In hyperlattice the join and meet operations are from L × Ł to power set (without empty set). In this paper we study the necessary and sufficient condition for a φrepresentation of hyperlattice. Copyright c © 2011 Yang’s Scientific Research Institute, LLC. All rights reserved.

We study hypercyclicity of Toeplitz operators in the Hardy space H2(D) with symbols form R(z‾)+φ(z), where R is a rational function and φ∈H∞(D). relate this problem to cyclicity certain families functions for analytic give new sufficient conditions based on deep results B. Solomyak.

Let X be a continuum and let φ:X→X homeomorphism. To construct dynamical system (X,φ) with interesting properties, the often needs to have some complicated topological structure. In this paper, we are interested in one such property: transitivity. By now, various examples of continua been constructed way that is transitive. Mostly, they not path-connected, as pseudo-arc or pseudo-circle, locall...

We considered the phantom cosmology with the lagrangian L = 1 η [1 − 1 + ηg µν φ , µ φ , ν ] − u(φ), which is original from the nonlinear Born-Infeld type scalar field with the lagrangian L = 1 η [1 − 1 − ηg µν φ , µ φ , ν ] − u(φ). This cosmological model can explain the accelerated expansion of the universe with the equation of state parameter ω < −1. We find that the potential u(φ) should be...

Consider A(x,D):C∞(Ω,E)→C∞(Ω,F) an elliptic and canceling linear differential operator of order ν with smooth complex coefficients in Ω⊂RN from a finite dimension vector space E to F A⁎(x,D) its adjoint. In this work we characterize the (local) continuous solvability partial equation A⁎(x,D)v=f (in distribution sense) for given f; more precisely show that any x0∈Ω is contained neighborhood U⊂Ω ...

Bochkariev's theorem states that for any uniformly bounded orthonormal system Φ, there is a Lebesgue integrable function such the Fourier series of it with respect to Φ diverges on set positive measure. In this paper, we extended some class variable exponent spaces. We characterized spaces Lp(⋅)[0;1], 1<p(x)<∞ a.e. [0;1], above mentioned Bochkarev's valid.

In this paper, we introduce the notion of generalized (α, φ, ψ)- Geraghty contractive type mappings in setup Sb-metric spaces and α-orbital admissible with respect to φ. Furthermore, fixed-point theorems for such complete are proven without assuming subadditivity ψ. Some examples provided supporting our main results. Also, gave an application integral equations as well Homotopy.

* Firstly, we wish to find a lower bound, i.e. the functional I(φ) such that for every family {φε}ε>0, satisfying φε → φ as ε → 0 , we have limε→0+ Iε(φε) ≥ I(φ). ** Secondly, we wish to find an upper bound, i.e. the functional I(φ) such that there exists the family {ψε}ε>0, satisfying ψε → φ as ε → 0 , and we have limε→0+ Iε(ψε) ≤ I(φ). *** If we obtain I(φ) = I(φ) := I(φ), then I(φ) will be t...

and Applied Analysis 3 Proof. First we show thatN ̸ = 0. From (15) and (16), we rewrite J (φ, ψ) = 1 2 ( 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 E1 − ω 1 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 l 2) + 1 2 ( 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 E2 − ω 2 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 l 2) − 1 4 ∑ n∈Z (a 1 φ 4 n + a 2 ψ 4 n + 2a 3 φ 2 n ψ 2 n ) , (18) I (φ, ψ) = 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 E1 − ω 1 󵄩󵄩󵄩󵄩φ 󵄩󵄩󵄩󵄩 2 l 2 + 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 E2 − ω 2 󵄩󵄩󵄩󵄩ψ 󵄩󵄩󵄩󵄩 2 l 2 − ∑ n∈Z (a 1 φ 4 n + a 2 ψ 4 n + 2a 3 φ 2 n ψ 2 n )...

In this paper, we show that for any positive integer k, the set {( φ(Fn+1) φ(Fn) , φ(Fn+2) φ(Fn) , . . . , φ(Fn+k) φ(Fn) )