Related papers: Hirotaka's problem 028
We propose a new shared task for tactical data-to-text generation in the domain of source code libraries. Specifically, we focus on text generation of function descriptions from example software projects. Data is drawn from existing…
In this paper, we enumerate enumeration problems and algorithms. This survey is under construction. If you know some results not in this survey or there is anything wrong, please let me know.
This paper is devoted to Riemann-Hilbert problems with constraints. We obtain results characterizing the existence of solutions as well as the dimension of the solution space in terms of certain indices. As an application, we show how such…
An algorithm computing the restriction of a holonomic D-module to a linear subspace was given by T.Oaku in 1997. We consider a problem of computing the restriction for a given holonomic D-module with parameters. We will give a partial…
A variety of logical frameworks support the use of higher-order abstract syntax in representing formal systems; however, each system has its own set of benchmarks. Even worse, general proof assistants that provide special libraries for…
We present a solvable two-dimensional piecewise linear chaotic map which arises from the duplication map of a certain tropical cubic curve. Its general solution is constructed by means of the ultradiscrete theta function. We show that the…
In this paper we give a closed expression for a multiple factorial series, solving Open Problem 3.137 in a recent book by O. Furdui. The method is based on properties of divided differences. It applies also to similar series and certain…
This is a survey of algorithmic problems in group theory, old and new, motivated by applications to cryptography.
Thanks to the interest of many people, a mistake has been found in our way of counting limit cycles. We are working on a new version.
Consider a problem where we are given a bipartite graph H with vertices arranged on two horizontal lines in the plane, such that the two sets of vertices placed on the two lines form a bipartition of H. We additionally require that H admits…
In this note we present a brief overview of variational methods to solve homogenization problems. The purpose is to give a first insight on the subject by presenting some fundamental theoretical tools, both classical and modern. We conclude…
We discuss an elementary, yet unsolved, problem of Niederreiter concerning the enumeration of a class of subspaces of finite dimensional vector spaces over finite fields. A short and self-contained account of some recent progress on this…
In this short article, we study different problems described as initial value problems of discrete differential equations and develop a a transform method called the sigma transform, a discrete version of the continuous Laplace transform to…
This is a collection of open problems in group theory proposed by hundreds of mathematicians from all over the world. It has been published every 2--4 years since 1965. This is the 21st edition, which contains 150 new problems and a number…
We relate the graph isomorphism problem to the solvability of certain systems of linear equations with nonnegative variables. This version replaces the two previous versions of this paper.
The paper is motivated on the open problem of resolution of singularities in positive characteristic. The aim is to present a form of induction which is different from that used by Hironaka. In characteristic zero induction is formulated by…
In order to obtain solutions to problem $$ {{array}{c} -\Delta u=\dfrac{A+h(x)} {|x|^2}u+k(x)u^{2^*-1}, x\in {\mathbb R}^N, u>0 \hbox{in}{\mathbb R}^N, {and}u\in {\mathcal D}^{1,2}({\mathbb R}^N), {array}. $$ $h$ and $k$ must be chosen…
We develop a new discrete mathematical model which includes the classical Sudoku puzzle, Latin Squares and gerechte designs. This problem is described by integer equations and a special type of inequality constraint. We consider solutions…
For family $x'=(a_0+a_1\cos t+a_2 \sin t)|x|+b_0+b_1 \cos t+b_2 \sin t$, we solve three basic problems related with its dynamics. First, we characterize when it has a center (Poincar\'e center focus problem). Second, we show that each…
It is a collection of problems and exercises of geodesy and the theory of errors.