Double k-sets in symplectic generalized quadrangles

In classical projective geometry, a double six of lines consists of 12 lines ? ₁, ? ₂, . . . , ? ₆, m ₁, m ₂, . . . , m ₆ such that the ? _i are pairwise skew, the m _i are pairwise skew, and ? _i meets m _j if and only if i ≠ j. In the 1960s Hirschfeld studied this configuration in finite projective spaces PG(3, q) showing they exist for almost all values of q, with a couple of exceptions when q is too small. We will be considering double-k sets in the symplectic geometry W(q), which is constructed from PG(3, q) using an alternating bilinear form. This geometry is an example of a generalized quadrangle, which means it has the nice property that if we take any line ? and any point P not on ?, then there is exactly one line through P meeting ?. We will discuss all of this in detail, including all of the basic definitions needed to understand the problem, and give a result classifying which values of k and q allow us to construct a double k-set of lines in W(q).     

Introducing nonlinear,multivariate ‘Predictor Surfaces’ for quantitative modeling of chemical systems with higher-order,coupled predictor variables

Innovations in chemometrics are required for studies of chemical systems which are governed by nonlinear responses to chemical parameters and/or interdependencies (coupling) among these parameters. Conventional and linear multivariate models have limited use for quantitative and qualitative investigations of such systems because they are based on the assumption that the measured data are simple superpositions of several input parameters. ‘Predictor Surfaces’ were developed for studies of more chemically complex systems such as biological materials in order to ensure accurate quantitative analyses and proper chemical modeling for in-depth studies of such systems. Predictor Surfaces are based on approximating nonlinear multivariate model functions by multivariate Taylor expansions which inherently introduce the required coupled and higher-order predictor variables.     

Synthesis of thermosensitive guar‐based hydrogels with tunable physico‐chemical properties by click chemistry

Thermosensitive guar‐based hydrogels are obtained in water solutions by copper‐catalyzed 1,3‐dipolar cycloaddition between alkyne‐functionalized guars and α,ω‐diazido‐poly[(ethylene glycol)‐co‐(propylene glycol)]. Characterization by TGA, HR‐MAS ¹H NMR, and rheology have shown that hydrogels with tunable physico‐chemical properties, such as crosslinking density, viscoelasticity, swelling ratio, and so forth, could be obtained by varying the guar molar mass, the degree of alkyne functionality, the guar/crosslinker weight ratio, and the reaction temperature. Based on swelling measurements, it has been shown that the thermal sensitiveness of guar‐based hydrogels is fast, reversible, and intimately related to the weight fraction of the thermosensitive crosslinker in the network. Finally, the monitoring of doxorubicin hydrochloride release has demonstrated the potential of these hydrogels as temperature‐dependent drug release devices. The robust, efficient, and orthogonal approach described herein represents a general approach towards the development of well‐controlled guar‐based hydrogels using α,ω‐diazido crosslinkers. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 48: 2733–2742, 2010     

Ethynyl and Propynylpyrene Inhibitors of Cytochrome P450

Abstract  

The single-crystal X-ray structures and in vivo activities of three aryl acetylenic inhibitors of cytochromes P450 1A1, 1A2, 2A6, and 2B1 have been determined and are reported herein. These are 1-ethynylpyrene, 1-propynylpyrene, and 4-propynylpyrene. To investigate electronic influences on the mechanism of enzyme inhibition, the experimental electron density distribution of 1-ethynylpyrene has been determined using low-temperature X-ray diffraction measurements, and the resulting net atomic charges compared with various theoretical calculations. A total of 82,390 reflections were measured with Mo Kα radiation to a (sinθ/λ)_max = 0.985 Å⁻¹. Averaging symmetry equivalent reflections yielded 8,889 unique reflections. A least squares refinement procedure was used in which multipole parameters were added to describe the distortions of the atomic electron distributions from spherical symmetry. A map of the model electron density distribution of 1-ethynylpyrene was obtained. Net atomic charges calculated from refined monopole population parameters yielded charges that showed that the terminal acetylenic carbon atom (C18) is more negative than the internal carbon (C17). Net atomic charges calculated by ab initio, density functional theory, and semi-empirical methods are consistent with this trend suggesting that the terminal acetylenic carbon atom is more likely to be the site of oxidation. This is consistent with the inhibition mechanism pathway that results in the formation of a reactive ketene intermediate. This is also consistent with assay results that determined that 1-ethynylpyrene acts as a mechanism-based inhibitor of P450s 1A1 and 1A2 and as a reversible inhibitor of P450 2B1. Crystallographic data: 1-ethynylpyrene, C₁₈H₁₀, P2₁/c, a = 14.571(2) Å, b = 3.9094(5) Å, c = 20.242(3) Å, β = 105.042(2)°, V = 1,113.5(2) Å³; 1-propynylpyrene, C₁₉H₁₂, P2₁/n, a = 8.970(2) Å, b = 10.136(1) Å, c = 14.080(3) Å, β = 99.77(2)°, V = 1,261.5(4) Å³; 4-propynylpyrene, C₁₉H₁₂, Pbca, a = 9.904(1) Å, b = 13.174(2) Å, c = 19.401(1) Å, V = 2,531.4(5) Å³.     

Isoperimetric balls in cones over tori

In the cone over a cubic three-torus T ³, balls about the vertex are isoperimetric if the volume of T ³ is less than π/16 times the volume of the unit three-sphere. The conjectured optimal constant is 1.     

Two sample applications of a classical isoperimetric problem of the calculus of variations to fluid mechanical problems in fluidization and spouting

This paper is devoted to outlining precisely the basic mathematics of a classical isoperimetric problem of the calculus of variations and showing how significant fluid mechanical problems in fluidization and spouting can be addressed using this approach.     

Effect of thermal history on the deformation and failure of polyimides

Thermal‐processing structure‐property relationships for polyetherimide (PEI), poly(4,4′‐oxydiphenylene pyromellitimide) (POPPI), and phenylethynyl‐terminated imide (PETI‐5) composite matrices are reported from a fundamental perspective. For thermoplastic PEI, deformation and failure depend primarily on free volume as evidenced by moisture‐absorption, mechanical‐property, and mass‐density changes as a function of annealing. The deformation of POPPI can be divided into the following three regimes as a function of annealing temperature: (1) physical aging‐induced glassy state free‐volume decreases, (2) thermally activated microvoid collapse, and (3) chemical degradation. In the case of PETI‐5, macroscopic defects, free volume, and polymer morphology control deformation. The effects of residual crystallinity on deformation are reported, and it is shown that mechanical toughness can be significantly decreased upon annealing below the glass‐transition temperature. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2947–2959, 2001