Related papers: Polynomial Term Structure Models
We provide an up-to-date review of the recent constructive program for field theories of the vector, matrix and tensor type, focusing not on the models themselves but on the mathematical tools used.
A new algebraic treatment of dependent type theory is proposed using ideas derived from topos theory and algebraic set theory.
A class of Cantor-type spaces and related geometric structures are discussed.
The purpose of this note is to survey a methodology to solve systems of polynomial equations and inequalities. The techniques we discuss use the algebra of multivariate polynomials with coefficients over a field to create large-scale linear…
Native type systems are those in which type constructors are derived from term constructors, as well as the constructors of predicate logic and intuitionistic type theory. We present a method to construct native type systems for a broad…
Matrices over the ring of formal power series are considered. Normal forms with respect to various sub-groups of the two-sided transformations are constructed. The construction is based on the special property of the action: it induces a…
Polynomial jump-diffusions constitute a class of tractable stochastic models with wide applicability in areas such as mathematical finance and population genetics. We provide a full parameterization of polynomial jump-diffusions on the unit…
This paper focuses on polynomial dynamical systems over finite fields. These systems appear in a variety of contexts, in computer science, engineering, and computational biology, for instance as models of intracellular biochemical networks.…
Say a trinomial $x^n+A x^m+B \in \Q[x]$ has reducibility type $(n_1,n_2,...,n_k)$ if there exists a factorization of the trinomial into irreducible polynomials in $\Q[x]$ of degrees $n_1$, $n_2$,...,$n_k$, ordered so that $n_1 \leq n_2 \leq…
Solving polynomial equations is a subtask of polynomial optimization. This article introduces systems of such equations and the main approaches for solving them. We discuss critical point equations, algebraic varieties, and solution counts.…
We discuss the use of methods coming from integrable systems to study problems of enumerative and algebraic combinatorics, and develop two examples: the enumeration of Alternating Sign Matrices and related combinatorial objects, and the…
We define nodal finite dimensional algebras and describe their structure over an algebraically closed field. For a special class of such algebras (type A) we find a criterion of tameness.
We classify two-variable polynomials which are rational of simple type. These are precisely the two-variable polynomials with trivial homological monodromy.
In this note, we provide a conceptual explanation of a well-known polynomial identity used in algebraic number theory.
We extend the classical notion of solvability to a lambda-calculus equipped with pattern matching. We prove that solvability can be characterized by means of typability and inhabitation in an intersection type system P based on…
We describe a method to evaluate multivariate polynomials over a finite field and discuss its multiplicative complexity.
In this paper we consider a new class of Hamiltonian hydrodynamic type systems, whose conservation laws are polynomial with respect to one of field variables.
We study matrix three term relations for orthogonal polynomials in two variables constructed from orthogonal polynomials in one variable. Using the three term recurrence relation for the involved univariate orthogonal polynomials, the…
This is a largely expository paper about how groups arise or are of interest in model theory. Included are the following topics: classifying groups definable in specific structures or theories and the relation to algebraic groups, groups…
We present functional forms allowing a broader range of analytic solutions to common economic equilibrium problems. These can increase the realism of pen-and-paper solutions or speed large-scale numerical solutions as computational…