This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

We present explicit formulae for the eccentric connectivity index and Wiener index of 2-dimensional square and comb lattices with open ends. The formulae for these indices of 2-dimensional square lattices with ends closed at themselves are also derived. The index for closed ends case divided by the same index for open ends case in the limit N →&infin defines a novel quantity we call compression...

Lubell proved this by observing that the left-hand side is a probability: it is simply the probability that a maximal chain, chosen uniformly at random, intersects A. The LYM inequality implies that an antichain in P([n]) has size at most ( n bn/2c ) , the size of the ‘middle layer’ in P([n]). (This can also be proved by partitioning P([n]) into ( n bn/2c ) disjoint chains.) Bollobás’ Inequalit...

In this paper, we establish the theory of fuzzy ideal convergence on completely distributive lattices and give characterizations of some topological notions. We also study fuzzy limit structures and discuss the relationship between fuzzy co-topologies and fuzzy limit structures.

The objective of this paper is to establish a complete characterization of multiwavelet packets associated with matrix dilation on general lattices $Gamma$ in $mathbb R^d$ by virtue of time-frequency analysis, matrix theory and operator theory.

The metastable zero field magnetic states of elongated Permalloy islands on square lattices of different geometries are investigated by means of magnetic force microscopy and numerical calculations. Keeping the island shape L /w=10 fixed while varying the interparticle distances a, it is demonstrated that the relative frequencies of observed magnetic configuration at remanence strongly depend o...

Almost all results in model theory of arithmetic are about elementary extensions. I will talk about an effort to systematize those results. If M and N are models of arithmetic and M ≺ N , how much information is there in Th((N,M)) in relation to Th(N)? In what situations is there a form of elimination of quantifiers for Th((N,M))? Is there a complete set of isomorphism invariants for such pairs...

Preferential affinity of cholesterol for saturated rather than unsaturated lipids underlies the thermodynamic process of the formation of lipid nanostructures in cell membranes, that is, of rafts. In this context, phase segregation of two-dimensional ternary lipid mixtures is formally studied from two different perspectives. The simplest approach is based on Monte Carlo simulations of an Ising ...

Deformation microstructures are widely used for reconstructing tectono-metamorphic events recorded in rocks. In crustal settings deformation is often accompanied and/or succeeded by fluid infiltration and dissolution-precipitation reactions. However, the microstructural consequences of dissolution-precipitation in minerals have not been investigated experimentally. Here we conducted experiments...