A generalization of Connor's inequality to t-designs with automorphisms

In this paper the incidence algebra for t-designs with automorphisms and the fundamental theorem discovered in [4] are exploited to obtain a generalization of Connor's inequality.     

A simple approximation for the vibrational partition function of a hindered internal rotation

A simple formula is presented for calculating the approximate partition function of a hindered internal rotational mode of a polyatomic molecule. The formula gives useful accuracy over the whole range from harmonic oscillator to hindered rotator to free rotator.     

The evolution of the viscoelastic retardation spectrum during the development of an epoxy resin network

The evolution of the viscoelastic behavior of an epoxy resin at various stages of curing has been followed with the changes in the retardation spectrum. The creep J(t) and recoverable creep compliance J_r(t) curves of the neat epoxy resin Epon l00lF (Shell) were determined at temperatures between 30 and 77°C. The viscosity decreased over 8 orders of magnitude as the temperature was increased. Specimens with eight stages of network development were prepared by reacting all of the epoxy resin's oxirane rings with amine hydrogens from varying ratios of a monofunctional amine (methyl aniline) and a tetrafunctional amine 4,4′-diamino diphenyl sulfone (DDS). Preparations in which 25, 35, and 40% DDS were used did not result in a molecular network, so they were viscoelastic liquids. With 45% DDS, the product had a nascent network and was judged to be just beyond the point of incipient gelation. The remaining preparations from 0.50, 0.60, 0.70, and 1.0 DDS yielded tighter less compliant molecular networks. The creep and recoverable compliance curves were measured over a range of temperatures above the glass transition temperature, T_g. They were reduced to T_g, and retardation spectra L(ln τ) were calculated.     

Asymmetric intramolecular Diels-Alder reaction of a sulphoximine-substituted triene

The synthesis and thermally-induced intramolecular Diels-Alder (IMDA) reaction of (S)_s-(+)-S-[(1E,7E)-1,7,9-decatrienyl]-S-phenyl-N-(p-tolylsulphonyl)sulphoximine 4 is described. A model is proposed for the cis-selectivity of the cycloaddition based on previous results from the reactions of sulphonyl-substituted trienes. The stereochemistry of the major cis-fused cycloadduct is determined by single-crystal X-ray analysis of that obtained from reaction of racemic 4.     

Physical aging of a polyetherimide: Creep and DSC measurements

Creep and differential scanning calorimetry (DSC) measurements have been used to study the physical aging behavior of a polyetherimide. Isothermal aging temperatures ranged from 160°C to T_g with aging times ranging from 10 min to 8 days. The only measurable effect of physical aging on the short-time creep curves is a shift of the creep compliance to longer times. Andrade plots of the compliance versus the cube root of time are linear at short times with the slope β decreasing with increasing aging time to a constant value once equilibrium is reached. Log β³ is related directly to the degree to which the creep curves shift to longer times with physical aging, and is used in this work as a measure of physical aging. A reduced curve of log β³ versus log aging time is obtained for the aging temperatures investigated by appropriate vertical and horizontal shifts. The enthalpy change during aging increases linearly with the logarithm of the aging time, t_a, leveling off at equilibrium at values which increase with decreasing aging temperature. Hence, both nonequilibrium and equilibrium temperature shift factors can be calculated from the DSC data. Good agreement is observed between the equilibrium temperature shift factors obtained from the creep and DSC data. The temperature dependence of the nonequilibrium temperature shift factors is found to be an order of magnitude smaller than that of the equilibrium shift factors. The time scales to reach equilibrium for enthalpy and for mechanical measurements are found to be the same within experimental error. © 1995 John Wiley & Sons, Inc.     

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Promiscuity in Antibody Catalysis: Esterolytic Activity of the Decarboxylase 21D8

The high structural similarity of decarboxylase antibody 21D8 and esterase antibody 48G7 suggests that 21D8 might also possess hydrolytic activity. Kinetic investigations show that 21D8 does promote the selective hydrolysis of methyl 4‐nitrophenyl carbonate and sodium 4‐(acetoxy)benzenesulfonate with catalytic proficiencies (k_cat/K_m)/k_un of ca. 10⁵ M ^?1. The ability of 21D8 to accelerate a reaction for which it was not developed suggests that certain antibody scaffolds are intrinsically predisposed toward catalysis, a property that can be enhanced and refined during affinity maturation in response to a transition‐state analog. At the same time, however, the restricted structural diversity of the immune system may ultimately limit the catalytic efficiency that can be achieved.     

Total Positivity Properties of Generalized Hypergeometric Functions of Matrix Argument

In multivariate statistical analysis, several authors have studied the total positivity properties of the generalized (₀ F ₁) hypergeometric function of two real symmetric matrix arguments. In this paper, we make use of zonal polynomial expansions to obtain a new proof of a result that these ₀ F ₁functions fail to satisfy certain pairwise total positivity properties; this proof extends both to arbitrary generalized ( _r F _s ) functions of two matrix arguments and to the generalized hypergeometric functions of Hermitian matrix arguments. In the case of the generalized hypergeometric functions of two Hermitian matrix arguments, we prove that these functions satisfy certain modified pairwise TP₂properties; the proofs of these results are based on Sylvester's formula for compound determinants and the condensation formula of C. L. Dodgson [Lewis Carroll] (1866).