We study the extent to which properties of infinite-dimensional dynamical systems can be accurately detected by examining observations of such systems. Let H be a separable Hilbert space. Let f : H → H be a map and let A ⊂ H be a compact set satisfying f(A) = A. We prove that for almost every (in the sense of prevalence) continuous observable φ : H → RM , if f induces a map f̄ satisfying f̄ ◦ φ =...

in this paper,  we introduce the notion of  generalized multivalued  $f$- weak contraction and we prove some fixed point theorems related to introduced  contraction for multivalued mapping in complete metric spaces.  our results extend and improve the results announced by many others with less hypothesis. also, we give some illustrative examples.

The object of the present paper is to study generalized φ− recurrent and generalized concircular φ− recurrent P-Sasakian manifold. AMS Mathematics Subject Classification (2010): 53B20, 53D15.

Let A be an algebra, and let θ, φ be ring automorphisms of A. An additive mapping H : A → A is called a θ, φ -derivation if H xy H x θ y φ x H y for all x, y ∈ A. Moreover, an additive mapping F : A → A is said to be a generalized θ, φ -derivation if there exists a θ, φ derivation H : A → A such that F xy F x θ y φ x H y for all x, y ∈ A. In this paper, we investigate the superstability of gene...

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...

A compatible point-shift f maps, in a translation invariant way, each point of a stationary point process Φ to some point of Φ. It is fully determined by its associated point-map, gf , which gives the image of the origin by f . The initial question of this paper is whether there exist probability measures which are left invariant by the translation of −gf . The point-map probabilities of Φ are ...

There is a one-to-one correspondence between l-quasi-cyclic codes over a finite field Fq and linear codes over a ring R = Fq[Y ]/(Y m − 1). Using this correspondence, we prove that every l-quasi-cyclic self-dual code of length ml over a finite field Fq can be obtained by the building-up construction, provided that char (Fq) = 2 or q ≡ 1 (mod 4), m is a prime p, and q is a primitive element of F...

For a continuous map f on a compact metric space we study the geometry and entropy of the generalized rotation set Rot(Φ). Here Φ = (φ1, ..., φm) is a m-dimensional continuous potential and Rot(Φ) is the set of all μ-integrals of Φ and μ runs over all f -invariant probability measures. It is easy to see that the rotation set is a compact and convex subset of R. We study the question if every co...

In this paper, we consider the oscillation behavior of following second-order nonlinear dynamic equation. λ(s)Ψ1φΔ(s)y(φ(s))ΔΔ+η(s)Φ(y(τ(s)))=0,s∈[s0,∞)T. By employing generalized Riccati transformation and inequality scaling technique, establish some criteria.