Global results on rational systems in the plane,part 1

Edited by Gerry Ladas

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas: Email: gladas@math.uri.edu     

图的连通因子

连通因子问题与Hamilton问题和信息网络有着密切的联系．1993年，首先由M.Kano就该问题在[6]中提出了许多问题和猜想，接下来他又在[16]中提出了一些猜想，本文就连通因子问题在过去十年的主要进展进行了回顾并提出了若干可进一步研究的问题和猜想．     

Open problems and conjectures

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.     

Open problems and conjectures

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relavant information to G.Ladas     

On the recursive sequence

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.     

Open problems and conjectures,optimal rearrangement problems related to discrete loaded strings

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.     

Open problem and conjectures,countably many solutions for a bvp on a measure chain

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.     

Convergence in Conformal Field Theory

Convergence and analytic extension are of fundamental importance in the mathematical construction and study of conformal field theory. The author reviews some main convergence results, conjectures and problems in the construction and study of conformal field theories using the representation theory of vertex operator algebras. He also reviews the related analytic extension results, conjectures and problems. He discusses the convergence and analytic extensions of products of intertwining operators (chiral conformal fields) and of q-traces and pseudo-q-traces of products of intertwining operators. He also discusses the convergence results related to the sewing operation and the determinant line bundle and a higher-genus convergence result. He then explains conjectures and problems on the convergence and analytic extensions in orbifold conformal field theory and in the cohomology theory of vertex operator algebras.     

Open problems and conjectures

In this section we present some pen problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas.     

Open problems and conjectures

In this section we present some open problems and conjectures about some interesting types of difference equations, Please submit your problems and conjectures with all relevant information to G. Ladas.     

Convergence to periodic solutions

Open Problems and Conjectures Edited by Gerry Ladas In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjectures with all relevant information to G. Ladas     

How Many Conjectures Can You Stand? A Survey

We survey results and open problems in hamiltonian graph theory centered around two conjectures of the 1980s that are still open: every 4-connected claw-free graph (line graph) is hamiltonian. These conjectures have lead to a wealth of interesting concepts, techniques, results and equivalent conjectures.     

A survey: Recent results,conjectures, and open problems in labeling graphs

In this paper we organize and summarize much of the work done on graceful and harmonious labelings of graphs. Many open problems and conjectures are included.     

Three Conjectures on Shepard Interpolatory Operators

After establishing direct and converse approximation theorems for the Shepard interpolatory operators, J. Szabados (Approx. Theory Appl.7, No. 3, 1991, 63–76) left some open saturation problems (“the most intriguing questions” as he said), which he raised as three conjectures. The present paper proves the second parts of some conjectures, but constructs counterexamples to show that the first parts of three conjectures are not true. The constructive procedure uses some novel ideas and techniques.     

Hilbert schemes and multiple q-zeta values

We present several conjectures on multiple q-zeta values and on the role which they play in certain problems of enumerative geometry.     

Uniform convergence and integrability of Fourier integrals

Firstly, we study the uniform convergence of cosine and sine Fourier transforms. Secondly, we obtain Pitt-Boas type results on Lp-integrability of Fourier transforms with the power weights. The solutions of both problems are written as criteria in terms of general monotone functions.     

A Resistance Bound Via An Isoperimetric Inequality

An isoperimetric upper bound on the resistance is given. As a corollary we resolve two problems, regarding mean commute time on finite graphs and resistance on percolation clusters. Further conjectures are presented.     

Theory of permanents 1982-1985

This is a survey of developments in the theory of permanents during the last quadrennium. It is a sequel to the monograph Permanents and the survey article Theory of Permanents 1978-1981. Many of the significant results obtained during the last four years are described in some detail. The current status of the conjectures and unsolved problems listed in previous surveys is described, and new conjectures proposed during the present period are listed. A comprehensive bibliography is appended. together with a list of addenda to previous bibliographies. Each item on either list is followed by an abstract.     

Problems and conjectures concerning connectivity, paths, trees and cycles in tournament-like digraphs

In this paper we collect a substantial number of challenging open problems and conjectures on connectivity, paths, trees and cycles in tournaments and classes of digraphs which contain tournaments as a subclass. The list is by no means exhaustive but is meant to show that the area has a large number of interesting open problems. We also mention problems for general digraphs when they are relevant in the context.     

Open problems and conjectures

In this section we present some open problems and conjectures about some interesting types of difference equations. Please submit your problems and conjecutures with all relevant informations to G. Ladas