a non-malleable code is a variant of an encoding scheme which is resilient to tampering attacks. the main idea behind nonmalleable coding is that the adversary should not be able to obtain any valuable information about the message. non-malleablecodes are used in tamper-resilient cryptography and protecting memories against tampering attacks. many different types of nonmalleability have already...

We show that if F :S1 → S1 is a homeomorphism of the unit circle S1 and the rotation number α(F ) of F is irrational, then the Schröder equation Φ ( F(z) = e2πiα(F Φ(z), z ∈ S1, has a unique (up to a multiplicative constant) continuous at a point of the limit set of F solution. We apply this result to prove that if F is a non-trivial continuous and disjoint iteration group or semigroup on S1 an...

We introduce the notion of semigroup with a tight ideal series and investigate their closures in semitopological semigroups, particularly inverse semigroups with continuous inversion. As a corollary we show that the symmetric inverse semigroup of finite transformations I n λ of the rank 6 n is algebraically closed in the class of (semi)topological inverse semigroups with continuous inversion. W...

1. Basic Assumptions. Assume that (i) {Tt} is a strongly-continuous semigroup of bounded linear operators on the Banach space B = C0(I) = { f continuous on I = [0, 1] : f(0) = f(1) = 0 } (ii) If f(x) ≥ 0 and f ∈ B, then Ttf(x) ≥ 0 and Ttf(x) ≤ maxy∈I f(y). In general, the infinitesimal generator of a strongly-continuuous semigroup of linear operators Tt on any Banach space B is defined by Af = ...

Bowen showed that a continuous expansive map with specification has a unique measure of maximal entropy. We show that the conclusion remains true under weaker non-uniform versions of these hypotheses. To this end, we introduce the notions of obstructions to expansivity and specification, and show that if the entropy of such obstructions is smaller than the topological entropy of the map, then t...

We consider dynamic programming problems with a large time horizon, and give sufficient conditions for the existence of the uniform value. As a consequence, we obtain an existence result when the state space is precompact, payoffs are uniformly continuous and the transition correspondence is non expansive. In the same spirit, we give an existence result for the limit value. We also apply our re...

In this paper we study the preservation of strong stability of strongly continuous semigroups on Hilbert spaces. In particular, we study a situation where the generator of the semigroup has a finite number of spectral points on the imaginary axis and the norm of its resolvent operator is polynomially bounded near these points. We characterize classes of perturbations preserving the strong stabi...

Recently, parabolic equations in infinite dimensions have received much attention in literature (see, for example, Pa Prato [DP] and Da Prato Zabczyk [DZ]). In particular, Cannarsa and Da Prato [CD1] showed that the Laplacian (with a certain weight) generates a semigroup on BUC(H), the space of all bounded uniformly continuous functions on a separable Hilbert space H, which is called the heat s...

We give conditions on a strongly continuous semigroup T and a bounded perturbation B such that the perturbed semigroup S preserves asymptotic properties as boundedness, asymptotic almost periodicity, uniform ergodicity and total uniform ergodicity. In the rst systematic treatise on perturbation of semigroups, R.S.Phillips 10] proved in 1953 that, if A is the innnitesimal generator of a strongly...