Postbuckling of angle-ply and anisotropic plates

Summary An analysis based on the von Kármán-type large-deflection equations of plates is presented for the postbuckling behavior of homogeneous and symmetrically laminated anisotropic rectangular plates. Boundary conditions for both simply supported and clamped edges are considered. A solution is obtained by expressing the force function and transverse deflection as double series involving the appropriate beam eigen-functions. Numerical results are presented for graphite-epoxy angle-ply laminates and homogeneous anisotropic plates. In the cases of buckling of anisotropic plates and postbuckling of isotropic and orthotropic plates, the present solution is in good agreement with existing solutions.

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Übersicht Es wird das Nachbeulverhalten von homogenen, symmetrisch geschichteten, anisotropen Rechteckplatten auf der Grundlage der von Kármán angegebenen Platten-Gleichungen für große Auslenkungen untersucht. Dabei werden sowohl einfach aufliegende, wie auch eingespannte Ränder als Randbedingungen berücksichtigt. Lösungen werden dadurch gewonnen, daß die Belastungsfunktion und die Querauslenkung als doppelte Reihen von geeigneten Balken-Eigenfunktionen angesetzt werden. Für Graphit-Epoxid-Schichtplatten und anisotrope homogene Platten werden numerische Ergebnisse mitgeteilt. Die erhaltenen Lösungen stimmen in den Fällen des Beulens von anisotropen Platten sowie des Nachbeulens von isotropen und orthotropen Platten gut mit bekannten Lösungen überein.

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The results presented in this paper were obtained in the course of research sponsored by the National Research Council of Canada.     

IR,Raman, and Surface‐enhanced Raman Spectroscopic Study on Triruthenium Dipyridylamide Diruthenium Nickel Dipyridylamide Family: Metal‐metal Bonding and Structures

We report the infrared, Raman, and surface‐enhanced Raman scattering (SERS) spectra of triruthenium dipyridylamido complexes and of diruthenium mixed nickel metal‐string complexes. From the results of analysis on the vibrational modes, we assigned their vibrational frequencies and structures. The infrared band at 323–326 cm^?1 is assigned to the Ru₃ asymmetric stretching mode for [Ru₃(dpa)₄Cl₂]^0–2+. In these complexes we observed no Raman band corresponding to the Ru₃ symmetric stretching mode although this mode is expected to have substantial Raman intensity. There is no frequency shift in the Ru₃ asymmetric stretching modes for the complexes with varied oxidational states. No splitting in Raman spectra for the pyridyl breathing line indicates similar bonding environment for both pyridyls in dpa^– , thus a delocalized structure in the [Ru₃]^6–8+ unit is proposed. For Ru₃(dpa)₄(CN)₂ complex series, we assign the infrared band at 302 cm^?1 to the Ru₃ asymmetric stretching mode and the weak Raman line at 285 cm^?1 to the Ru₃ symmetric stretching. Coordination to the strong axial ligand CN^– weakens the Ru‐Ru bonding. For the diruthenium nickel complex [Ru₂Ni(dpa)₄Cl₂]^0–1+, the diruthenium stretching mode ν_Ru‐Ru is assigned to the intense band at 327 and 333 cm^?1 in the Raman spectra for the neutral and oxidized forms, respectively. This implies a strong Ru‐Ru metal‐metal bonding.     

Determination of melamine in milk powder using gas chromatography-high-resolution isotope dilution mass spectrometry

A GC-high-resolution isotope dilution MS (IDMS) method for the quantification of melamine in milk powder is described. The developed technique is compared to the LC-IDMS/MS technique, typically used for the determination of melamine in various matrices. The accuracy of the GC-high-resolution IDMS method was demonstrated when a small degree of equivalence was obtained in a regional comparative study involving the determination of melamine in milk powder.     

Liquid-phase catalytic transfer hydrogenation and cyclization of levulinic acid and its esters to γ-valerolactone over metal oxide catalysts

Levulinic acid and its esters are converted to γ-valerolactone over metal oxide catalysts by catalytic transfer hydrogenation via the Meerwein-Ponndorf-Verley reaction.     

Chow’s Theorem for Semi-abelian Varieties and Bounds for Splitting Fields of Algebraic Tori

A theorem of Chow concerns homomorphisms of two abelian varieties under a primary field extension base change. In this paper, we generalize Chow's theorem to semi-abelian varieties. This contributes to different proofs of a well-known result that every algebraic torus splits over a finite separable field extension. We also obtain the best bound for the degrees of splitting fields of tori.     

Linearly implicit time discretization of non-linear parabolic equations

We give a stability and error analysis of linearly implicitone-step methods for time discretization of non-linear parabolicequations. We derive precise error bounds for Rosenbrock andW-methods, and we explain the error reduction by Richardsonextrapolation of the linearly implicit Euler method which occursin spite of the breakdown of asymptotic expansions. The parabolicequations are studied in a Hilbert space framework that includessemilinear and quasilinear parabolic equations, and also stiffreaction-diffusion equations with reactions at different timescales.     

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A reliable synthesis of 2- and 6-amino-β-cyclodextrin and permethylated-β-cyclodextrin

A new, reliable method for the introduction of an amine group at positions 2 or 6 of β-cyclodextrin and permethyl-β-cyclodextrin is described. It involves selective tosylation followed by azide substitution and almost quantitative reduction with triphenylphosphine followed by hydrolysis of the phosphinimine intermediate.     

Stability of streaming layer in an unbounded self-gravitational fluid

The stability of a streaming layer of incompressible, inviscid, self-gravitational fluid bounded in an infinite similar medium is investigated. The critical wave numbers are found when the layer has a linear streaming velocity profile.