By A.O. Barut, Heinz D. Doebner

ISBN-10: 3540171630

ISBN-13: 9783540171638

This quantity includes contributions awarded at a world Symposium on Conformal teams and Conformal constructions held in August 1985 on the Arnold Sommerfeld Institute for Mathematical Physics in Clausthal. we are hoping that the big variety of matters handled the following will provide an image of the current prestige of the significance of the conformal teams, different similar teams and linked mathematical buildings (such as superconformal algebra, Kac-Moody algebras), and spin buildings. Symmetry, with crew thought and algebras as its mathematical version, has regularly performed a vital and demanding function within the improvement of actual theories. one of many top purposes for the curiosity within the conformal staff is that it truly is probably crucial of the bigger teams containing the Poincare staff. It opens the door to purposes a long way past the normal kinematical framework supplied via the neighborhood symmetries of flat space-time.

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Néer. Sci. , Sér. II 6, 1–24 (1901) 40. : Kontinuumstheorie der Versetzungen und Eigenspannungen. Springer, Berlin (1958) 41. Kröner, E. ): Generalized Continua. Proc. IUTAM Symp. Freudenstadt. A. Maugin 42. : Nichtlokal Elastostatik: Ableitung aus der Gittertheorie. Z. Phys. 196(3), 203–211 (1966) 43. : Model of elastic medium with simple structure and space dispersion. Prikl. Mat. Mekh. 30, 542–550 (1966) 44. : Elastic Media with Microstructure I & II. Springer, Berlin (1982). Translated from the 1975 Russian edition 45.

Dyskin ( ) · E. au E. A. V. V. Dyskin and E. Pasternak in such a modeling even if all distances are equally accessible in the continuum. When the higher order continua such as Cosserat continuum are employed, they bring their own characteristic lengths. Then the interplay between the characteristic lengths of the continuum and the scale of averaging becomes important and in some cases can control the results of the modeling. This paper investigates crack propagation in the Cosserat continua whose characteristic lengths commensurate with the microstructural length of the material (the particle size or the layer thickness).

Proof. 21). As a direct corollary of this proposition, we can propose the following definition. 1. A non-holonomic Cosserat medium is said to be semi-holonomic at X if its constitutive law at X is independent of the deformation gradient of the macro-medium. From the mathematical standpoint, it is necessary to note that this definition does not imply the existence of a canonical projection of a non-holonomic jet onto a semi-holonomic part. In fact, such a canonical projection does not exist. 21).

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Conformal Groups and Related Symmetries Physical Results and Mathematical Background by A.O. Barut, Heinz D. Doebner


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