Thermally Crosslinkable and Chemically Modifiable Aromatic Polyesters Possessing Pendant Propargyloxy Groups

New aromatic (co)polyesters containing pendant propargyloxy groups were synthesized by phase transfer‐catalyzed interfacial polycondensation of 5‐(propargyloxy)isophthaloyl chloride (P‐IPC) and various compositions of P‐IPC and isophthaloyl chloride with bisphenol A. FTIR and NMR spectroscopic data, respectively, revealed successful incorporation of pendant propargyloxy groups into (co)polyesters and formation of (co)polyesters with desired compositions. (Co)polyesters exhibited good solubility in common organic solvents such as chloroform, dichloromethane, and tetrahydrofuran and could be cast into transparent, flexible, and tough films from chloroform solution. Inherent viscosities and number average molecular weights of (co)polyesters were in the range 0.77–1.33 dL/g and 43,600–118,000 g/mol, respectively, indicating the achievement of reasonably high‐molecular weights. The 10% weight loss temperatures of (co)polyesters were in the range 390–420 °C, demonstrating their good thermal stability. (Co)polyesters exhibited T_g in the range 146–170 °C and T_g values decreased with increase in mol % incorporation of P‐IPC. The study of non‐isothermal curing by DSC indicated thermal crosslinking of (co)polyesters via propargyloxy groups. The utility of pendant propargyloxy group was demonstrated by post‐modification of the selected copolyester with 1‐(4‐azidobutyl)pyrene, 9‐(azidomethyl)anthracene, and azido‐terminated poly(ethyleneglycol) monomethyl ether via copper(I)‐catalyzed Huisgen 1,3‐dipolar cycloaddition reaction. FTIR and ¹H NMR spectra confirmed that click reaction was quantitative. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 588–597     

Extended Rees algebras and mixed multiplicities

Partially supported by the general research fund at the University of Kansas     

Solid-phase approach towards the synthesis of functionalized imidazo[1,2-b]pyrazol-2-ones

The solid-phase synthesis of a series of imidazo[1,2-b]pyrazol-2-ones, an interesting 5,5-fused ring system, based on diverse set of hydrazine acids and malanonitriles is described. The method involves formation of 5-aminopyrazoles on solid support and subsequent cyclizative cleavage off the resin. Compounds were obtained in acceptable to excellent yields and are suitable for biological evaluation without further purification.     

Proteins Entrapped in Silica Monoliths Prepared from Glyceroxysilanes

The preparation of discrete polyol based silane precursors derived from glycerol by a simple one-pot process is described. These polyol-based silanes could be hydrolyzed under mild pH conditions and upon gelation resulted in the formation of optically clear, monolithic, mesoporous silica. The hydrolysis and condensation reactions lead to cure rates that are very sensitive to ionic strength, but are almost unaffected by pH in contrast to those of alkoxysilanes derived from primary alcohols such as Si(OEt)₄. Residual glycerol in the silica monolith could be removed by washing, or could be left in the silica to reduce the magnitude of shrinkage during long term storage. The biocompatible glyceroxysilane precursors lead to materials that were able to retain the activity of entrapped enzymes over repeated cycles of use for periods of up to several months.     

Brominated poly(isobutylene‐co‐para‐methylstyrene) (BIMS)‐clay nanocomposites: Synthesis and characterization

In this work, preparation and properties of different nanoclays modified by organic amines (octadecyl amine, a primary amine, and hexadecyltrimethylammonium bromide, a tertiary amine) and brominated polyisobutylene‐co‐paramethylstyrene (BIMS)‐clay nanocomposites are reported. The clays and the rubber nanocomposites have been characterized with the help of Fourier transform infrared spectroscopy (FTIR), transmission electron microscopy (TEM), and X‐ray diffraction (XRD). The X‐ray diffraction peaks observed in the range of 3 °–10 ° for the modified clays disappear in the rubber nanocomposites. TEM photographs show predominantly exfoliation of the clays in the range of 12 ± 4 nm in the BIMS. In the FTIR spectra of the nanocomposites, there are common peaks of virgin rubber as well as those of the clays. Excellent improvement in mechanical properties like tensile strength, elongation at break, and modulus is observed on incorporation of the nanoclays in the BIMS. Structure‐property correlation in the above nanocomposites is attempted. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4489–4502, 2004     

Deciding confluence of certain term rewriting systems in polynomial time

We present a characterization of confluence for term rewriting systems, which is then refined for special classes of rewriting systems. The refined characterization is used to obtain a polynomial time algorithm for deciding the confluence of ground term rewrite systems. The same approach also shows the decidability of confluence for shallow and linear term rewriting systems. The decision procedure has a polynomial time complexity under the assumption that the maximum arity of a function symbol in the signature is a constant.     

Barycentric coordinates for convex sets

In this paper we provide an extension of barycentric coordinates from simplices to arbitrary convex sets. Barycentric coordinates over convex 2D polygons have found numerous applications in various fields as they allow smooth interpolation of data located on vertices. However, no explicit formulation valid for arbitrary convex polytopes has been proposed to extend this interpolation in higher dimensions. Moreover, there has been no attempt to extend these functions into the continuous domain, where barycentric coordinates are related to Green’s functions and construct functions that satisfy a boundary value problem. First, we review the properties and construction of barycentric coordinates in the discrete domain for convex polytopes. Next, we show how these concepts extend into the continuous domain to yield barycentric coordinates for continuous functions. We then provide a proof that our functions satisfy all the desirable properties of barycentric coordinates in arbitrary dimensions. Finally, we provide an example of constructing such barycentric functions over regions bounded by parametric curves and show how they can be used to perform freeform deformations.      

Cyclic voltammetric studies of certain industrially potential iron chelate catalysts

 For the analysis of infrared spectroscopic bands and complex patterns partial cross correlation functions of a sample spectrum with reference spectra are calculated. The chosen ranges of the spectra are based on empirical knowledge of infrared spectrum structure correlations. The normalised maxima of the partial cross correlation functions are interpreted as fuzzy truth values and are combined by fuzzy logical operators. By application of that procedure larger common substructures will be derived from the reference spectra than by a maximum common substructure search based on the complete spectra. Received: 30 October 1996/Revised: 24 February 1997/Accepted: 26 February 1997