For μ ≥ 0, we consider a linear operator Lμ : A → A defined by the convolution fμ∗f , where fμ = (1−μ)z2F1(a,b,c;z)+μz(z2F1(a,b,c;z))′. Let φ∗(A,B) denote the class of normalized functions f which are analytic in the open unit disk and satisfy the condition zf ′/f ≺ (1+Az)/1+Bz, −1 ≤ A < B ≤ 1, and let Rη(β) denote the class of normalized analytic functions f for which there exits a number η∈ (...

We define a statistic an(w), the size of the atmosphere of a self-avoiding walk, w, of length n, with the property that 〈an(w)〉 → μ as n → ∞, where μ is the growth constant of lattice self-avoiding walks. Both μ and the entropic exponent γ may be estimated to high precision from 〈a(w)〉 using canonical Monte Carlo simulations of self-avoiding walks. Previous Monte Carlo measurements of μ and γ h...

       The binding of drugs by plasma proteins is an important phenomenon, because it influences the size of the free fraction of the drugs in plasma. In this study the influence of dipyridamole (DP) on the protein binding of propranolol (PL) and PL on the protein binding of DP were studied alone and in the presence of nicotine (NC).        The equilibrium dialysis was employed for protein bin...

We prove the inequality E[(X/μ)k]≤(k/μlog(1+k/μ))k≤exp(k2/(2μ)) for sub-Poissonian random variables X, such as Binomially or Poisson distributed variables, with mean μ. The asymptotic behaviour E[(X/μ)k]=1+O(k2/μ) matches a lower bound of 1+Ω(k2/μ) small k2/μ. This improves over previous uniform raw moment bounds by factor exponential in k.

background: cystoid macular edema (cme) is one of the most common and sight threatening complications of uveitis. intravitreal injection of corticosteroids and anti-vegf antibody are two routine options for treatment. objective: to compare the effects of intravitreal injections of bevacizumab and triamcinolone acetonide for the treatment of persistent macular edema in non-infectious uveitis. me...

We solve the Milne, constant-source and albedo problems for isotropic scattering in a two-dimensional “Flatland” half-space via the Wiener-Hopf method. The Flatland H-function is derived and benchmark values and some identities unique to Flatland are presented. A number of the derivations are supported by Monte Carlo simulation. 1. Intro The study of linear transport theory [1, 2] in lower-dime...

Let G be a connected reductive complex algebraic group with maximal torus T. We denote by Λ the coweight lattice of Λ+⊂Λ submonoid dominant coweights. For λ∈Λ+,μ∈Λ,μ⩽λ, in [7], authors defined generalized transversal slice W‾μλ. This is an variety dimension 〈2ρ∨,λ−μ〉, where 2ρ∨ sum positive roots G. In this paper, we construct isomorphism W‾μλ≃W‾μ+λ×A〈2ρ∨,μ+−μ〉 for μ∈Λ such that 〈α∨,μ〉⩾−1 any r...