In this article we present applications of smooth numbers to the unconditional derandomization of some well-known integer factoring algorithms. We begin with Pollard’s p−1 algorithm, which finds in random polynomial time the prime divisors p of an integer n such that p− 1 is smooth. We show that these prime factors can be recovered in deterministic polynomial time. We further generalize this re...

Consider the Floquet operator of a time independent quantum system, periodically perturbed by a rank one kick, acting on a separable Hilbert space: e0 e |φ〉〈φ| where T and κ are the period and the coupling constant respectively. Assume the spectrum of the self adjoint operator H0 is pure point, simple, bounded from below and the gaps between the eigenvalues (λn) grow like: λn+1 − λn ∼ Cn with d...

Some operator inequalities for synchronous functions that are related to the c̆ebys̆ev inequality are given. Among other inequalities for synchronous functions it is shown that ‖φ (f (A) g (A))− φ (f (A))φ (g (A))‖ ≤ max {∥∥φ (f2 (A))− φ (f (A))∥∥ , ∥∥φ (g2 (A))− φ (g (A))∥∥} whereA is a self-adjoint and compact operator on B (H ), f, g ∈ C (sp (A)) continuous and non-negative functions and φ : B...

In this paper, Φ-pseudo-contractive operators and Φ-accretive operators, more general than the strongly pseudo-contractive operators and strongly accretive operators, are introduced. By setting up a new inequality, authors proved that if → : T X X is a uniformly continuous Φ-pseudo-contractive operator then T has unique fixed point q and the Mann iterative sequence with random errors approximat...

In this paper, we prove the Spanne-Guliyev type boundedness of the generalized fractional integral operator Iρ from the vanishing generalized local Morrey spaces V LM {x0} p,φ1 to V LM {x0} q,φ2 , 1 < p < q < ∞, and from the space V LM {x0} 1,φ1 to the weak space VWLM {x0} q,φ2 , 1 < q < ∞. We also prove the Adams-Guliyev type boundedness of the operator Iρ from the vanishing generalized Morrey...

In this paper, we introduce the factorable surfaces in the pseudo-Galilean space G3 and completely classify such surfaces with null Gaussian and mean curvature. Also, in a special case, we investigate the factorable surfaces which fulfill the condition that the ratio of the Gaussian curvature and the mean curvature is constant in G3.

We prove that two dual operator spaces X and Y are stably isomorphic if and only if there exist completely isometric normal representations φ and ψ of X and Y , respectively, and ternary rings of operators M1,M2 such that φ(X) = [M ∗ 2 ψ(Y )M1] −w ∗ and ψ(Y ) = [M2φ(X)M ∗ 1 ]. We prove that this is equivalent to certain canonical dual operator algebras associated with the operator spaces being ...

Two-dimensional compactly supported, orthogonal wavelets and lter-banks having linear phase are presented. Two cases are discussed, wavelets with twofold symmetry (centrosymmetric), and wavelets with four-fold symmetry that are symmetric (or anti-symmetric) about the vertical and horizontal axes. We show that imposing the requirement of linear phase in the case of factorable wavelets, imposes a...

Let La be a Bergman space. We are interested in an intermediate Hankel operator H M φ from La to a closed subspace M of L 2 which is invariant under the multiplication by the coordinate function z. It is well known that there do not exist any nonzero finite rank big Hankel operators, but we are studying same types in case H φ is close to big Hankel operator. As a result, we give a necessary and...