The univalent polynomial of Suffridge as a summability kernel

A positive summability trigonometric kernel {K(n)(theta)}(infinity)(n=1) is generated through a sequence of univalent polynomials constructed by Suffridge. We prove that the convolution {K(n) * f} approximates every continuous 2 pi-periodic function f with the rate omega(f, 1/n), where omega(f, delta) denotes the modulus of continuity, and this provides a new proof of the classical Jackson`s theorem. Despite that it turns out that K(n)(theta) coincide with positive cosine polynomials generated by Fejer, our proof differs from others known in the literature.

Paper surfaces and dynamical limits

It is very common in mathematics to construct surfaces by identifying the sides of a polygon together in pairs: For example, identifying opposite sides of a square yields a torus. In this article the construction is considered in the case where infinitely many pairs of segments around the boundary of the polygon are identified. The topological, metric, and complex structures of the resulting surfaces are discussed: In particular, a condition is given under which the surface has a global complex structure (i.e., is a Riemann surface). In this case, a modulus of continuity for a uniformizing map is given. The motivation for considering this construction comes from dynamical systems theory: If the modulus of continuity is uniform across a family of such constructions, each with an iteration defined on it, then it is possible to take limits in the family and hence to complete it. Such an application is briefly discussed.

Comparative study of liponucleosides in Langmuir monolayers as cell membrane models

Liponucleosides may assist the anchoring of nucleic acid nitrogen bases into biological membranes for tailored nanobiotechnological applications. To this end precise knowledge about the biophysical and chemical details at the membrane surface is required. In this paper, we used Langmuir monolayers as simplified cell membrane models and studied the insertion of five lipidated nucleosides. These molecules varied in the type of the covalently attached lipid group, the nucleobase, and the number of hydrophobic moieties attached to the nucleoside. All five lipidated nucleosides were found to be surface-active and capable of forming stable monolayers. They could also be incorporated into dipalmitoylphosphatidylcholine (DPPC) monolayers, four of which induced expansion in the surface pressure isotherm and a decrease in the surface compression modulus of DPPC. In contrast, one nucleoside possessing three alkyl chain modifications formed very condensed monolayers and induced film condensation and an increase in the compression modulus for the DPPC monolayer, thus reflecting the importance of the ability of the nucleoside molecules to be arranged in a closely packed manner. The implications of these results lie on the possibility of tuning nucleic acid pairing by modifying structural characteristics of the liponucleosides. (C) 2010 Elsevier B.V. All rights reserved.

Effects of Extrusion on the Emulsifying Properties of Rumen and Soy Protein

Defatted rumen protein and soy protein concentrate were extruded in a 15.5:1 L/D single-screw extruder at the optimum conditions for their expansion (150A degrees C and 35% moisture, and 130A degrees C and 35% moisture, respectively). Emulsions were produced with these proteins and studied by rheology and time domain low-resolution (1)H nuclear magnetic resonance (TD-NMR). Extrusion increased storage modulus of rumen protein emulsions. The opposite was observed for soy protein. Mechanical relaxation showed the existence of three relaxing components in the emulsions whose relative contributions were changed by extrusion. Likewise, spin-spin relaxation time constants (T (2)) measured by TD-NMR also showed three major distinct populations of protons in respect to their mobility that were also altered by extrusion. Extrusion increased surface hydrophobicity of both rumen and soy protein. Solubility of rumen protein increased with extrusion whereas soy protein had its solubility decreased after processing. Extrusion promoted molecular reorganization of protein, increasing its superficial hydrophobicity, affecting its interfacial properties and improving its emulsifying behavior. The results show that extrusion can promote the use of rumen, a by-product waste from the meat industry, in human nutrition by replacing soy protein in food emulsions.