Synthesis of Cyclophosphazenes with P-CAR Bonds for Supramolecular Chemistry

Abstract

We describe the synthesis of new cyclotritphosphazenes in which the phosphorus substituents are either free-rotating or rigid planar heterocyclic groups, through phosphorus-carbon bonds.     

Interactions between flaxseed gums and WPI-stabilized emulsion droplets assessed in situ using diffusing wave spectroscopy

Diffusing wave spectroscopy (DWS) was used to investigate the behavior of flaxseed gums when added to WPI-stabilized emulsions. The effect of different concentrations (0–0.33% (w/v)) of flaxseed gum, derived from two seed varieties, namely Emerson and McDuff, was studied at acidic and neutral pH. At pH 7.0 and low gum concentrations the dynamic and spatial characteristics of the system remained unchanged. While at gum concentrations from 0.075% to 0.20% a rapid phase separation was observed, at higher concentrations phase separation was retarded because of the increased background viscosity slowing down the mobility of the emulsion droplets. At pH 3.5, the difference in overall electrical charge between the gum (negative) and the protein on the emulsion surface (positive) led to electrostatic interactions. While at low concentration of flaxseed gum the general characteristics of the emulsions were not significantly different, at intermediate concentrations, bridging flocculation occurred. When sufficient flaxseed gum was present, the emulsion droplets mobility was arrested in a gel-like state. In spite of the compositional differences in the ratio of acidic and neutral fraction between the two polysaccharides extracted from different seed varieties, at both values of pH the behavior of the emulsions after addition of the polysaccharide was comparable.     

Some results related to the Corach-Porta-Recht inequality

Let be the algebra of all bounded operators on a complex Hilbert space and let be an invertible self-adjoint (or skew-symmetric) operator of . Corach-Porta-Recht proved that

The problem considered here is that of finding (i) some consequences of the Corach-Porta-Recht Inequality; (ii) a necessary condition (resp. necessary and sufficient condition, when for the invertible positive operators to satisfy the operator-norm inequality for all in ; (iii) a necessary and sufficient condition for the invertible operator in to satisfy

     

Fonctions finement harmoniques et l'axiome de domination

In a harmonic space with the domination Axiom (axiom D), B. Fuglede [5] has introduced the sheaf property of the cones of the finely hyperharmonic functions (defined in the fine opens). In [7], [8], J. Luke, J. Malý and L. Zajíek have studied a notion analogous to the finely hyperharmonic functions without supposing axiom D, and have proved ([8] theorem 12.16) that if the cones of the positive finely hyperharmonic functions make a sheaf, then axiom D is satisfied. See N. Boboc, Gh. Bucur and A. Cornea [3] for the first result of this type given within the context of theH-cones.In this paper, we prove axiom D is a consequence of the sheaf property even for the smallest class of the functions (the class of the finely harmonic functions; absolute-value bounded in a convenient sense). This result implies that of Lukeet al. cited above. Consequently, the tow fine properties of the sheaf are equivalent, which has not been evident previously.

     

Anisotropic adaptive stabilized finite element solver for RANS models

Aerodynamic characteristics of various geometries are predicted using a finite element formulation coupled with several numerical techniques to ensure stability and accuracy of the method. First, an edge‐based error estimator and anisotropic mesh adaptation are used to detect automatically all flow features under the constraint of a fixed number of elements, thus controlling the computational cost. A variational multiscale‐stabilized finite element method is used to solve the incompressible Navier‐Stokes equations. Finally, the Spalart‐Allmaras turbulence model is solved using the streamline upwind Petrov‐Galerkin method. This paper is meant to show that the combination of anisotropic unsteady mesh adaptation with stabilized finite element methods provides an adequate framework for solving turbulent flows at high Reynolds numbers. The proposed method was validated on several test cases by confrontation with literature of both numerical and experimental results, in terms of accuracy on the prediction of the drag and lift coefficients as well as their evolution in time for unsteady cases.     

On the injective norm and characterization of some subclasses of normal operators by inequalities or equalities

Let B(H) be the C^*-algebra of all bounded linear operators acting on a complex Hilbert space H. In this note, we shall show that if S is an invertible normal operator in B(H) the following estimation holds

     

Universal bound for global solution of nonlinear heat equation

Positivity - The aim of this paper is to study some properties of positive solutions to the nonlinear diffusion equation $$\begin{aligned} \frac{\partial u(x,t)}{\partial t} = \Delta _p u(x,t) +...     

Biharmonic maps, conformal deformations and the Hopf maps

We consider harmonic semi-conformal maps between two Riemannian manifolds. By deforming conformally the codomain metric, we construct new examples of non-harmonic biharmonic maps.     

Continuum-mechanical, Anisotropic Flow model for polar ice masses, based on an anisotropic Flow Enhancement factor

A complete theoretical presentation of the Continuum-mechanical, Anisotropic Flow model, based on an anisotropic Flow Enhancement factor (CAFFE model) is given. The CAFFE model is an application of the theory of mixtures with continuous diversity for the case of large polar ice masses in which induced anisotropy occurs. The anisotropic response of the polycrystalline ice is described by a generalization of Glen’s flow law, based on a scalar anisotropic enhancement factor. The enhancement factor depends on the orientation mass density, which is closely related to the orientation distribution function and describes the distribution of grain orientations (fabric). Fabric evolution is governed by the orientation mass balance, which depends on four distinct effects, interpreted as local rigid body rotation, grain rotation, rotation recrystallization (polygonization) and grain boundary migration (migration recrystallization), respectively. It is proven that the flow law of the CAFFE model is truly anisotropic despite the collinearity between the stress deviator and stretching tensors.     

The numerical range of elementary operators

For n-tuplesA=(A ₁,...,A _n ) andB=(B ₁,...,B _n ) of operators on a Hilbert spaceH, letR _A,B denote the operator onL(H) defined by . In this paper we prove that