We survey some open problems in matrix theory by briefly describing their history and current state. 2000 Mathematics Subject Classification: 15A15, 15A18, 15A60, 15A29, 15-02, 05B20, 05C07.

Centre for Mathematical Physics and Stochastics (funded by the Danish National Research Foundation). Mathematics Subject Classification 2000. Primary 60H05, 60J55, 60G44. Secondary 60J60, 60J65, 35R35.

This article discusses Paul Halmos’s crucial work on Toeplitz operators and the consequences of that work. Mathematics Subject Classification (2000). 47B35.

In this paper connectedness is studied in weaker (monotone, quasi-directed) spaces and we examine sets having the ending property (e.p.). 2000 Mathematics Subject Classification: 54A99, 54C05

We describe some combinatorial problems in finite projective planes and indicate how Rédei’s theory of lacunary polynomials can be applied to them. 2000 Mathematics Subject Classification: 05.

Sufficient conditions for computation of the H-functions with complex parameters by means of residues are derived and some examples are given. 2000 Mathematics Subject Classification. Primary 33C60.

We discuss the characterization of relative equilibria of Lagrangian systems with symmetry. Mathematics Subject Classification (2000). 34A05, 34A26, 37J15, 37J15, 70H03.

In this paper we study weakly symmetric and special weakly Ricci symmetric Lorentzian β-Kenmotsu manifolds and obtained some interesting results. 2000 Mathematics Subject Classification: 53C10, 53C15.

We prove a result on the value distribution of differential polynomials which improves some earlier results. 2000 Mathematics Subject Classification. 30D35.

We give an elementary proof of the Mazur-TateTeitelbaum conjecture for elliptic curves by using Kato’s element. 2000 Mathematics Subject Classification: 11F85, 11G05, 11G07, 11G40, 11S40.