Related papers: Linear degree growth in lattice equations
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.
Let $A$ be an integer matrix, and let $f_A$ be the associated monomial map. We give a connection between the eigenvalues of $A$ and existence of a linear recurrence relation in the sequence of degrees.
The main aim of this paper is to study the growth of solutions of higher order linear differential equations using the concepts of $(\alpha ,\beta ,\gamma )$-order and $(\alpha ,\beta ,\gamma )$-type. We obtain some results which improve…
We study the tractability of conjunctive query answering for queries with unbounded arity. It is well known that tractability of the problem can be characterised in terms of the queries treewidth under the assumption of bounded arity. We…
First we solve the problem of finding minimal degree families on toric surfaces by reducing it to lattice geometry. Then we describe how to find minimal degree families on, more generally, rational complex projective surfaces.
We characterize the order of principal congruences of a bounded lattice as a bounded ordered set. We also state a number of open problems in this new field.
This article studies the sequence of iterative degrees of a birational map of the plane. This sequence is known either to be bounded or to have a linear, quadratic or exponential growth. The classification elements of infinite order with a…
We study the limiting behavior for the solutions of a nonlinear recurrent relation which arises from the study of Navier-Stokes equations. Some stability theorems are also shown concerning a related class of linear recurrent relations.
We describe a natural generalization of irreducibility in order lattices with arbitrary metrics. We analyse the special cases of valuation metrics and more general metrics for lattices. This article is mainly based on a part of the author's…
The linear preferential attachment hypothesis has been shown to be quite successful to explain the existence of networks with power-law degree distributions. It is then quite important to determine if this mechanism is the consequence of a…
Linearization problem of ordinary differential equations by a new set of tangent transformations is considered in the paper. This set of transformations allows one to extend the set of transformations applied for the linearization problem.…
We classify unital associative conformal algebras of linear growth and provide new examples of such.
We give upper bounds on the minimal degree of a model in $\mathbb{P}^2$ and the minimal bidegree of a model in $\mathbb{P}^1 \times \mathbb{P}^1$ of the curve defined by a given Laurent polynomial, in terms of the combinatorics of the…
We present a generalized notion of degree for rotating solutions of planar systems. We prove a formula for the relation of such degree with the classical use of Brouwer's degree and obtain a twist theorem for the existence of periodic…
Graphs, and sequences of growing graphs, can be used to specify the architecture of mathematical models in many fields including machine learning and computational science. Here we define structured graph "lineages" (ordered by level…
Most of lipschitz regularity results for nonlinear strictly elliptic equations are obtained for a suitable growth power of the nonlinearity with respect to the gradient variable (subquadratic for instance). For equations with superquadratic…
We focus on various dynamical invariants associated to toric correspondences, using algebraic geometry or arithmetic. We find a formula for the dynamical degrees, relate the exponential growth of the degree sequences with a strict…
Continuous reducibilities are a proven tool in computable analysis, and have applications in other fields such as constructive mathematics or reverse mathematics. We study the order-theoretic properties of several variants of the two most…
In this study, a recursive solution technique in conjunction with generalized integrating factors is presented and applied to address first and second order linear differential equations. This approach demonstrates practical utility in…
A first order differential equation of Green's Function, at the origin G(0), for the one- dimensional lattice is derived by simple recurrence relation. Green's Function at site (m)is then calculated in terms of G(0). A simple recurrence…