Four-dimensional twisted group lattices are used as models for spacetime structure. Compared to other attempts at space-time deformation, they have two main advantages: They have a physical interpretation and there is no difficulty in putting field theories on these structures. We present and discuss ordinary and gauge theories on twisted group lattices. We solve the free field theory case by f...

The usual definition of average degree for a non-regular lattice has the disadvantage that it takes the same value for many lattices with clearly different connectivity. We introduce an alternative definition of average degree, which better separates different lattices. These measures are compared on a class of lattices and are analyzed using a Markov chain describing a random walk on the latti...

The problem of enumerating spanning trees on graphs and lattices is considered. We obtain bounds on the number of spanning trees NST and establish inequalities relating the numbers of spanning trees of different graphs or lattices. A general formulation is presented for the enumeration of spanning trees on lattices in d 2 dimensions, and is applied to the hypercubic, body-centred cubic, face-ce...

We give a representation of distributive lattices with the existential quantifier in terms of spectral spaces, which is an alternative to Cignoli’s representation in terms of Priestley spaces. Then we describe dual spectral spaces of subdirectly irreducible and simple Q-distributive lattices and prove that the variety QDist of Q-distributive lattices does not have the congruence extension prope...

We address the problem of the continuum limit for a system of Hausdorff lattices (namely lattices of isolated points) approximating a topological space M . The correct framework is that of projective systems. The projective limit is a universal space from which M can be recovered as a quotient. We dualize the construction to approximate the algebra C(M) of continuous functions onM . In a compan...

In this paper, we study the decomposition of semirings with a semilattice additive reduct. For, we introduce the notion of principal left $k$-radicals $Lambda(a)={x in S | a stackrel{l}{longrightarrow^{infty}} x}$ induced by the transitive closure $stackrel{l}{longrightarrow^{infty}}$ of the relation $stackrel{l}{longrightarrow}$ which induce the equivalence relation $lambda$. Again non-transit...

In this article, we present new random walk methods to solve flow and transport problems in saturated/unsaturated porous media, including coupled processes soils, heterogeneous systems modeled through hydraulic conductivity recharge fields, at the field regional scales. The numerical schemes are based on global algorithms (GRW) which approximate solution by moving large numbers of computational...

one of the important problems in earthquake geotechnical engineering is liquefaction phenomenon that happens in loose saturated granular soils. in this study, 11 boreholes from govanjik and dayalar area in downstream of sattarkhan dam collected and evaluated. results of research are showed that with assuming cementation in soils, liquefaction potential is weak to moderate than non-cemented cond...

this note introduces a new general conjecture correlating the dimensionality dt of an infinitelattice with n nodes to the asymptotic value of its wiener index w(n). in the limit of large nthe general asymptotic behavior w(n)≈ns is proposed, where the exponent s and dt are relatedby the conjectured formula s=2+1/dt allowing a new definition of dimensionality dw=(s-2)-1.being related to the topol...