The zeros distribution of Z_5-symmetric model on a triangular lattice

We study the -symmetric model with the nearest neighbour interaction between molecular dipole of five spin directions i.e. Q=5 which called as the -symmetric model on a triangular lattice. We investigate the zeros of partition function and the relationship to the phase transition. Initially, the model is defined on a triangular lattice graph with the nearest neighbour interaction. The partition function is then computed using a transfer matrix approach. We analyse the system by computing the zeros of the polynomial partition function using the Newton-Raphson method and then plot the zeros in a complex plane. For this lattice, the result shows that for specific type of energy level there are multiple line curves approaching real axis in the complex plane. The equation of the specific heat is produced and then plotted for comparison. Motivated from the work by Martin (1991) on models on square lattice, we extend the previous study to different lattice type that is triangular lattice.

Вычислительные аспекты задачи перечисления разбиений

The problems of performing exact calculations using the classical Kasteleyn formula for calculating the number of perfect matching of a lattice graph are considered. Two tests are formulated that provide the software with automatic correction of the calculation accuracy.

Some Metrical Properties of Lattice Graphs of Finite Groups

This paper is concerned with the combinatorial facts of the lattice graphs of Z p 1 × p 2 × ⋯ × p m , Z p 1 m 1 × p 2 m 2 , and Z p 1 m 1 × p 2 m 2 × p 3 1 . We show that the lattice graph of Z p 1 × p 2 × ⋯ × p m is realizable as a convex polytope. We also show that the diameter of the lattice graph of Z p 1 m 1 × p 2 m 2 × ⋯ × p r m r is ∑ i = 1 r m i and its girth is 4.

Geodesic graphs for a homotopy class of virtual knots

We consider a local move, denoted by [Formula: see text], on knot diagrams or virtual knot diagrams.If two (virtual) knots [Formula: see text] and [Formula: see text] are transformed into each other by a finite sequence of [Formula: see text] moves, the [Formula: see text] distance between [Formula: see text] and [Formula: see text] is the minimum number of times of [Formula: see text] moves needed to transform [Formula: see text] into [Formula: see text]. By [Formula: see text], we denote the set of all (virtual) knots which can be transformed into a (virtual) knot [Formula: see text] by [Formula: see text] moves. A geodesic graph for [Formula: see text] is the graph which satisfies the following: The vertex set consists of (virtual) knots in [Formula: see text] and for any two vertices [Formula: see text] and [Formula: see text], the distance on the graph from [Formula: see text] to [Formula: see text] coincides with the [Formula: see text] distance between [Formula: see text] and [Formula: see text]. When we consider virtual knots and a crossing change as a local move [Formula: see text], we show that the [Formula: see text]-dimensional lattice graph for any given natural number [Formula: see text] and any tree are geodesic graphs for [Formula: see text].

A New Pattern-Based Flexible Approach for Maintaining a Constrained Workflow

The context of any workflow has functional and non functional characteristics. Functional characteristics give rise to Workflow Patterns (WPs) in a workflow. Changes may occur to the relationships amongst patterns in a workflow after the initial enactment. Run-time changes could occur due to roles executing the patterns. Design-time changes could occur due to changing user specifications and subsequent decisions being taken by the workflow composer. An approach of accommodating and propagating such changes is required. These changes are to be accommodated in a manner that the relationships amongst the existing patterns remain consistent. This paper formalizes an approach that facilitates composition and accommodation of changes into a composed workflow maintaining consistency. We make use of tools and algorithms from Formal Concept Analysis (FCA) to organize WPs as a lattice. Graph searching techniques are exploited for composition of the workflow graph. For accommodating changes into the composed workflow, we consider the WPs as Reference Intervals from Allen's Interval Algebra (IA) framework. Change accommodation in our approach is achieved by three functionalities - a transform function that traces a Reference Interval Hierarchy (RIH) from the workflow graph; a constraint propagation function that accommodates raised changes into the RIH; an inverse transform function that updates the corresponding workflow graph with the changes in the RIH.