An analogue of the notion of uniformly separated sequences, expressed in terms of canonical divisors, is shown to yield a necessary and sufficient condition for interpolation in the Bergman space Ap, 0 < p < ∞. A sequence Γ = {zj} of distinct points in the open unit disk D = {z : |z| < 1} of the complex plane is a classical interpolation sequence if for every bounded sequence {aj}, there is a b...

In [Tal94], Talagrand showed a generalization of the celebrated KKL theorem. In this work, we prove that the converse of this generalization also holds. Namely, for any sequence of numbers 0 < a1, a2, . . . , an ≤ 1 such that ∑n j=1 aj/(1 − log aj) ≥ C for some constant C > 0, it is possible to find a roughly balanced Boolean function f such that Infj [f ] < aj for every 1 ≤ j ≤ n.

In this paper, we show that if two non-constant meromorphic functions f and g satisfy E(aj , k, f) = E(aj , k, g) for j = 1, 2, . . . , 5, where aj are five distinct small functions with respect to f and g, and k is a positive integer or ∞ with k ≥ 14, then f ≡ g. As a special case this also answers the longstanding problem on uniqueness of meromorphic functions concerning small functions.

BACKGROUND/AIMS Acerola (Malpighia emarginata DC.) is a fruit that is known to contain high amounts of ascorbic acid (AA) and various phytochemicals. We have previously reported that AA deficiency leads to ultraviolet B (UVB)-induced skin pigmentation in senescence marker protein 30 (SMP30)/gluconolactonase (GNL) knockout (KO) hairless mice. The present study was undertaken to investigate the e...

(3) To prove that Zp forms a field, we first have to make sense of what Zp actually is, and what the addition/product operations are. Consider the set of integers Z. For i = 0, 1, . . . , p − 1, let Ai be the subset of Z consisting of all j such that j ≡ i (mod p) (i.e. p|(j − i)). For example, A0 comprises of all multiples of p, while A1 = {. . . , 1, p + 1, 2p + 1, . . . }. Then the disjoint ...

Note that for f(x) = e − 1, (1.1) becomes a logistic equation with piecewise constant arguments. Definition 1.1 The zero solution of (1.1) is said to be uniformly stable, if for any ε > 0 and nonnegative integer n0, there is a δ = δ(ε) > 0 such that max{|x(n0 − j)| | j = −k,−k + 1, · · · , 0} < δ, implies that the solution {x(n)}n=0 of (1.1) satisfies |x(n)| < ε, n = n0, n0 + 1, · · · . Definit...

Consider random symmetric Toeplitz matrices Tn = (ai−j) n i,j=1 with matrix entries aj , j = 0, 1, 2, · · · , being independent real random variables such that E[aj ] = 0, E[|aj |] = 1 for j = 0, 1, 2, · · · , (homogeneity of 4-th moments) κ = E[|aj |], and further (uniform boundedness) sup j≥0 E[|aj |] = Ck <∞ for k ≥ 3. Under the assumption of a0 ≡ 0, we prove a central limit theorem for line...

k=1 |ak|, in which C = (cj,k) and the parameter p are assumed fixed (p > 1), and the estimate is to hold for all complex sequences a. The lp operator norm of C is then defined as the p-th root of the smallest value of the constant U : ||C||p,p = U 1 p . Hardy’s inequality thus asserts that the Cesáro matrix operator C, given by cj,k = 1/j, k ≤ j and 0 otherwise, is bounded on lp and has norm ≤ ...

Based on constant term evaluation, we present a new method to compute a closed form of the summation ∑n−1 k=0 ∏r j=1 Fj(ajn+bjk+cj), where {Fj(k)} are C-finite sequences and aj and aj+bj are nonnegative integers. Our algorithm is much faster than that of Greene and Wilf. Résumé. En s’appuyant sur l’évaluation de termes constants, nous présentons une nouvelle méthode pour calculer une forme clos...

Transformation of cultured chick lens epithelial cells with a temperature-sensitive mutant of Rous sarcoma virus (tsRSV) leads to radical changes in cell shape and interactions. When cultured at the restrictive temperature (42 degrees C), the transformed cells largely retained epithelial morphology and intercellular adherens junctions (AJ), whereas on switch to the permissive temperature (37 de...