Coordination properties of 3-functionalized beta-cyclodextrins. Thermodynamic stereoselectivity of copper(II) complexes of the A,B-diamino derivative and its exploitation in LECE

The bis-amino AB derivative of beta-cyclodextrin on the secondary rim was synthesised and spectroscopically characterised by different techniques. Its binary systems both with protons and copper(II) were thermodynamically characterised by pH-metric potentiometry. In addition the ternary systems with each of the enantiomers of tryptophan and alanine were investigated. A thermodynamic stereoselectivity was observed for the tryptophan enantiomers and this was exploited to separate them by capillary electrophoresis through a ligand exchange mechanism (LECE). LECE separation of racemates of phenylalanine and tyrosine was also obtained.     

How To Make Davies' Theorem Visible

We prove that for an arbitrary measurable set A R² and a -finiteBorel measure µ on the plane, there is a Borel set oflines L such that for each point in A, the set of directionsof those lines from L containing the point is a residual set,and, moreover, We show how this result may be used to characterise the sets of the planefrom which an invisible set is visible. We also characterisethe rectifiable sets C₁, C₂ for which there is a set which isvisible from C₁ and invisible from C₂.     

On mappings preserving equilateral triangles

Let E be a Euclidean space, dim E 2. We say that f : E E preserves equilateral triangles if for all triples of points x, y, z E we have We show that if E is a finite-dimensional Euclidean space, dim E 2, f:E E is measurable and preserves equilateral triangles, then it is a similarity transformation (an isometry multiplied by a positive constant). Moreover, in spaces at least three-dimensional we get a similarity transformation without any regularity assumption. Some generalizations as well as some interesting examples are also presented in the paper.     

Asymptotics of eigenfrequencies and eigenmodes of non‐homogeneous inextensible filament with an end load

We consider a class of non‐selfadjoint operators generated by the equation and the boundary conditions, which govern small vibrations of an ideal filament with non‐conservative boundary conditions at one end and a heavy load at the other end. The filament has a non‐constant density and is subject to a viscous damping with a non‐constant damping coefficient. The boundary conditions contain two arbitrary complex parameters. We derive the spectral asymptotics for the aforementioned two‐parameter family of non‐selfadjoint operators. In the forthcoming papers, based on the asymptotical results of the present paper, we will prove the Riesz basis property of the eigenfunctions. The spectral results obtained in the aforementioned papers will allow us to solve boundary and/or distributed controllability problems for the filament using the spectral decomposition method. Copyright © 2001 John Wiley & Sons, Ltd.     

Asymptotic analysis of aircraft wing model in subsonic air flow

This paper is the first in a series of several works devotedto the asymptotic and spectral analysis of an aircraft wingin a subsonic air flow. This model has been developed in theFlight Systems Research Center of UCLA and is presented in theworks of Balakrishnan. The model is governed by a system oftwo coupled integro-differential equations and a two parameterfamily of boundary conditions modelling the action of the self-strainingactuators. The unknown functions (the bending and the torsionangle) depend on time and one spatial variable. The differentialparts of the above equations form a coupled linear hyperbolicsystem; the integral parts are of convolution type. The systemof equations of motion is equivalent to a single operator evolution–convolutiontype equation in the state space of the system equipped withthe so-called energy metric. The Laplace transform of the solutionof this equation can be represented in terms of the so-calledgeneralized resolvent operator. The generalized resolvent operatoris an operator-valued function of the spectral parameter. Thisgeneralized resolvent operator is a finite meromorphic functiondefined on the complex plane having the branch cut along thenegative real semi-axis. The poles of the generalized resolventare precisely the aeroelastic modes, and the residues at thesepoles are the projectors on the generalized eigenspaces. Inthis paper, our main object of interest is the dynamics generatorof the differential parts of the system. It is a non-selfadjointoperator in the state space with a pure discrete spectrum. Inthe present paper, we show that the spectrum consists of twobranches, and we derive their precise spectral asymptotics.Based on these results, in the next paper we will derive theasymptotics of the aeroelastic modes and approximations forthe mode shapes.     

Rheology and Physical Properties of Polyethylene/Polyethylene‐Ionomer Blends and their Clay Nanocomposites

Rheological and solid‐state physical properties of blends containing high‐density polyethylene (HDPE) and a polyampholyte derivative (PE‐g‐PA) are assessed along with their onium ion‐exchanged montmorillonite clay (NR‐MM) nanocomposites. Strong deviations from the log‐additivity rule of zero‐shear viscosity, combined with synergistic behavior in tensile moduli, are consistent with a multi‐phase blend morphology. While this affects clay dispersion in filled blends, PE‐g‐PA/HDPE based nanocomposites are shown to exhibit a favorable balance between material stiffness and ductility.

     

Racemic dipeptide glycyl‐dl‐leucine at 120 K

The structure of glycyl‐dl ‐leucine, C₈H₁₆N₂O₃, has been determined at 120 K by single‐crystal X‐ray diffraction. In addition to three N—H?O‐type hydrogen bonds of the positively charged RNH₃⁺ group of the zwitterionic mol­ecule, an intermolecular N—H?O contact exists between the peptide bond and the carboxyl­ate group. Four hydrogen‐bond cycles were identified, giving a complex pattern.