Axisymmetric frictionless contact of functionally graded materials

The main interest of this study is a new method to solve the axisymmetric frictionless contact problem of functionally graded materials (FGMs). Based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into a series of sub-layers with shear modulus varying linearly in each sub-layer and continuous at the sub-interfaces. With this model, the axisymmetric frictionless contact problem of a functionally graded coated half-space is investigated. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a Cauchy singular integral equation. The contact pressure, contact region and indentation are calculated for various indenters by solving the equations numerically. An erratum to this article can be found at     

Water wave radiation by a sphere submerged in water with an ice-cover

Using the multipoles method, we formulate the problems of radiation (both heave and sway) of water waves by a submerged sphere in deep as well as in uniform finite depth water with an ice-cover, with the ice-cover being modelled as an elastic plate of very small thickness. In each case this leads to an infinite system of linear equations which are solved numerically by standard techniques. The added-mass and damping coefficients for a heaving and swaying sphere are obtained and depicted graphically against the wave number for various values of the radius of the submerged sphere and flexural rigidity of the ice-cover to show the effect of the presence of ice-cover on these quantities. When the flexural rigidity is taken to be zero, the numerical results for the added-mass and damping coefficient for water with a free surface are recovered.     

Numerical method and models for anti-plane strain of a system with a thin elastic wedge

The paper presents a general method to find asymptotics for a (multi-)wedge system containing a thin wedge. It employs separation of the symmetric and anti-symmetric parts of the boundary displacements and tractions of the wedge. The method is applicable when the angle of the thin wedge turns to zero. A physical interpretation of the derived equations is obtained by using power expansions of non-polynomial functions, which appear after the Mellin transform. We establish that the first term in the expansion of the symmetric part corresponds to shear, while the first term of the anti-symmetric part describes deflection of the wedge axis. Numerical experiments, performed by using a code developed on the basis of the theory, show that using only the first terms of the expansions insignificantly influence accuracy: the approximate results coincide with the exact values of roots to the third significant digit even for the wedge angle of 30°.     

Differentiation of chiral phosphorus enantiomers by P and H NMR spectroscopy using amino acid derivatives as chemical solvating agents

The ability of commercially available amino acid derivatives, especially Fmoc-Trp(Boc)-OH, to differentiate enantiomers of chiral phosphonates, phosphinates, phosphates, phosphine oxides, and phosphonamidates is demonstrated with (31)P, (13)C, and (1)H NMR spectroscopy. The chiral differentiation provided a rapid and convenient method for measuring the enantiomeric purity of these phosphorus compounds.     

Synthesis of a biotinated amphiphile

The synthesis of a biotinated amphiphile assembled from d-(+)-biotin, ethylene diamine as spacer, galactaric acid and 1-dodecylamine was achieved in six steps. The key step was the synthesis of a bisacetonide protected galactaric ester, the structure of which was determined by X-ray analysis. Aminolysis, spacer attachment, coupling with biotin and deprotection led to the amphiphilic galactaramide.     

Integral approximations for molecular orbital theory

The electron repulsion integrals arising in LCAO-MO theory are approximated by replacement of the product of two orbitals on different centers by linear combinations of one-center products. The approximation differs from those previously proposed in that the coefficients of the various terms are determined by requiring agreement for certain integrals, and in the emphasis of the role of symmetry in selecting the one-center products. For two-center integrals, the new approximation is significantly better than older approximate methods. Reasons are given for expecting this improvement to extend also to multi-center integrals.

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Zusammenfassung Es wird ein Verfahren zur näherungsweisen Berechnung von Elektronenwechselwirkungsintegralen der LCAO-MO-Theorie beschrieben, bei welchem das Produkt zweier Zustandsfunktionen an verschiedenen Zentren durch eine Linearkombination von Produkten am gleichen Zentrum ersetzt wird. Der Unterschied zu ähnlichen Ansätzen liegt in der Justierung der Koeffizienten. Für Zweizentrenintegrale liefert die hier vorgeschlagene Methode bedeutend bessere Ergebnisse als das Mulliken-Verfahren.

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Résumé Les intégrales de répulsion électroniques intervenant dans la théorie LCAO MO sont calculées d'une manière approchée en remplaçant le produit de deux orbitales sur des centres différents par des combinaisons linéaires de produits à un centre. Cette approximation diffère de celles proposées auparavant par la détermination des coefficients des différents termes au moyen de l'ajustement de certaines intégrales et par l'importance du rôle de la symétrie dans le choix des produits monocentriques. Cette nouvelle approximation est bien meilleure que les anciennes en ce qui concerne les intégrales bi-centriques. Nous donnons des raisons d'espérer que cette amélioration s'étendra aux intégrales polycentriques.

     

Template synthesis in the nickel(II)–thiocarbohydrazide–propanone triple system

The complexing process proceeding in the Ni^II–thiocarbohydrazide (H₂N–H–NC(=S)–NH–NH₂)–propanone triple system in EtOH solution and nickel(II)hexacyanoferrate(II) gelatin-immobilized matrix has been studied. It has been found that in the first case, template synthesis leading, as a minimum, to formation of three coordination compounds of Ni^II with (N,N,S,S)-donor tetradentate ligands having NiL¹, NiL² and NiL³compositions where L¹ is 4,6,6-trimethyl-2,3,7,8-tetraazanonen-3-di(thiohydrazide)-1,9, L² is 4,6,6,12-tetrametyl-1,9-dithio-2,3,7,8,10,11-hexaazatridekadien-3,11-hydrazide-1 and L³ is 2,8,10,10,16-pentamethyl-5,13-dithio-3,4,6,7,11,12,14,15-octaazaheptadekatrien-2,7,15 is observed, whereas in the gelatin-immobilized matrix, a complexing process in the system considered does not occur.