In this paper, we deal with the problem for finding a common element of finite sets in a Banach space. We first prove that an operator given by a convex combination of sunny generalized nonexpansive retractions in a Banach space is asymptotically regular. Using this result, we obtain a weak convergence theorem which is connected with the problem of image recovery. Further, using another weak co...

Conventional class of weak keys on RC4 stream cipher is defined as a specific case that combinations of the first three bytes of secret key satisfy two relational equations. This paper expands and generalizes the classes of weak keys using generalized relational equations and special classes of the internal state (called predictive state). We derive the probability that generalized classes of w...

We study a nonlinear p(x)-Kirchhoff type problem with Dirichlet boundary condition, in the case of reaction term depending also on gradient (convection). Using topological approach based Galerkin method, we discuss existence two notions solutions: strong generalized solution and weak solution. Strengthening bound Kirchhoff (positivity condition), establish solution, this time using theory opera...

In [2, Chapter VII (p. 133)], Ritt shows an example of two irreducible differential variety of differential dimension 2 in U whose intersection consists of a single point: the origin. The details below follow Ritt’s exposition using more modern language and notation. The first part is taken from my tutorial paper [3], with some change in notation. That paper provides the basic background needed...

Interactive theorem provers based on dependent type theory have the flexibility to support both constructive and classical reasoning. Constructive reasoning is supported natively by dependent type theory and classical reasoning is typically supported by adding additional non-constructive axioms. However, there is another perspective that views constructive logic as an extension of classical log...

In the last twenty years several methods for computing primary decompositions of ideals in multivariate polynomial rings over fields (Seidenberg (1974), Lazard (1985), Kredel (1987), Eisenbud et al. (1992)), the integers (Seidenberg, 1978), factorially closed principal ideal domains (Ayoub (1982), Gianni et al. (1988)) and more general rings (Seidenberg, 1984) have been proposed. A related prob...