It is proved under mild regularity assumptions on the data that the Navier-Stokes equations in bounded and unbounded noncylindrical regions admit a unique local-in-time strong solution. The result is based on maximal regularity estimates for the in spatial regions with a moving boundary obtained in [16] and the contraction mapping principle.

‎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 $A$‎ .

We consider optimality systems of Karush-Kuhn-Tucker (KKT) type, which arise, for example, as primal-dual conditions characterizing solutions of optimization problems or variational inequalities. In particular, we discuss error bounds and Newton-type methods for such systems. An exhaustive comparison of various regularity conditions which arise in this context is given. We obtain a new error bo...

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 ...

A predicate f : {−1, 1} 7→ {0, 1} with ρ(f) = Ex∈{−1,1}k [f(x)] is said to be strongly approximation resistant if, for every ε > 0, given a near-satisfiable instance of MAX k-CSP(f), it is hard to find an assignment such that the fraction of constraints satisfied is outside the range [ρ(f)−ε, ρ(f) +ε]. A predicate which is not strongly approximation resistant is known as weakly approximable. We...

The Frieze-Kannan regularity lemma is a powerful tool in combinatorics. It has also found applications in the design of approximation algorithms and recently in the design of fast combinatorial algorithms for boolean matrix multiplication. The algorithmic applications of this lemma require one to efficiently construct a partition satisfying the conditions of the lemma. Williams [25] recently as...

‎our contribution in this paper is to propose an iterative algorithm which does not require prior knowledge of operator norm and prove a strong convergence theorem for approximating a solution of split equality fixed point problem for quasi-nonexpansive mappings in a real hilbert space‎. ‎so many have used algorithms involving the operator norm for solving split equality fixed point problem‎, ‎...

Valdis Laan in [5] introduced an extension of strong flatness which is called weak pullback flatness. In this paper we introduce a new property of acts over monoids, called U-WPF which is an extension of weak pullback flatness and give a classification of monoids by this property of their acts and also a classification of monoids when this property of acts implies others. We also show that regu...

We study strong unique continuation for products of elliptic operators. The main tools are Carleman inequalities for second order elliptic operators. We obtain strong unique continuation assuming either Gevrey regularity of the coefficients or some pointwise conditions on the coefficients.

Explicit algorithms are presented for the generation of Daubechies compact orthogonal least asymmetric wavelet filter coefficients and the computation of their Holder regularity. The algorithms yield results for any number N of vanishing moments for the wavelets. These results extend beyond order N = 10 those produced by Daubechies for the values of the filter coefficients and those produced by...