let $a$ be an arbitrary banach algebra and $varphi$ a homomorphism from $a$ onto $bbb c$. our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain a; |a|=varphi(a)=1}$ in $a^{**}$.

In this paper we prove that every n-Jordan homomorphis varphi:mathcal {A} longrightarrowmathcal {B} from unital Banach algebras mathcal {A} into varphi -commutative Banach algebra mathcal {B} satisfiying the condition varphi (x^2)=0 Longrightarrow varphi (x)=0, xin mathcal {A}, is an n-homomorphism. In this paper we prove that every n-Jordan homomorphism varphi:mathcal {A} longrightarrowmathcal...

Let $A$ be an arbitrary Banach algebra and $varphi$ a homomorphism from $A$ onto $Bbb C$. Our first purpose in this paper is to give some equivalent conditions under which guarantees a $varphi$-mean of norm one. Then we find some conditions under which there exists a $varphi$-mean in the weak$^*$ cluster of ${ain A; |a|=varphi(a)=1}$ in $A^{**}$.

The B domain of staphylococcal protein A (BdpA) is a small helical protein that has been studied intensively in kinetics experiments and detailed computer simulations that include explicit water. The simulations indicate that BdpA needs to reorganize in crossing the transition barrier to facilitate folding its C-terminal helix (H3) onto the nucleus formed from helices H1 and H2. This process su...

We find limiting distributions of the nonparametric maximum likelihood estimator (MLE) of a log-concave density, i.e. a density of the form f(0) = exp varphi(0) where varphi(0) is a concave function on R. Existence, form, characterizations and uniform rates of convergence of the MLE are given by Rufibach (2006) and Dümbgen and Rufibach (2007). The characterization of the log-concave MLE in term...

The fluidity of liquid metals, like that of simple nonmetallic liquids, is a linear function of the ratio of unoccupied volume to intrinsic volume over long ranges as expressed by the equation varphi = B[(V/V(0)) - 1]. Values of V(0) obtained by extrapolating to varphi = 0 agree well with molal volumes of compact crystals at 20 degrees C calculated from densities.Values of the ratio varphi/[(V/...

Recent efforts to broaden understanding of the molecular mechanisms of membrane receptors in signal transduction make use of rate-equilibrium free-energy relationships (REFERs), previously applied to chemical reactions, enzyme kinetics, and protein folding. For oligomeric membrane receptors, we distinguish between a), the Leffler parameter alpha(L), to characterize the global transition state f...

‎Let $\Omega_X$ be a bounded‎, ‎circular and strictly convex domain in a complex Banach space $X$‎, ‎and $\mathcal{H}(\Omega_X)$ be the space of all holomorphic functions from $\Omega_X$ to $\mathbb{C}$‎. ‎The growth space $\mathcal{A}^\nu(\Omega_X)$ consists of all $f\in\mathcal{H}(\Omega_X)$‎ ‎such that $$|f(x)|\leqslant C \nu(r_{\Omega_X}(x)),\quad x\in \Omega_X,$$‎ ‎for some constant $C>0$‎...

We show that a qubit can be used to substitute for a classical analog system requiring an arbitrarily large number of classical bits to represent digitally. Let a physical system S interact locally with a classical field varphi(x) as S travels directly from point A to point B. Our task is to use S to answer a simple yes/no question about varphi(x). If S is a qubit, the task can be done perfectl...

We study by molecular dynamics the interplay between arrest and crystallization in hard spheres. For state points in the plane of volume fraction (0.54 <or= varphi <or= 0.63) and polydispersity (0 <or= s <or= 0.085), we delineate states that spontaneously crystallize from those that do not. For noncrystallizing (or precrystallization) samples we find isodiffusivity lines consistent with an idea...