Existence and Uniqueness to a Dynamic Bilateral Frictional Contact Problem in Viscoelasticity

In this paper we examine an evolution problem which describes the dynamic bilateral contact of a viscoelastic body and a foundation. The contact is modeled by a friction multivalued subdifferential boundary condition which incorporates the Coulomb law of friction, the SJK model and the orthotropic friction law. The main result concerns the existence and uniqueness of weak solutions to the hyperbolic variational inequality when the friction coefficient is sufficiently small. The proof is based on a surjectivity result for multivalued operators and a fixed point argument. Research supported in part by the State Committee for Scientific Research of the Republic of Poland (KBN) under Grants no. 2 P03A 003 25 and 4 T07A 027 26.     

From multiplicative unitaries to quantum groups II

It is shown that all important features of a C^∗-algebraic quantum group (A,Δ) defined by a modular multiplicative W depend only on the pair (A,Δ) rather than the multiplicative unitary operator W. The proof is based on thorough study of representations of quantum groups. As an application we present a construction and study properties of the universal dual of a quantum group defined by a modular multiplicative unitary—without assuming existence of Haar weights.     

X-ray structure of 3′,4-dimethylthio-3,4′-diquinolinyl sulfide

The title compound (C₂₀H₁₆N₂S₃) is monoclinic, witha=31.550(9),b=8.504(3),c=14.745(3) Å,=114.14(3)°,Z=8 and space groupC2/c. The structure was solved by direct methods and refined toR=0.038 for 3012 reflections. The molecule exists in an uncommon conformation. Two quinoline moieties are nearly perpendicular to each other (80.9(3)°). Both methylthio groups have different orientation (the 4-SCH₃ group is nearly perpendicular and the 3-SCH₃ is nearly coplanar to the quinoline moieties). Two pairs of sulfur atoms in ortho-positions remain in very close contact. The conformation of the molecule explains an unusual¹H NMR spectrum.Part XVI in the series of Azinyl Sulfides.     

Cleavage of different ether bonds in butyl glycidyl ether and allyl glycidyl ether by K, K(15-crown-5)2

The kind of substituent in alkyl glycidyl ethers affects the course of their reaction with K⁻, K⁺(15-crown-5)₂. The cyclic oxirane ring is exclusively cleaved in the case of butyl glycidyl ether whereas the presence of the unsaturated allyl group in the glycidyl ether molecule unexpectedly prefers the scission of the linear ether bond. In both the systems organometallic intermediates are formed. They react with crown ether causing its ring opening. Allylpotassium formed from allyl glycidyl ether reacts also with another glycidyl ether molecule; the oxirane ring is opened in this case.     

Potentiometric studies on the complex formation of lanthanides with proline and hydroxyproline

The formation of the lanthanide (La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Lu) complexes with proline and hydroxyproline has been investigated by potentiometric methods as well as by a turbidimetric one which has provided some additional conclusions. It has been found that 11 and a slight amount of 21 complexes are formed. The deviation from the typical course of the formation function is discussed. It is suggested that the perturbations of complex formation in the systems are caused by hydrolysis. The stability constants of the complexes are reported.

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Potentiometrische Untersuchungen an Lanthanid-Komplexen von Prolin und Hydroxyprolin

Zusammenfassung Die Bildung von Lanthanid-Komplexen (La, Pr, Nd, Sm, Eu, Gd, Tb, Dy, Ho, Er, Tm, Lu) mit Prolin und Hydroxyprolin wurde potentiometrisch und mit Hilfe von Trübungsmessungen untersucht. Es wurde festgestellt, daß sich Komplexe der Zusammensetzung 11 und in kleiner Menge auch 21 bilden. Die Abweichung von typischem Verlauf der Bildungskurven wurde untersucht. Es wurde dabei festgestellt, daß für die Störungen in der Komplexbildung die Hydrolyse verantwortlich ist. Die Stabilitätskonstanten wurden bestimmt.

     

Combustion synthesis as a novel method for production of 1-D SiC nanostructures

1-D nanostructures of cubic phase silicon carbide (beta-SiC) were efficiently produced by combustion synthesis of mixtures containing Si-containing compounds and halocarbons in a calorimetric bomb. The influence of the operating parameters on 1-D SiC formation yield was studied. The heat release, the heating rate, and the chamber pressure increase were monitored during the process. The composition and structural features of the products were characterized by elemental analysis, X-ray diffraction, differential thermal analysis/ thermogravimetric technique, Raman spectroscopy, scanning and transmission electron microscopy, and energy-dispersive X-ray spectrometry. This self-induced growth process can produce SiC nanofibers and nanotubes ca. 20-100 nm in diameter with the aspect ratio higher than 1000. Bulk scale Raman studies showed the product to be comprised of mostly cubic polytype of SiC and that finite size effects are present. We believe that the nucleation mechanism involving radical gaseous species is responsible for 1-D nanostructures growth. The present study has enlarged the family of nanofibers and nanotubes available and offers a possible, new general route to 1-D crystalline materials.     

Spectrophotometric Determination of bis(O,O-dialkyldithiophosphoryl) disulfides

A new simple method has been developed for determining the bis(O,O-dialkyldithiophosphoryl) disulfide content up to 16 nM/ml with good reproducibility.The procedure is based on the dithiofluorescein—disulfide interchange reaction. The average value of the molar extinction coefficient obtained was 4.1 × 10⁴ ± 2500 liters M⁻¹cm⁻¹.The use of ion-exchange separation seems to be quite satisfactory for determination of this disulfide in the presence of dithiophosphate salts interference.     

Error bounds for a near-minimax approximation

It is known that a near minimax polynomial approximation tof C [–1, 1] is provided by a finite carrier projectionM _n fromC[–1, 1] onto the subspace of all polynomials of degree n, such thatM _nf is a weighted least squares approximation off on the set consisting of the extreme points of the Chebyshev polynomialT _{2n + 1}. In this paper, upper bounds for the error f–M _n f are given in terms of divided differences.