Hölder estimates for spatial second derivatives are proved for solutions of fully nonlinear parabolic equations in two space variables. Related techniques extend the regularity theory for fully nonlinear parabolic equations in higher dimensions.

This paper is a survey and systematic presentation of decidability and complexity issues for modal and non-modal two-variable logics. A classical result due to Mortimer says that the two-variable fragment of rst-order logic, denoted FO 2 , has the nite model property and is therefore decidable for satissability. One of the reasons for the signiicance of this result is that many propositional mo...

The problem whether the set of all equations that are satisfiable in some free semigroup or, equivalently, in an algebra of words with concatenation is recursive (usually called the satisfiability problem for semigroup equations) was first formulated by A.A. Markov in early sixties (see [3]). Special cases of the problem were solved affirmatively by A.A. Markov (see [3]), Yu.I. Khmelevskiı̆ [8],...

We present a method, based on series expansions and symmetric polynomials, by which a mean of two variables can be extended to several variables. We apply it mainly to the logarithmic mean.

We study the correctness of shared data structures under reads-write concurrency. A popular approach to ensuring correctness of read-only operations in the presence of concurrent update, is read-set validation, which checks that all read variables have not changed since they were first read. In practice, this approach is often too conservative, which adversely affects performance. In this paper...