SYNTHESIS OF A NOVEL POLYSACCHARIDE HYDROGEL

ABSTRACT

A modified hyaluronic acid (HA) biopolymer was synthesized that can be photocrosslinked to form a stable hydrogel. The chemical and physical properties including the amount of modification of the polymer with methacrylate anhydride, the viscosity of the modified biopolymer, and the solute diffusion characteristics of the polymer have been determined.     

Discrete l1 Approximation by Rational Functions

The problem of finding a best approximation by a rational functionto discrete data, using the l₁ norm, is considered. An algorithmis developed which is frequently convergent in a finite numberof steps, and failing this usually has a second-order convergencerate. Details are given of the application of the algorithmto a number of rational approximation problems.     

Multiple groups in the symmetry classification of adiabatic electronic wavefunctions

It was originally shown by Longuet-Higgins and colleagues that when the electronic Schrödinger equation is solved as a function of the nuclear coordinates the adiabatic electronic wavefunction can undergo a change of sign after completing a closed circuit. This geometric phase occurs for a circuit around a conical intersection, and in particular around a conical intersection corresponding to a linear Jahn—Teller effect. The adiabatic wavefunctions are classified here under a group called the adiabatic multiple group, which is a generalization of the ‘vibronic double group’ of C _3v introduced by Hougen, and is distinct from the familiar electron-spin double group. Although the real electronic wavefunctions can be only double-valued, the groups can have higher multiplicity because of the possibility of different circuits. For a number of symmetric- and spherical-top point groups, the adiabatic multiple group is shown to be the direct product of the point group with a phase group. The adiabatic multiple group can be applied to individual adiabatic orbitals, and so to configurations built from these orbitals. This leads to the rule that the linear Jahn—Teller effect vanishes in the single-configuration approximation for configurations containing non-degenerate electrons plus an even number of e electrons. There does not appear to be any cancellation effect for electron configurations of cubic molecules containing f electrons.     

A Method for Calculating Best Non-linear Chebyshev Approximations

A method for solving continuous non-linear Chebyshev approximationproblems is presented and illustrated by examples.     

LOW-OSCILLATION COMPLEX WAVELETS

In this paper we explore the use of two low-oscillation complex wavelets—Mexican hat and Morlet—as powerful feature detection tools for data analysis. These wavelets, which have been largely ignored to date in the scientific literature, allow for a decomposition which is more “temporal than spectral” in wavelet space. This is shown to be useful for the detection of small amplitude, short duration signal features which are masked by much larger fluctuations. Wavelet transform-based methods employing these wavelets (based on both wavelet ridges and modulus maxima) are developed and applied to sonic echo NDT signals used for the analysis of structural elements. A new mobility scalogram and associated reflectogram is defined for analysis of impulse response characteristics of structural elements and a novel signal compression technique is described in which the pertinent signal information is contained within a few modulus maxima coefficients. As an example of its usefulness, the signal compression method is employed as a pre-processor for a neural network classifier. The authors believe that low oscillation complex wavelets have wide applicability to other practical signal analysis problems. Their possible application to two such problems is discussed briefly—the interrogation of arrhythmic ECG signals and the detection and characterization of coherent structures in turbulent flow fields.     

Towards the Minimum Drag on a Body of Given Volume in Slow Viscous Flow

By merging a natural variational principle with a minimizingprocedure it is possible to obtain an upper bound on the minimumpossible drag on a body of given volume moving through a fluidat zero Reynolds number, and constant speed. A discussion isalso given of the possibility of finding a lower bound to thisquantity.