Note on static and dynamic instability of a non-uniform beam

The instability of a non-uniform beam analyzed by Lee and Reissner from a static point of view is reanalyzed by a dynamic approach. The beam is loaded by a parallel or tangential compressive force respectively. As expected the load causing static instability, obtained by both approaches, is exactly the same. A peculiar behaviour of the frequency for both cases of loading is revealed by the dynamic method. The tangential load causing dynamic instability is obtained.

---

Zusammenfassung Die Instabilität eines Stabes mit konstantem Querschnitt, welche durch Lee und Reissner vom statischen Standpunkt aus untersucht worden ist, wird einer dynamischen Analyse unterzogen. Der Stab steht unter einer axialen bzw. tangentialen Drucklast. Wie erwartet, ist die Belastung, welche statische Instabilität erzeugt, bei beiden Untersuchungsmethoden dieselbe. Ein besonderes Verhalten der Frequenz für beide Lastfälle wird durch die dynamische Methode aufgezeigt, und es wird die tangentiale Last erhalten, welche dynamische Instabilität erzeugt.

---

---

Preparation of this note has been supported by Sherutei Teuffa, Ltd., Haifa, Israel.     

Buckling of cylindrical shells under combined axial preload,nonuniform heating and torque

Thin aluminum-alloy cylinders were tested under different combinations of torque and circumferentially varying axial thermal stress. The methods of application of the required loads and the measuring techniques employed are discussed. The buckling process is described and interaction curves are presented.     

Maximality of analytic operator algebras

LetM be a σ-finite von Neumann algebra andα be an action ofR onM. LetH ^∞(α) be the associated analytic subalgebra; i.e.H ^∞(α)={X ∈M: sp_∞(X) [0, ∞]}. We prove that every σ-weakly closed subalgebra ofM that containsH ^∞(α) isH ^∞(γ) for some actionγ ofR onM. Also we show that (assumingZ(M)∩M ^α = Ci)H ^∞(α) is a maximal σ-weakly closed subalgebra ofM if and only if eitherH ^∞(α)={A ∈M: (I−F)xF=0} for some projectionF ∈M, or sp(α)=Γ(α).     

Stepwise pyrolysis of macerals

Kerogen separates which consist predominantly of single maceral types at maturity levels lower than 0.7% vitrinite reflectance (R ₀) were pyrolysed in a single step and stepwise between 50 and 600°C. The total hydrocarbon yield and the yield of hydrocarbon gases (C₁−C₄) were determined along with the detailed composition of the gaseous fraction (C₁−C₄ alkanes and alkenes) and the C₅₊-fraction. The distribution of hydrocarbons, particularly in the C₁−C₃ range and the alkene/alkane ratio are useful as specific indicators for the various maceral types. The residue was analysed by reflected white light and fluorescence microscopy. The different types of reactive macerals i.e. algae, altered algae, particulate liptinites, amorphous liptinites and amorphous humic matter are transformed into particular types of inertinite. The reconstruction of the original maceral composition from its residue after katagenesis in a natural assemblage seems however difficult, due to the small amount of residue of the reactive macerals and the presence of original inertinite. Qualitative and quantitative data derived from these pyrolysis experiments may be useful on a comparative basis for the prediction of hydrocarbon generation by these maceral groups during katagenesis. Dedicated to Professor Lisa Heller-Kallai on the occasion of her 65^th birthday     

Carbon monoxide binding by de novo heme proteins derived from designed combinatorial libraries.

Carbon monoxide binding was studied in a collection of de novo heme proteins derived from combinatorial libraries of sequences designed to fold into 4-helix bundles. The design of the de novo sequences was based on the previously reported "binary code" strategy, in which the patterning of polar and nonpolar amino acids is specified explicitly, but the exact identities of the side chains are varied extensively.(1) The combinatorial mixture of amino acids included histidine and methionine, which ligate heme iron in natural proteins. However, no attempt was made to explicitly design a heme binding site. Nonetheless, as reported previously, approximately half of the binary code proteins bind heme.(2) This collection of novel heme proteins provides a unique opportunity for an unbiased assessment of the functional potentialities of heme proteins that have not been prejudiced either by explicit design or by evolutionary selection. To assess the capabilities of the de novo heme proteins to bind diatomic ligands, we measured the affinity for CO, the kinetics of CO binding and release, and the resonance Raman spectra of the CO complexes for eight de novo heme proteins from two combinatorial libraries. The CO binding affinities for all eight proteins were similar to that of myoglobin, with dissociation constants (K(d)) in the low nanomolar range. The CO association kinetics (k(on)) revealed that the heme environment in all eight of the de novo proteins is partially buried, and the resonance Raman studies indicated that the local environment around the bound CO is devoid of hydrogen-bonding groups. Overall, the CO binding properties of the de novo heme proteins span a narrow range of values near the center of the range observed for diverse families of natural heme proteins. The measured properties of the de novo heme proteins can be considered as a "default" range for CO binding in alpha-helical proteins that have neither been designed to bind heme or CO, nor subjected to genetic selections for heme or CO binding.     

The effects of cross-linking and anodic surface roughening on quinone polymer/carbon electrodes

A polymer in which anthraquinone-2-carbonyl groups were bound to polyethyleneimine was coated onto a glassy carbon electrode. Electrodes of this kind were studied using cyclic voltammetry and pH 7 aqueous solutions. At pH <10 only those quinone units in contact with the carbon surface are electroactive. It was shown that anodic surface roughening increased the limited number of electroactive groups in the polymer film and gave more stable activity and narrower voltammetric peaks. Above pH 10 redox propagation through the layer is more rapid but the anionic product desorbs. This desorption was inhibited by cathodically cross-linking a layer of mixed polymers on a polyethyleneimine backboned polymer containing fluorenone units as well as anthraquinone units.     

Electronic and vibrational resonance Raman spectra of octamethyluranocene

The Raman spectrum of bis(tetramethylcyclo-octatetraene)uranium (U(TMCOT)₂), excited in resonance with its visible charge-transfer transitions shows an anomalously polarized electronic band at 473 cm^?1, twice as broad as the analogous band of uranocene, at 466 cm^?1. The broadening is attributed to crystal-field splitting associated with the lowered symmetry introduced by the methyl group, and/or a distribution of rotamer populations. Totally symmetric vibrational modes are observed at 879, 750, 580, 513 and 95 cm^?1; possible assignments are discussed.     

Analysis of organic amines and acids for water

Conventional methods for the determination of cyanide in effluents associated with steel-making procedures are compared with a method based on a cyanide-selective electrode. For cyanide levels above 1.0 mg l^-1, the standard argentimetric titration and electrode method give similar results. At lower levels (0.1–1.0 mg l^-1 and 0.01–0.10 mg l^-1), the potentiometric method is compared with pyridine-pyrazolone and pyridine—barbituric acid colorimetric procedures; the pyrazolene method tends to give higher results than the other two methods. Synthetic standards and actual effluent samples are discussed. Problems associated with the determination of cyanide in effluents containing complex iron cyanides and sulphides are examined. Sulphide removal with lead carbonate or cadmium carbonate above pH 11 should not be done until after the distillation.     

Four-dimensional Einstein-like manifolds and curvature homogeneity

The aim of this paper is to classify 4-dimensional Einstein-like manifolds whose Ricci tensor has constant eigenvalues (this being a special kind of curvature homogeneity condition). We give a full classification when the Ricci tensor is of Codazzi type; when the Ricci tensor is cyclic parallel, we classify all such manifolds when not all Ricci curvatures are distinct. In this second case we find a one-parameter family of Riemannian metrics on a Lie groupG as the only possible ones which are irreducible and non-symmetric.