Problems Solved

Solved Problems in Random Processes

Solved and unsolved problems in generalized notions of Connes amenability

We survey the recent investigations on (bounded, sequential) approximate Connes amenability and pseudo-Connes amenability for dual Banach algebras. We will discuss the core problems concerning these notions and address the signicance of any solutions to them to the development of the eld.

Data completion problems solved as Nash games

Abstract. We consider the Cauchy problem for an elliptic operator, formulated as a Nash game. The over specified Cauchy data are split among two players : the first player solves the elliptic equation with the Dirichlet part of the Cauchy data prescribed over the accessible boundary, and a variable Neumann condition (which we call first player’s strategy) prescribed over the inaccessible part o...

On Generating Solved Instances of Computational Problems

We consider the e cient generation of solved instances of computational problems. In particular, we consider invulnerable generators. Let S be a subset of f0; 1g and M be a Turing Machine that accepts S; an accepting computation w of M on input x is called a \witness" that x 2 S. Informally, a program is an -invulnerable generator if, on input 1 n , it produces instancewitness pairs hx; wi, wit...

Fuzzy Implications: Some Recently Solved Problems

In this chapter we discuss some open problems related to fuzzy implications, which have either been completely solved or those for which partial answers are known. In fact, this chapter also contains the answer for one of the open problems, which is hitherto unpublished. The recently solved problems are so chosen to reflect the importance of the problem or the significance of the solution. Fina...