A recursive method for enumerating clusters on a hypercubic lattice in d spatial dimensions is presented from which the weak embedding constants are determined as polynomials in d. A tabulation for all clusters having no free ends is available for nb≤15, where nb is the number of bonds. As illustrated here and elsewhere, this tabulation can be used to generate many series expansions. A novel me...

Random walks on general graphs play an important role in the understanding of the general theory of stochastic processes. Beyond their fundamental interest in probability theory, they arise also as simple models of physical systems. A brief survey of the physical relevance of the notion of random walk on both undirected and directed graphs is given followed by the exposition of some recent resu...

the aim of this paper is to extend results established by h. onoand t. kowalski regarding directly indecomposable commutative residuatedlattices to the non-commutative case. the main theorem states that a residuatedlattice a is directly indecomposable if and only if its boolean center b(a)is {0, 1}. we also prove that any linearly ordered residuated lattice and anylocal residuated lattice are d...

In the context of a general lattice ? in R n and a strictly expanding map M which preserves the lattice, we characterize all the wavelet families, all the MSF wavelets, all the multiwavelets associated with a Multiresolution Analysis (MRA) of multiplicity d 1; and all the scaling functions. Moreover , we give several examples: in particular, we construct a single, MRA and C 1 (R n) wavelet, whi...

Connes’ distance formula is applied to endow linear metric to three 1D lattices of different topology, 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. PACS: 02.40.Gh, 11.15.Ha

The general deterministic recombination equation in continuous time is analysed for various lattices, with special emphasis on the lattice of interval (or ordered) partitions. Based on the recently constructed [4] general solution for the lattice of all partitions, the corresponding solution for interval partitions is derived and analysed in detail. We focus our attention on the recursive struc...

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...

We describe a general procedure to produce fundamental domains for complex hyperbolic triangle groups. This allows us new nonarithmetic lattices, bringing the number of known commensurability classes in PU(2,1) 22.

Abstract 2D spontaneous valley polarization attracts great interest both for its fundamental physics and potential applications in advanced information technology, but it can only be obtained from inversion asymmetric single-layer crystals, while the possibility to create symmetric lattices remains unknown. Here, starting lattices, a general design principle realizing based on van der Waals int...