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More on deformed oscillator algebras and extended umbral calculus

Kwaśniewski, A. K., Grądzka, E. (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

This paper deals with ϕ ( q ) calculus which is an extension of finite operator calculus due to Rota, and leading results of Rota’s calculus are easily ϕ -extendable. The particular case ϕ n ( q ) = [ n q 1 ] - 1 is known to be relevant for quantum group investigations. It is shown here that such ϕ ( q ) umbral calculus leads to infinitely many new ϕ -deformed quantum like oscillator algebra representations. The authors point to several references dealing with new applications of q umbral and ϕ ( q ) calculus in which new families of ϕ ( q ) extensions...

Multisymplectic forms of degree three in dimension seven

Bureš, Jarolím, Vanžura, Jiří (2003)

Proceedings of the 22nd Winter School "Geometry and Physics"

A multisymplectic 3-structure on an n -dimensional manifold M is given by a closed smooth 3-form ω of maximal rank on M which is of the same algebraic type at each point of M , i.e. they belong to the same orbit under the action of the group G L ( n , ) . This means that for each point x M the form ω x is isomorphic to a chosen canonical 3-form on n . R. Westwick [Linear Multilinear Algebra 10, 183–204 (1981; Zbl 0464.15001)] and D. Ž. Djoković [Linear Multilinear Algebra 13, 3–39 (1983; Zbl 0515.15011)] obtained...

Natural affinors on the extended r -th order tangent bundles

Gancarzewicz, Jacek, Kolář, Ivan (1993)

Proceedings of the Winter School "Geometry and Physics"

The authors prove that all natural affinors (i.e. tensor fields of type (1,1) on the extended r -th order tangent bundle E r M over a manifold M ) are linear combinations (the coefficients of which are smooth functions on ) of four natural affinors defined in this work.

Natural lifting of connections to vertical bundles

Kolář, Ivan, Mikulski, Włodzimierz M. (2000)

Proceedings of the 19th Winter School "Geometry and Physics"

One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order ( r , s , q ) on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold Y into connections on an arbitrary vertical bundle over Y . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over Y under which every natural operator in question has finite order.

Natural liftings of foliations to the r -tangent bunde

Mikulski, Włodzimierz M. (1994)

Proceedings of the Winter School "Geometry and Physics"

Let F be a p -dimensional foliation on an n -manifold M , and T r M the r -tangent bundle of M . The purpose of this paper is to present some reltionship between the foliation F and a natural lifting of F to the bundle T r M . Let L q r ( F ) ( q = 0 ,...

Natural operations of Hamiltonian type on the cotangent bundle

Doupovec, Miroslav, Kurek, Jan (1997)

Proceedings of the 16th Winter School "Geometry and Physics"

The authors study some geometrical constructions on the cotangent bundle T * M from the viewpoint of natural operations. First they deduce that all natural operators transforming functions on T * M into vector fields on T * M are linearly generated by the Hamiltonian vector field with respect to the canonical symplectic structure of T * M and by the Liouville vector field of T * M . Then they determine all natural operators transforming pairs of functions on T * M into functions on T * M . In this case, the main generator is...

Natural operators between vector valued differential forms

Cap, Andreas (1991)

Proceedings of the Winter School "Geometry and Physics"

[For the entire collection see Zbl 0742.00067.]This paper is devoted to a method permitting to determine explicitly all multilinear natural operators between vector-valued differential forms and between sections of several other natural vector bundles.

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