Solution of Dynamic Problems for Thin-Walled Structural Elements with Nonuniform Dynamic Boundary Conditions

The characteristics of the stress–strain state of thin-walled structural elements are determined in the case where dynamic boundary loads or displacements described by pulse functions are specified. A general scheme for realization of the method of natural-mode expansion is stated as applied to differential equations with unknown functions of one spatial coordinate and time. Theoretical relations for rods, plates, and shells are given. The potential of the approach developed is illustrated by solving specific problems     

A Facile Synthesis of 1,4-Diketones from Organolithium Reagents and N,N,N′,N′-Tetramethylsuccinamide

The reaction of organolithium reagents (alkyl, aryl, heteroaryl) with N,N,N′,N′-tetramethylsuccinamide at 0 °C gives good yields of the corresponding 1,4-diketones.     

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     

Finite-dimensional representations of a shock algebra

Abstruct The algebra describing a shock measure in the asymmetric simple exclusion model, seen from a second class particle, has finite-dimensional representations if and only if the asymmetry parameterp of the model and the left and right asymptotic densitiesp _± of the shock satisfy [(1−p)/p] ^r =p ₋(1−p ₊)/p ₊(1−p ₋) for some integerr≥1; the minimal dimension of the representation is then 2r. These representations can be used to calculate correlation functions in the model.     

Structural properties of a family of hydrogen-bonded co-crystals formed between gemfibrozil and hydroxy derivatives of t-butylamine, determined directly from powder X-ray diffraction data

We report the formation and structural properties of co-crystals containing gemfibrozil and hydroxy derivatives of t-butylamine H₂NC(CH₃)_3−n(CH₂OH)_n, with n=0, 1, 2 and 3. In each case, a 1:1 co-crystal is formed, with transfer of a proton from the carboxylic acid group of gemfibrozil to the amino group of the t-butylamine derivative. All of the co-crystal materials prepared are polycrystalline powders, and do not contain single crystals of suitable size and/or quality for single crystal X-ray diffraction studies. Structure determination of these materials has been carried out directly from powder X-ray diffraction data, using the direct-space Genetic Algorithm technique for structure solution followed by Rietveld refinement. The structural chemistry of this series of co-crystal materials reveals well-defined structural trends within the first three members of the family (n=0, 1, 2), but significantly contrasting structural properties for the member with n=3.     

Hamiltonian torus actions on symplectic orbifolds and toric varieties

In the first part of the paper, we build a foundation for further work on Hamiltonian actions on symplectic orbifolds. Most importantly, we prove the orbifold versions of the abelian connectedness and convexity theorems. In the second half, we prove that compact symplectic orbifolds with completely integrable torus actions are classified by convex simple rational polytopes with a positive integer attached to each open facet and that all such orbifolds are algebraic toric varieties.