The recoil of rigid PVC

Polyvinyl chloride (PVC) is widely used in industry, but it is difficult to find any extensive discussion of theological relations that describe it. The present paper discusses the behaviour of rigid PVC in extensional deformations at various temperatures. In the tests, a step elongation was applied at an initial time, then after a delay the specimen was cut, permitting recoil. Both linear and nonlinear strain regimes were studied; the linear relaxation properties (relaxation function, storage modulus) were cross-checked with eccentric-disk measurements. In the non-linear strain regime a single-integral constitutive equation of the KBKZ Wagner type was used. Separability of time and strain effects was demonstrated in our tests and so a damping function could be found which was only a function of strain. Video recordings of recoil were made, and detailed predictions of the strain-time behaviour were checked against experiments.Various constitutive equation proposals were used in the comparison, and the separated kernel integral irreversible model performed reasonably well; some other models of a differential type, and a Doi-Edwards model were not as accurate.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.     

Debonding of thin external layer exerted by thermodiffusive fluxes

Summary The stress distributions in a matrix, generated by thermodiffusive fluxes, are determined for the case of a thin, inextensible membrane bonded to the bounding plane over the outer regionr (b>0, ). The problem has been reduced to solving a corresponding system of dual integral equations. There exist singularities in the distribution of contact shear stresses, namely one over square root type atr=b while a logarithmic one at the lines of jumps of temperature and/or mass diffusion.

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Ablösung einer dünner Schicht infolge thermodiffusiver Flüsse

Übersicht Es wird die sich in einer Matrix infolge thermodiffusiver Flüsse einstellende Spannungsverteilung ermittelt wobei auf einen Teil der Grenzfläche (im Bereichr (b>0, )) eine dünne und unverschiebliche Membran aufgebracht ist. Zur Lösung wird das Problem auf ein System von dualen Integralgleichungen reduziert. Die in den Kontaktschubspannungen auftretenden Singularitäten sind einerseits vom reziproken Quadratwurzeltyp am Innenrand, andererseits vom logarithmischen Typ bei Sprüngen in der Temperatur und/oder Massendiffusion.

     

Die Strommer-Zykliden des Flaggenraumes

According to H. BRAUNER a flag space is a three-dimensional affine space with an absolute {,f,F}, wheref is a line in the plane of infinity andF a point onf. A cyclide is a surface of order 4 that intersects only atf. A STROMMER-cyclide is a cyclide generated by translation of a circle in an isotropic plane. In this paper we proof that all STROMMER-cyclides can be generated by translation of an isotropic circle along a divergent Newton-parabola or a conic in a full isotropic plane. We give normal-forms and CAD-pictures of these surfaces. Finaly some geometrical results about STROMMER-cyclides are developed.

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Herrn o.Prof. Dr. Gy. Strommer zum 70. Geburtstag gewidmet.     

Toeplitz and Hankel type operators on the upper half-plane

An orthogonal decomposition of admissible wavelets is constructed via the Laguerre polynomials, it turns to give a complete decomposition of the space of square integrable functions on the upper half-plane with the measurey dxdy. The first subspace is just the weighted Bergman (or Dzhrbashyan) space. Three types of Ha-plitz operators are defined, they are the generalization of classical Toeplitz, small and big Hankel operators respectively. Their boundedness, compactness and Schatten-von Neumann properties are studied.Research was supported by the National Natural Science Foundation of China.