Characteristic lengths and the structure of salt free polyelectrolyte solutions. A small angle neutron scattering study

We have studied salt free semi dilute polyelectrolyte solutions by small angle neutron scattering. Specific labelling associated with an extrapolation method has allowed the separation of the form factor of a single polyelectrolyte chainS ₁(q) and the structure factorS ₂(q). Two lengths are deduced from these two factors: the persistence lengthb _t which characterizes the electrostatic interactions along the chain by a fitting ofS ₁(q) with calculation of the scattering function for a wormlike chain, and fromS ₂(q),q _m ^–1 which characterizes the interactions between chains. These two lengths vary in the same way with the concentration of polyions (b _t C _p ^–1/2 ,q _m ^–1 C _p ^–1/2 ) and a constant relation exists between them: only one length is then necessary to describe the structure of polyelectrolyte soltuion on this semidilute concentration range.Laboratoire Commun CEA-CNRS.     

The Cayley transform and uniformly bounded representations

Let G be a simple Lie group of real rank one, with Iwasawa decomposition and Bruhat big cell . Then the space may be (almost) identified with N and with K/M, and these identifications induce the (generalised) Cayley transform . We show that is a conformal map of Carnot-Caratheodory manifolds, and that composition with the Cayley transform, combined with multiplication by appropriate powers of the Jacobian, induces isomorphisms of Sobolev spaces and . We use this to construct uniformly bounded and slowly growing representations of G.     

Uniform convexity of ψ-direct sums of Banach spaces

Let X and Y be Banach spaces and ψ a continuous convex function on the unit interval [0,1] satisfying certain conditions. Let X⊕_ψY be the direct sum of X and Y equipped with the associated norm with ψ. We show that X⊕_ψY is uniformly convex if and only if X,Y are uniformly convex and ψ is strictly convex. As a corollary we obtain that the ?_p,q-direct sum (not p=q=1 nor ∞), is uniformly convex if and only if X,Y are, where ?_p,q is the Lorentz sequence space. These results extend the well-known fact for the ?_p-sum . Some other examples are also presented.     

Global Behavior of Rational Sequences Involving Piecewise Power Function

In this paper, we are concerned with the global behavior ofthe solutions of the difference equation

Strong Convergence of an Iterative Method with Perturbed Mappings for Nonexpansive and Accretive Operators

A new iterative method for finding a zero of m-accretive operators is proposed. This method, involving a so-called perturbed mapping, provides a way to construct sunny nonexpansive retractions. Several strong convergence theorems for this method are established in a Banach space that is either uniformly smooth or reflexive with a weakly continuous duality map.     

Mechanical Constraint Effect on DNA Persistence Length

Persistence length is a significant criterion to characterize the semi-flexibility of DNA molecules. The mechanical constraints applied on DNA chains in new single-molecule experiments play a complex role in measuring DNA persistence length; however, there is a difficulty in quantitatively characterizing the mechanical constraint effects due to their complex interactions with electrostatic repulsions and thermal fluctuations. In this work, the classical buckling theory of Euler beam and Manning’s statistical theories of electrostatic force and thermal fluctuation force are combined for an isolated DNA fragment to formulate a quantitative model, which interprets the relationship between DNA persistence length and critical buckling length. Moreover, this relationship is further applied to identify the mechanical constraints in different DNA experiments by fitting the effective length factors of buckled fragments. Then, the mechanical constraint effects on DNA persistence lengths are explored. A good agreement among the results by theoretical models, previous experiments, and present molecular dynamics simulations demonstrates that the new superposition relationship including three constraint-dependent terms can effectively characterize changes in DNA persistence lengths with environmental conditions, and the strong constraint-environment coupling term dominates the significant changes of persistence lengths; via fitting effective length factors, the weakest mechanical constraints on DNAs in bulk experiments and stronger constraints on DNAs in single-molecule experiments are identified, respectively. Moreover, the consideration of DNA buckling provides a new perspective to examine the bendability of short-length DNA.     

Cohen-Host type idempotent theorems for representations on Banach spaces and applications to Figà-Talamanca-Herz algebras

Let G be a locally compact group, and let R(G) denote the ring of subsets of G generated by the left cosets of open subsets of G. The Cohen-Host idempotent theorem asserts that a set lies in R(G) if and only if its indicator function is a coefficient function of a unitary representation of G on some Hilbert space. We prove related results for representations of G on certain Banach spaces. We apply our Cohen-Host type theorems to the study of the Figà-Talamanca-Herz algebras Ap(G) with p∈(1,∞). For arbitrary G, we characterize those closed ideals of Ap(G) that have an approximate identity bounded by 1 in terms of their hulls. Furthermore, we characterize those G such that Ap(G) is 1-amenable for some—and, equivalently, for all—p∈(1,∞): these are precisely the abelian groups.     

Global Behavior of the Solutions of a Max-Equation and of a System of Two Max-Equations

In this paper we study the existence of generalized invariants, the periodicity, the boundedness and persistence of the solutions of a Max-equation and of a system of two Max-equations.     

Evaluation of the Fate of Aldicarb and Its Metabolites in Oranges

Abstract

The accumulation, persistence and fate of systemic pesticide aldicarb was melencholy evaluated in orange crops. The concentration of this pesticide and its two toxic metabolites, aldicarb sulfoxide and aldicarb sulfone was determined in leaves, rind and pulp of three orange varieties (Satsuma, Navelina and Clemetina de Nules) and in the top soil of the orange groves. The groves were located in two different places in the Valencia Community (Spain). The analysis showed that the aldicarb concentration was lower than those of aldicarb sulfoxide and aldicarb sulfone. In all cases, the residues persisted at least 160 days in vegetable samples and between 157 and 227 days in soil samples. Residue concentrations measured in the soil samples were highly variable but a relation with the organic matter content can be observed. The residue levels found in vegetal products were higher in leaves than in rind, and in rind than in pulp. The maximum residue values were obtained between 47 and 70 days after the application. One hundred days after treatment (Security period) the residue levels of total fruit were lower than the maximum residue level of 0.2 mg/kg established by law.     

Polymer physics inspired approaches for the study of the mechanical properties of amyloid fibrils

Amyloid structures constitute a class of highly ordered nanomaterials formed by insoluble protein aggregates. These aggregates are characterized by a cross‐β structural motif in which β‐sheets are oriented perpendicular to the fibril axis and bound together by a dense hydrogen bonding network. Although they have been associated with several neurodegenerative disorders, such as Alzheimer's and Parkinson's diseases, amyloid fibrils have also been found in many physiologically beneficial roles, for instance in adhesives and hormone storage. Inspired by this natural occurrence of functional amyloid, the hierarchal self‐assembly of these structures has recently been used to develop artificial biomaterials for applications in medicine and nanotechnology. In order to realize the full potential of amyloids as functional materials, it is important to understand their fundamental mechanical properties. This review explores a range of experimental strategies to determine the mechanical properties of amyloid fibrils and discusses the results in the context of polymer physics concepts. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 281–292