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Front Matter

(2009)

Towards a Digital Mathematics Library. Grand Bend, Ontario, Canada, July 8-9th, 2009

Front Matter

(2008)

Towards Digital Mathematics Library. Birmingham, United Kingdom, July 27th, 2008

Further remarks on extended umbral calculus

Kwaśniewski, A. K., Grądzka, E. (2002)

Proceedings of the 21st Winter School "Geometry and Physics"

The paper deals with extensions of the finite operator calculus of G.-C. Rota called ψ -extensions which give a framework for corresponding quantum group investigations. This also covers the instance of the well-known q -analogue of umbral calculus. The article also contains glossaries of the most important terms and notations used by Ward, Viskov, Markowsky and Roman on one side and the Rota-oriented notations on the other side.

Fuzzy sets and small systems

Považan, Jaroslav, Riečan, Beloslav (2013)

Applications of Mathematics 2013

Independently with [7] a corresponding fuzzy approach has been developed in [3-5] with applications in measure theory. One of the results the Egoroff theorem has been proved in an abstract form. In [1] a necessary and sufficient condition for holding the Egoroff theorem was presented in the case of a space with a monotone measure. By the help of [2] and [6] we prove a variant of the Egoroff theorem stated in [4].

Gamma-function and Gaussian-sum-function

Helversen-Pasotto, A. (1993)

Proceedings of the Winter School "Geometry and Physics"

After some remarks about the analogy between the classical gamma-function and Gaussian sums over finite fields a complete, very short explicit proof is given of an identity expressing a certain sum of products of Gaussian sums as a product of Gaussian sums. This identity is an analogue of the classical Barnes’ first lemma for the gamma-function. Four multiplicative characters of a finite field are concerned; the usually necessary restrictions on the triviality of certain products of these characters...

Gauge-natural field theories and Noether theorems: canonical covariant conserved currents

Palese, Marcella, Winterroth, Ekkehart (2006)

Proceedings of the 25th Winter School "Geometry and Physics"

Summary: We specialize in a new way the second Noether theorem for gauge-natural field theories by relating it to the Jacobi morphism and show that it plays a fundamental role in the derivation of canonical covariant conserved quantities. In particular we show that Bergmann-Bianchi identities for such theories hold true covariantly and canonically only along solutions of generalized gauge-natural Jacobi equations. Vice versa, all vertical parts of gauge-natural lifts of infinitesimal principal automorphisms...

General Nijenhuis tensor: an example of a secondary invariant

Studený, Václav (1996)

Proceedings of the Winter School "Geometry and Physics"

The author considers the Nijenhuis map assigning to two type (1,1) tensor fields α , β a mapping 〈 α , β 〉 : ( ξ , ζ ) ↦ [ α ( ξ ) , β ( ζ ) ] + α ∘ β ( [ ξ , ζ ] ) - α ( [ ξ , β ( ζ ) ] ) - β ( [ α ( ξ ) , ζ ) ] ) , where ξ , ζ are vector fields. Then 〈 α , β 〉 is a type (2,1) tensor field (Nijenhuis tensor) if and only if [ α , β ] = 0 . Considering a smooth manifold X with a smooth action of a Lie group, a secondary invariant may be defined as a mapping whose area of invariance is restricted to the inverse image of an invariant subset of X under another invariant mapping. The author recognizes a secondary invariant related to the...

Currently displaying 601 – 620 of 2199