Note that μ0 is simply normalized Lebesque measure on B. The k-th Bergman space, Ak, is defined as the space of analytic functions on B which are square integrable with respect to the measure μk. Note that Ak = H (μk), where H (μk) be the L2(μk) -closure of the ball algebra A, and that Aj c Ak for j < k. The standard orthonormal base for Ak is given by eka = c(a, k, n)z a = c{a, ky n)r^e i0Clθl...

A model function f(x1,. . .,xn) defined in the unit hypercube Hn with Lebesque measure dx= dx1. . .dxn is considered. If the unction is square integrable, global sensitivity indices provide adequate estimates for the influence of individual factors xi or roups of such factors. Alternative estimators that require less computer time can also be used. If the function f is differentiable, unctional...

The aim of this paper is to establish an extension of Minkowski’s inequality when p, s, t ∈ R−{0}, p > 0 are different such that s, t < 1, s, t = 0 and s−t p−t < 1, to isotonic linear functionals taking into account that the time scale Cauchy delta, Cauchy nabla, α-diamond, multiple Riemann, and multiple Lebesque integrals all are isotonic linear functionals. Several applications of these resul...

We extend Markov’s, Bernsteins’s, and Videnskii’s inequalities to arbitrary subsets of [−1, 1] and [−π,π], respectively. The primary purpose of this note is to extend Markov’s and Bernsteins’s inequalities to arbitrary subsets of [−1, 1] and [−π, π], respectively. We denote by Pn the set of all real algebraic polynomials of degree at most n and let m(·) denote the Lebesque measure of a subset o...

Let G=SL(2,R), T = SL(2,Z), u, ' l (where t e R) and let fi. be the G-invariant probability measure on G/Y. We show that if x is a non-periodic point of the flow given by the (w,)-action on G/Y then the («,)-orbit of x is uniformly distributed with respect to JU. ; that is, if SI is an open subset whose boundary has zero measure, and / is the Lebesque measure on R then, as T -> oo, T~l{0 < t < ...

Many physicists take it for granted that their theories can be either refuted or verified by comparison with experimental data. In order to evaluate such data, however, one must employ statistical estimation and inference methods which, unfortunately, always involve an ad hoc proposition. The nature of the latter depends upon the statistical method adopted; in the Bayesian approach, for example...

1 LL aszll o Lovv asz 2 and Mikll os Simonovits 3 Abstract. We study the smallest number (K) such that a given convex body K in IR n can be cut into two parts K 1 and K 2 by a surface with an (n ? 1)-dimensional measure (K)vol(K 1) vol(K 2)=vol(K). Let M 1 (K) be the average distance of a point of K from its center of gravity. We prove for the \isoperimetric coeecient" that and give other upper...

in this paper, we present an efficient method for determining the solution of the stochastic second kind volterra integral equations (svie) by using the taylor expansion method. this method transforms the svie to a linear stochastic ordinary differential equation which needs specified boundary conditions. for determining boundary conditions, we use the integration technique. this technique give...