We establish a connection between the function space BMO and theory of quasisymmetric mappings on \emph{spaces homogeneous type} $\widetilde{X} :=(X,\rho,\mu)$. The is that logarithm generalised Jacobian an $\eta$-quasisymmetric mapping $f: \widetilde{X} \rightarrow \widetilde{X}$ always in $\rm{BMO}(\widetilde{X})$. In course proving this result, we first show $\widetilde{X}$, reverse-H\"{o}ld...

In cite{p}, Park introduced the quadratic $rho$-functional inequalitiesbegin{eqnarray}label{E01}&& |f(x+y)+f(x-y)-2f(x)-2f(y)| \ && qquad le  left|rholeft(2 fleft(frac{x+y}{2}right) + 2 fleft(frac{x-y}{2}right)- f(x) -  f(y)right)right|,  nonumberend{eqnarray}where $rho$ is a fixed complex number with $|rho|

Let f be an entire function, f(0) = 1, F(z) zf′ (z)/f(z), and Γm $$\bigcup_{j=1}^{m}\left\{z:\mathrm{arg}z={\psi }_{j}\right\},$$ 0 ≤ ψ1 < ψ2 ...< ψm 2π. An function is called a of improved regular growth if for some ρ ∈ (0;+∞) ρ2 (0; ρ), 2π-periodic ρ-trigonometrically convex h(φ) ≢ −∞, there exists set U ⊂ $${\mathbb{C}}$$ contained in the union disks with finite sum radii such that $$\begin{...

The prospect of using linkage disequilibrium (LD) for fine-scale mapping in humans has attracted considerable attention, and, during the validation of a set of single-nucleotide polymorphisms (SNPs) for linkage analysis, a set of data for 4,833 SNPs in 538 clusters was produced that provides a rich picture of local attributes of LD across the genome. LD estimates may be biased depending on the ...

In the present work we study existence and non-existence of nonnegative solutions to a class deterministic KPZ system with nonlocal gradient term. More precisely will consider system$ \begin{equation*} \left\{ \begin{array}{rcll} (-\Delta)^{s} u &amp; = &amp;|\mathbb{D}_{s} v|^q + \rho f\,, \quad {\rm{in }}\; \Omega,\\ v |\mathbb{D}_{s} u|^p \tau g\,, v&amp; 0 &amp;\quad {\text{in }} \mathbb{R}...

In a difference or differential equation one is usually interested in finding solutions having certain properties, either intrinsic properties (e.g. bounded, periodic, almost periodic) or extrinsic properties (e.g. stable, asymptotically stable, globally asymptotically stable). In certain instances it may happen that the dependence of these equations on the state variable is such that one may (...

In this paper we present the following definitions P-asymptotically equivalent probability of multiple L and P-asymptotically probability regular. In addition to these definitions we asked and provide answers for the following questions. (1) If x Probability ≈ y then what type of four dimensional matrices transformation will satisfy the following μ(Ax) Probability ≈ μ(Ay)? (2) If [x] and [y] ar...

LRES, Faculty of Sciences Tunis, University Tunis El Manar, Tunisia EM [email protected] KW Asymptotically linear % variational method Schr?dinger equations Cerami sequence KR nema In this paper, we investigate a quasilinear problem under Dirichlet boundary condition in regular domain with asymptotically nonlinearities. We use version the mountain pass theorem to prove existence solution ...

rho-kinase is an effector molecule of rhoa, a monomeric gtp-binding protein, and causes ca2+ sensitization through inactivation of myosin phosphatase. the major physiological functions of rho/rho-kinase cascade include contraction, proliferation and migration in cells.there are some excellent reviews about rho/rho-kinase signal pathway, most of which focus on the specific proteins of the pathwa...