The thermal behavior of double complex compounds with the cation [Cr(ur)6]3+ in a reducing atmosphere

Journal of Thermal Analysis and Calorimetry - The thermal behavior of double complex compounds (DCC) [Cr(ur)6][Co(CN)6]·4H2O (I), [Cr(ur)6][Co(C2O4)3]·3.5H2O (II),...     

Uncorrelatedness and correlatedness of powers of random variables

Let x₁, ?, x_n \xi_1, \ldots, \xi_n be random variables and U be a subset of the Cartesian product \mathbbZ₊ⁿ, \mathbbZ₊ \mathbb{Z}_+^n, \mathbb{Z}_+ being the set of all non-negative integers. The random variables are said to be strictly U-uncorrelated if¶¶E(x₁^j₁ ?x_n^j_n) = E(x₁^j₁) ?E(x_n^j_n) ? (j₁, ... ,j_n) ? U. \textbf {E}\big(\xi_1^{j_1} \cdots \xi_n^{j_n}\big) = \textbf {E}\big(\xi_1^{j_1}\big) \cdots \textbf {E}\big(\xi_n^{j_n}\big) \iff (j_1, \dots ,j_n) \in U. ¶It is proved that for an arbitrary subset U \subseteqq \mathbbZ₊ⁿ U \subseteqq \mathbb{Z}_+^n containing all points with 0 or 1 non-zero coordinates there exists a collection of n strictly U-uncorrelated random variables.     

Polydiacetylene-supported silica films formed at the air/water interface

Mesostructured silica films have attracted interest as potential platforms for sensing, molecular sieving, catalysis, and others. The fabrication of free-standing silica films on water, however, is challenging due to the need for scaffolding agents that would constitute effective templates. We describe the assembly of thin film at the air/water interface comprising quaternary silicates and polydiacetylene (PDA), a unique chromatic polymer forming two-dimensional conjugated networks, and the use of these films for biological sensing. PDA exhibits a dual role in the system-both as the amphiphilic matrix facilitating immobilization of the silicate colloidal units at the air/water interface and additionally a chromatic reporter that undergoes visible blue-red transitions, accompanied by fluorescence transformations, in the presence of analytes. We demonstrate the application of the silicate/PDA thin films for the detection of bacterial proliferation.     

Microscopic visualization of alamethicin incorporation into model membrane monolayers

Lipid interactions and cooperative assembly properties are fundamental determinants for the action of antimicrobial membrane-active peptides. Here we analyze the interactions and aggregation properties of alamethicin, an antimicrobial pore-forming peptide, with films formed at the air/water interface. Surface-area/pressure isotherms, Brewster angle microscopy, and fluorescence-confocal microscopy provided detailed information on the morphologies and structural properties of the peptide and its effect on the film components. The pressure-area analysis and microscopy experiments facilitated unprecedented visualization of the structural consequences of alamethicin association at the air/water interface, with pure phospholipid films, and within mixed phospholipid/polydiacetylene (PDA) films. The analysis exposed the kinetic features and the interplay between the peptide aggregates and film constituents. In particular, the results demonstrate the use of phospholipid/PDA film assemblies for studying membrane-peptide association and interactions within two-dimensional films.     

The approximation by q-Bernstein polynomials in the case q ↓ 1

Let B_n (f, q; x), n=1, 2, ... , 0 < q < ∞, be the q-Bernstein polynomials of a function f, B_n (f, 1; x) being the classical Bernstein polynomials. It is proved that, in general, {B_n (f, q_n; x)} with q_n ↓ 1 is not an approximating sequence for f ∈C[0, 1], in contrast to the standard case q_n ↓ 1. At the same time, there exists a sequence 0 < δ_n ↓ 0 such that the condition implies the approximation of f by {B_n (f, q_n; x)} for all f ∈C[0, 1]. Received: 15 March 2005     

On the eigenvectors of the q‐Bernstein operators

In this article, both the eigenvectors and the eigenvalues of the q‐Bernstein operators have been studied. Explicit formulae are presented for the eigenvectors, whose limit behavior is determined both in the case 0 < q < 1 and in the case q > 1. Because the classical case, where q = 1, was investigated exhaustively by S. Cooper and S. Waldron back in 2000, the present article also discusses the related similarities and distinctions with the results in the classical case. Copyright © 2013 John Wiley & Sons, Ltd.     

Ultrathin film sensory system based on resonance energy transfer between the monolayers consisting of non-covalently linked fluorophores

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