相关论文: Lattice Basis and Entropy

We give the basic definition of algebraic entropy for lattice equations. The entropy is a canonical measure of the complexity of the dynamics they define. Its vanishing is a signal of integrability, and can be used as a powerful…

This paper studies the differential lattice, defined to be a lattice $L$ equipped with a map $d:L\to L$ that satisfies a lattice analog of the Leibniz rule for a derivation. Isomorphic differential lattices are studied and classifications…

Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.

The notion of multidimensional quadrilateral lattice is introduced. It is shown that such a lattice is characterized by a system of integrable discrete nonlinear equations. Different useful formulations of the system are given. The…

Three-dimensional lattices are fundamental to solid-state physics. The description of a lattice with an atomic basis constitutes the necessary information to predict solid phase properties and evolution. Here, we present a new algorithm for…

This paper introduces the order-theoretic concept of lattices along with the concept of consistent quantification where lattice elements are mapped to real numbers in such a way that preserves some aspect of the order-theoretic structure.…

Reliability of a system is considered where the components' random lifetimes may be dependent. The structure of the system is described by an associated "lattice polynomial" function. Based on that descriptor, general framework formulas are…

Diversities are a generalization of metric spaces, where instead of the non-negative function being defined on pairs of points, it is defined on arbitrary finite sets of points. Diversities have a well-developed theory. This includes the…

A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…

A periodic lattice in Euclidean space is the infinite set of all integer linear combinations of basis vectors. Any lattice can be generated by infinitely many different bases. This ambiguity was only partially resolved, but standard…

Some particular examples of classical and quantum systems on the lattice are solved with the help of orthogonal polynomials and its connection to continuous models are explored.

This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…

For large ranks, there is no good algorithm that decides whether a given lattice has an orthonormal basis. But when the lattice is given with enough symmetry, we can construct a provably deterministic polynomial-time algorithm to accomplish…

Whether a system is to be considered complex or not depends on how one searches for correlations. We propose a general scheme for calculation of entropies in lattice systems that has high flexibility in how correlations are successively…

This paper first gives a necessary and sufficient condition that a lattice $L$ can be represented as the collection of all up-sets of a poset. Applying the condition, it obtains a necessary and sufficient condition that a lattice can be…

We define and study structural properties of hypergraphs of models of a theory including lattice ones. Characterizations for the lattice properties of hypergraphs of models of a theory, as well as for structures on sets of isomorphism types…

Lattice models or structures are geometrical objects with mathematical forms, that are used to represent physical systems. They have been used widely in diverse fields, namely, in condensed matter physics, to study degrees of freedom of…

The lifetime of a system of connected units under some natural assumptions can be represented as a random variable Y defined as a weighted lattice polynomial of random lifetimes of its components. As such, the concept of a random variable Y…

We describe the basic lattice structures of attractors and repellers in dynamical systems. The structure of distributive lattices allows for an algebraic treatment of gradient-like dynamics in general dynamical systems, both invertible and…

In this paper, firstly we show that the entropy constants of the number of independent sets on certain plane lattices are the same as the entropy constants of the corresponding cylindrical and toroidal lattices. Secondly, we consider three…