相关论文: Rational Solution of the KZ equation (example)

We study the derivative expansion for the effective action in the framework of the Exact Renormalization Group for a single component scalar theory. By truncating the expansion to the first two terms, the potential $U_k$ and the kinetic…

A basic theory on the first order right and left linear quaternion differential systems (LQDS) is given systematic in this paper. To proceed the theory of LQDS we adopt the theory of column-row determinants recently introduced by the…

The n-point function for the integral over unitary matrices with Itzykson-Zuber measure is reduced to the integral over Gelfand-Tzetlin table; integrand (for generic n) is given by linear exponential times rational function. For $n=2$ and…

Let P(z) and Q(y) be polynomials of the same degree k>=1 in the complex variables z and y, respectively. In this extended abstract we study the non-linear functional equation P(z)=Q(y(z)), where y(z) is restricted to be analytic in a…

We consider the Zakharov-Kutznesov (ZK) equation posed in $\mathbb R^d$, with $d=2$ and $3$. Both equations are globally well-posed in $L^2(\mathbb R^d)$. In this paper, we prove local energy decay of global solutions: if $u(t)$ is a…

In 1923 Schur considered the following problem. Let f(X) be a polynomial with integer coefficients that induces a bijection on the residue fields Z/pZ for infinitely many primes p. His conjecture, that such polynomials are compositions of…

We consider the Zakharov-Kuznetsov equation (ZK) in space dimension 2. Solutions u with initial data u\_0 $\in$ H s are known to be global if s $\ge$ 1. We prove that for any integer s $\ge$ 2, u(t) H s grows at most polynomially in t for…

This paper is concerned with the connection coefficients between the local fundamental solutions of a $2\times 2$ linear ordinary differential system with two neighboring regular singular points at $z=0$ and $z=1$. We derive an asymptotic…

We study the problem of \emph{robust satisfiability} of systems of nonlinear equations, namely, whether for a given continuous function $f:\,K\to\mathbb{R}^n$ on a~finite simplicial complex $K$ and $\alpha>0$, it holds that each function…

For suitably discretized versions of the Kardar-Parisi-Zhang equation in one space dimension exact scaling functions are available, amongst them the stationary two-point function. We explain one central piece from the technology through…

In this note, we give an exact formula for a general family of rational zeta series involving the coefficient $\zeta(2n)$ in terms of Hurwitz zeta values. This formula generalizes two formulas from a previous paper of the first author. Our…

In this paper we firstly review how to \textit{explicitly} solve a system of $3$ \textit{first-order linear recursions }and outline the main properties of these solutions. Next, via a change of variables, we identify a class of systems of…

We derive the KPZ equation as a continuum limit of height functions in asymmetric simple exclusion processes with drift that depends on the local particle configuration. To our knowledge, it is a first such result for a class of particle…

We study Knizhnik-Zamolodchikov (KZ) connection in the presence of irregular singularities, that is, poles of higher order. We consider both the case of a universal connection and the case when it is associated with a specific simple Lie…

An irreducible quintic equation is solvable by radicals if and only if its Galois group is solvable. In this work, we provide necessary and sufficient conditions for solvability, expressed in terms of invariants of the quintic.

In this paper we deduce a lower bound for the rank of a family of $p$ vectors in $\R^k$ (considered as a vector space over the rationals) from the existence of a sequence of linear forms on $\R^p$, with integer coefficients, which are small…

Let K be an algebraically closed field of characteristic zero. Given a polynomial f(x,y) in K[x,y] with one place at infinity, we prove that either f is equivalent to a coordinate, or the family (f+c) has at most two rational elements. When…

We consider Mahler functions $f(z)$ which solve the functional equation $f(z) = \frac{A(z)}{B(z)} f(z^d)$ where $\frac{A(z)}{B(z)}\in \mathbb{Q}(z)$ and $d\ge 2$ is integer. We prove that for any integer $b$ with $|b|\ge 2$ either $f(b)$ is…

We show that three problems involving linear difference equations with rational function coefficients are essentially equivalent. The first problem is the generalization of the classical Skolem-Mahler-Lech theorem to rational function…

We propose a novel method for a solution of a system of linear equations with the non-negativity condition. The method is based on the Tikhonov functional and has better accuracy and stability than other well-known algorithms.