Thermal Degradation of Trioxane-Dioxqlane Copolymers Obtained with Boron Trifluoride-Acrylonitrile Complex as Initiator

The thermal degradation of certain trioxane-dioxolane copolymers obtained with boron trifluoride-acrylonitrile complex as initiator has been investigated. The thermal stability of samples, discussed in terms of topoenergetic values, was related both to copolymer composition and conversion. The most thermostable copolymers (～5% weight loss at 300°C in air), having 5–8% dioxolane units, had the highest intrinsic viscosity in the series and were isolated at 35–50% conversion. The results obtained were compared with similar data for a commercial tri-oxane-ethylene oxide copolymer containing 95% formal units.     

Non-negative hereditary polynomials in a free *−algebra

We prove a non-negative-stellensatz and a null-stellensatz for a class of polynomials called hereditary polynomials in a free *-algebra.Partially supported by NSF, DARPA and Ford Motor Co.Partially supported by NSF grant DMS-0140112Partially supported by NSF grant DMS-0100367     

Formulating Three-Dimensional Contact Dynamics Problems

ABSTRACT

Complementarity formulations are a promising approach for solving dynamic multi-rigid-body contact problems. Two aspects of simulating contact in a complementarity setting are addressed here. First, an explicit formulation of the differential equations governing contact points for bodies of general surface geometry is developed. These equations may be used to integrate the contact position and to set up the basic dynamics equations. Second, an efficient method for handling frictionless planar contacts of arbitrary boundary shape is presented. Throughout, the problem is set up as explicitly as possible, with special attention being given to the way that the contact geometry is related to the dynamics.     

Self-assembly of hybrid dendrons with complex primary structure into functional helical pores

The synthesis of three libraries of self-assembling hybrid dendrons containing a primary structure based on the sequence (4-3,4-3,5)12G2-CO(2)CH(3) generated from benzyl ether, biphenyl-4-methyl ether, and AB(2) repeat units constructed from (AB)(y)--AB(2) combinations of benzyl ethers, is reported. The structural and retrostructural analysis of their supramolecular dendrimers facilitated the discovery of new architectural principles that lead to the assembly of functional helical pores. The self-assembly of an example of hybrid dendron containing -H, -CO(2)CH(3), -CH(2)OH, -COOH, -COOK, -CONH(2), -CONHCH(3), -CO(2)(CH(2))(2)OCH(3), -(R) and -(S)-CONHCH(CH(3))C(2)H(5) as X-groups at the apex demonstrated that these self-assembling dendrons provide the simplest strategy for the design and synthesis of porous columns containing a diversity of hydrophilic and hydrophobic functional groups in the inner part of the pore. The results reported here expand the scope and limitations of dendrons available for the self-assembly of functional pores that previously were generated mostly from dendritic dipeptides, to simpler architectures based on hybrid dendrons.     

Editorial Board: Electrophoresis 18'14

Electrophoresis 2014, 35, 2673–2680. DOI: 10.1002/elps.201400210 pH‐responsive microcapsules manufactured by combining electrostatic droplets (ESD) and microfluidic droplets (MFD) techniques to produce mono‐disperse core (alginate) ‐ shell (chitosan) structure with controlled drug release behavior. The fabricated core‐shell microcapsules have a pH‐controlled drug delivery function according to acidic and alkaline environment, and present positive biocompatibility, indicating their potential use in biological and biomedical applications, such as pH‐responsive drug‐delivery systems, scaffolding for bone tissues, and as an oral drug‐delivery vehicle.

     

Potential application of the reaction between hydroquinone and chromate with respect to the kinetic determination of iron

The analytical potential of the reaction between hydroquinone and chromate in acidic media is explored with respect to the kinetic determination of iron in water samples. The extent of the reaction is followed spectrophotometrically at 350 nm. The reaction occurs more quickly in the presence of the metal ion, but the values of absorbance at reaction initiation and completion are not altered. No other transitional metal ion affects the course of the reaction, regardless of its concentration. This fact represents the most eye-catching and analytically exploitable aspect of this indicator reaction. Three procedures used to obtain calibration graphs from the same kinetic data are discussed: slope, fixed and variable time techniques. The reaction follows a sequence of two consecutive steps, both of first-order with respect to the colored species. First-order kinetics is preserved in the presence of iron. Curve fitting is used to determine the corresponding rate coefficients. The slope method requires much data and uses plots of rate constants against analyte concentration for calibration purposes. In this case, the best detection limit (0.5 mg l^–1) is given by the faster stage. On the other hand, the rate-determining step enables more precise results. The fixed and variable time methods rely on similar principles: they register either the value of absorbance achieved at a predetermined reaction time (here, 50 s) or the time interval required for the absorbance to drop to a predetermined value (here, 0.15 absorbance at 350 nm). In both cases, ratios between the average value from the blind runs and all individual values are plotted against the analyte concentration. The best results (detection limit of 0.3 mg l^–1) are derived from the variable time procedure. Advantageously, neither of the techniques require the entire kinetic curve, and so sophisticated equipment is not needed.     

A Class of Multiplicative Lattices

Czechoslovak Mathematical Journal - We study the multiplicative lattices L which satisfy the condition a = (a : (a : b))(a : b) for all a, b ∈ L. Call them sharp lattices. We prove that every...     

Perturbations of Christoffel–Darboux Kernels: Detection of Outliers

Foundations of Computational Mathematics - Two central objects in constructive approximation, the Christoffel–Darboux kernel and the Christoffel function, encode ample information about the...     

The Strauss conjecture on Kerr black hole backgrounds

We examine solutions to semilinear wave equations on black hole backgrounds and give a proof of an analog of the Strauss conjecture on the Schwarzschild and Kerr, with small angular momentum, black hole backgrounds. The key estimates are a class of weighted Strichartz estimates, which are used near infinity where the metrics can be viewed as small perturbations of the Minkowski metric, and a localized energy estimate on the black hole background, which handles the behavior in the remaining compact set.     

Approximation properties of the Generalized Finite Element Method

In this paper, we have obtained an approximation result in the Generalized Finite Element Method (GFEM) that reflects the global approximation property of the Partition of Unity (PU) as well as the approximability of the local approximation spaces. We have considered a GFEM, where the underlying PU functions reproduce polynomials of degree l. With the space of polynomials of degree k serving as the local approximation spaces of the GFEM, we have shown, in particular, that the energy norm of the GFEM approximation error of a smooth function is O(h ^l + k ). This result cannot be obtained from the classical approximation result of GFEM, which does not reflect the global approximation property of the PU.