We study the regularity of a parabolic free boundary problem of two-phase type with coefficients below the Lipschitz threshold. For the Lipschitz coefficient case one can apply a monotonicity formula to prove the optimal C x ∩ C t -regularity of the solution and that the free boundary is, near the so-called branching points, the union of two graphs that are Lipschitz in time and C in space. In ...

We give new versions of the global Newton method and the Kellogg & Li & Yorke method for calculating zero points and fixed points of nonlinear maps, which are numerically stable, but do not require an extra homotopy dimension. In addition, regularity results are established so that predictor-corrector continuation methods will lead to solutions if appropriate boundary conditions are satisfied.

After presenting an overview about variational problems on probability measures for functionals involving transport costs and extra terms encouraging or discouraging concentration, we look for optimality conditions, regularity properties and explicit computations in the case where Wasserstein distances and interaction energies are considered.

We consider the usual one-pile subtraction game with an extra feature, called a Muller twist. The twist is that the number of stones to be removed from the heap is dictated by our opponent to be either in a prescribed set S or not. We investigate regularity in the sequences of Grundy values for such games.

For a word S, let f(S) be the largest integer m such that there are two disjoint identical (scattered) subwords of length m. Let f(n,Σ) = min{f(S) : S is of length n, over alphabet Σ}. Here, it is shown that 2f(n, {0, 1}) = n− o(n) using the regularity lemma for words. In other words, any binary word of length n can be split into two identical subwords (referred to as twins) and, perhaps, a rem...

in this article we study two different generalizations of von neumann regularity, namely strong topological regularity and weak regularity, in the banach algebra context. we show that both are hereditary properties and under certain assumptions, weak regularity implies strong topological regularity. then we consider strong topological regularity of certain concrete algebras. moreover we obtain ...

We study topological von Neumann regularity and principal von Neumann regularity of Banach algebras. Our main objective is comparing these two types of Banach algebras and some other known Banach algebras with one another. In particular, we show that the class of topologically von Neumann regular Banach algebras contains all $C^*$-algebras, group algebras of compact abelian groups and ...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

‎Let $X$‎, ‎$Y$ and $Z$ be Banach spaces and $f:Xtimes Y‎ ‎longrightarrow Z$ a bounded bilinear map‎. ‎In this paper we‎ ‎study the relation between Arens regularity of $f$ and the‎ ‎reflexivity of $Y$‎. ‎We also give some conditions under which the‎ ‎Arens regularity of a Banach algebra $A$ implies the Arens‎ ‎regularity of certain Banach right module action of $A$‎ .

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...