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°.     

Novel route to synthesis of allyl starch and biodegradable hydrogel by copolymerizing allyl‐modified starch with methacrylic acid and acrylamide

Maize starch was modified by allyl chloride adopting an interfacial reaction technique with cetyltrimethyl ammonium bromide as a phase‐transfer catalyst and pyridine as an acid acceptor. The degree of substitution was determined from an increasing carbon content of the modified starch. The percentage of carbon and hydrogen of the allyl‐modified starch was estimated by elemental analysis (C, H, and N), and the product characterization was done through ¹H NMR and ¹³C NMR analyses. The allyl‐modified starch was then copolymerized with methacrylic acid and a combination of methacrylic acid and acrylamide at 50 and 70 °C with potassium persulfate as an initiator. The copolymer thus formed swelled in distilled water after neutralization with sodium carbonate. The percentage of absorption capacity of the hydrogels was determined with distilled water and 0.9% NaCl solution. The highest percentage of absorption, 6500%, was achieved for the developed hydrogel containing allyl starch and acrylic monomer in a 1.7:1 w/w ratio and acrylic monomer, namely, methacrylic acid and acrylamide in a 3.2:1 w/w ratio. The study on biodegradability of the developed hydrogel showed that the hydrogel is degradable in the presence of diastase (amylase). © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1650–1658, 2003     

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.     

Studies on antimony oxides: Part I

Thermogravimetry (TG), differential thermal analysis (DTA) and X-ray diffraction studies of antimony(III) oxide, (Sb₂O₃), in air, nitrogen and argon atmospheres have been made. In air Sb₂O₃ becomes oxidized to Sb₂O₄ above 510°. The oxidation reaction proceeds in two stages as revealed by the TG and DTA curves. The behaviour of Sb₂O₃ is similar in both N₂ and Ar. Sb₂O₃ remains unaffected up to 430°, above which there is a slow, and continuous mass loss up to 550°. Above 550° Sb₂O₃ volatilizes resulting in an enormous weight loss. X-ray studies of the sublimate and the residue indicate the former to be the cubic form of Sb₂O₃ (Senarmontite) while the residue is the orthorhombic (Valentinite) structure. From the DTA curves in air, N₂ and Ar, the transition temperature for the cubic to the orthorhombic modification has been estimated to be around 610°.     

Chemische Vitamin D<Subscript>3</Subscript>-Bestimmung in Lebertran

The different aspects of Vitamin D₃ determination and the data reported in the literature are discussed. The spectrophotometric determination of Vitamin D₃ in cod-liver oil is carried out after the alkaline saponification, extraction of unsaponified parts, precipitation of accompanying sterols and the column- and thin-layer chromatographic purification and separation of vitamin D₃ on 40 cm plates from other vitamins. The dyestuff α-naphtholbenzein is suited well as standard substance for the better location and identification of vitamin D₃ zone on the thin-layer plate. The results obtained from the chemical method were checked through the simultaneous biological determination.     

The compensation effect: A fact or a fiction

In this article, the facts and fictions surrounding the compensation effect is explored. False compensation effect occurs mainly due to: propagation of computational and experimental errors resulting in inaccurate estimates of the Arrhenius parameters; and, the natural compensation between InA andE. Since Arrhenius parameters are sensitive to errors in temperature; the errors due to uncertainty in temperature should be minimized to eliminate false compensation effect. Increasing the experimental temperature range is helpful in minimizing errors due to uncertainty in temperature. A point of concurrence in a plot of Ink and 1/T establishes the occurrence of true compensation effect. True compensation effect has been shown to be a useful tool in chemical research for: identifying the governing reaction mechanism; predicting the effects of various reaction parameters; and, correlating and reducing experimental data.

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Zusammenfassung In dieser Mitteilung werden Fakten und Vorstellungen betreffs des Kompensationseffektes untersucht. Falsche Kompensationseffekte werden hauptsächlich verursacht durch: eine ungenaue Ermittlung der Arrheniusparameter durch die Fortpflanzung von rechnerischen und experimentellen Fehlern sowie dem natürlichen Kompensationseffektes zwischen InA undE. Das Arrheniusparameter gegenüber Fehler im Temperaturwert sehr empfindlich sind, sollten Temperaturungenäuigkeitsfehler zur Vermeidung eines falschen Kompensationseffektes minimalisiert werden. Zur Verminderung der aus der Temperaturungenauigkeit resultierenden Fehler ist es von Nutzen, den Temperaturbereich des Experimentes zu erweitern. Ein wahrer Kompensationseffekt wird durch einen Schnittpunkt in einem Ink-1/T Diagramm angezeigt. Es wird gezeigt, daß der wahre Kompensationseffekt ein nutzvolles Mittel in der chemischen Forschung darstellt: zur Feststellung des dominierenden Reaktionsmechanismus, zur Vorhersage der einflüsse verschiedener Reaktionsparameter und zur Aufarbeitung und Schlußfolgerung von bzw. aus experimentellen Daten.

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, . , , lnA E. , , . . Ink-1/T . , , , .

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The author would like to thank the reviewer for his constructive criticisms.