice mismatch between InAs and GaAs layers,the three-fold degenerate energy level at the top of valence band splits into two levels with a spacing of 0.29 eV.The splitting of energy level is also estimated and explained using the effective-mass theory.

Linear Dynamical System over Finite Distributive Lattice

A finite dynamical system(FDS)over a lattice L is a pair(S(L),f),where S(L)is a left-L module and f is a mapping from S into itself.The phase space of(S(L),f)is a digraph whose vertex set is S(L)and there is an arc from x to y if y=f(x).Let L be a finite distributive lattice,A an n×n matrix over L,and f(x)=Ax.The structure of the phase space of the FDS(Ln,f)is discussed.The number of limit cycles in the phase space of(Ln,f)is described in Möbius function.The phase spaces of some invertible,nilpotent,and idempotent FDS(Ln,f)are characterized explicitly.

Connes' Distance of One-Dimensional Lattices:General Cases

Connes' distance formula is applied to endow linear metric to three 1D lattices of different topologies with a generalization of lattice Dirac operator written down by Dimakis et al.to contain a non-unitary link-variable.Geometric interpretation of this link-variable is lattice spacing and parallel transport.

Phonon relaxation and heat conduction in one-dimensional Fermi Pasta Ulam β lattices by molecular dynamics simulations

The phonon relaxation and heat conduction in one-dimensional Fermi Pasta-Ulam （FPU） β lattices are studied by using molecular dynamics simulations. The phonon relaxation rate, which dominates the length dependence of the FPU β lattice, is first calculated from the energy autoeorrelation function for different modes at various temperatures through equilibrium molecular dynamics simulations. We find that the relaxation rate as a function of wave number k is proportional to k^1.688, which leads to a N^0.41 divergence of the thermal conductivity in the framework of Green-Kubo relation. This is also in good agreement with the data obtained by non-equilibrium molecular dynamics simulations which estimate the length dependence exponent of the thermal conductivity as 0.415. Our results confirm the N^2/5 divergence in one-dimensional FPU β lattices. The effects of the heat flux on the thermal conductivity are also studied by imposing different temperature differences on the two ends of the lattices. We find that the thermal conductivity is insensitive to the heat flux under our simulation conditions. It implies that the linear response theory is applicable towards the heat conduction in one-dimensional FPU β lattices.

Particle-Wave Duality Resulting from the Granulation of Fields in a Hypercubic Lattice

The possibility of granulated discrete fields is considered in which there are at least three distinct base granules. Because of the limited size of the granules, the motion of an endlessly extended particle field must to be split into an inner and an outer part. The inner part moves gradually in a point particle-like fashion, the outer is moving step-wise in a wave-like manner. This dual behaviour is reminiscent of the particle-wave duality. Field granulation can be caused by deviations of the structure of the lattice at the boundaries of the granule, causing some axes of the granule to be tilted. The granules exhibit relativistic effects, inter alia, caused by the universality of the coordination number of the lattice.

The Universe at Lattice-Fields

We formulate the idea of a Universe crossing different evolving phases where in each phase one can define a basic field at lattice structure (Uk) increasing in mass (Universe-lattice). The mass creation in Uk has a double consequence for the equivalence “mass-space”: Increasing gravity (with varying metric) and increasing space (expansion). We demonstrate that each phase is at variable metric beginning by open metric and to follow a flat metric and after closed. Then we define the lattice-field of intersection between two lattice fields of base into universe and we analyse the universe in the Nucleo-synthesis phase (intersection-lattice ) and in the that of recombination (intersection-lattice ). We show that the phase is built on the intersection of the lattices of the proton (Up) and electron (Ue) or . We show UH to be at variable metric (open in the past, flat in the present and closed in the future). Then, we explain some fundamental aspects of this universe UH: Hubble’s law by creating the mass-space in it, its age (13.82 million of Years) as time for reaching the flat metric phase and the value of critic density. In last we talk about dark universe lattice , having hadronic nature, and calculating its spatial step and its density in present phase of .

Lattice Reduction Aided MMSE Tomlinson-Harashima Precoding Based on VBLAST Algorithm for MIMO Systems

A lattice reduction aided (LRA) minimum mean square error (MMSE) Tomlinson-Harashima pre-coding (THP) was proposed based on vertical Bell Labs layered space time (VBLAST) algorithm for multiple input multiple output (MIMO) systems. The extended channel was used to provide optimal tradeoff between residual interference and noise amplification. The processing based on lattice reduction method helps achieve maximal diversity order. The VBLAST algorithm was applied to get the optimal processing ordering for successive interference cancellation (SIC) at transmitter. Simulation results show that the proposed algorithm outperforms conventional THP and the LRA zero-forcing (ZF) THP with full diversity order.

Optimization for Maximum Nonlinear Buckling Load and Topics on Imperfection of Latticed Shells

The present paper represents comparison of continuum shells and latticed shells with qualitative analysis. For shells, the mechanical characteristics in the two perpendicular directions are continuous and related to each other, and any change in thickness will result in change in stiffness in any direction. In latticed shells, members are discrete and stiffnesses in two mutually perpendicular directions are discontinuous and independent of each other. Therefore, sensitivity of geometrical imperfection for buckling of latticed shells should be different from that of continuum shells. The author proposes a shape optimization method for maximum buckling load of a latticed shell. A single layer latticed dome is taken as a numerical example, and the results show that the buckling load parameter for full area loading case increases 32.75% compared to that of its initial shape. Furthermore, the numerical example demonstrates that an optimum latticed shell with maximum buckling load, unlike an optimum continuum shell, may not be sensitive to its geometrical imperfection.

A Rearrangement Inequality on Positive Tensor Products of Banach Lattices

In 1934, Hardy, Littlewood and Polya introduced a rearrangement inequality：∑i=1,aib（m＋1-i）≤∑i=1maibp（i）≤∑i=1,aibi,in which the real sequences {ai}i and {bi}i are in increasing order, and p（i） indicates a random permutation. We now consider a sequence in lp with 1 〈 p 〈 ∞, and a sequence in a Banach lattice X. Instead of normal multiplication, we consider the tensor product of lp and X. We show that in Wittstock injective tensor product, lp iX, and Fremlin projective tensor product, lp FX, the rearrangement inequality still exists.

Notes on Preregular Operators in Banach Lattices

Some characterizations of preregular operators between two Banach lattices are presented. Then several sufficient conditions for preregular operators being regular are given, and some related results are also obtained.