Monoton konvergente Iterationsprozesse zur Lösung diskretisierter nichtlinearer Randwertprobleme
This paper deals with calculus which is an extension of finite operator calculus due to Rota, and leading results of Rota’s calculus are easily -extendable. The particular case is known to be relevant for quantum group investigations. It is shown here that such umbral calculus leads to infinitely many new -deformed quantum like oscillator algebra representations. The authors point to several references dealing with new applications of umbral and calculus in which new families of extensions...
A multisymplectic 3-structure on an -dimensional manifold is given by a closed smooth 3-form of maximal rank on which is of the same algebraic type at each point of , i.e. they belong to the same orbit under the action of the group . This means that for each point the form is isomorphic to a chosen canonical 3-form on . 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...
We give a survey of the joint papers of Lawrence Somer and Michal Křížek and discuss the beginning of this collaboration.
The authors prove that all natural affinors (i.e. tensor fields of type (1,1) on the extended -th order tangent bundle over a manifold ) are linear combinations (the coefficients of which are smooth functions on ) of four natural affinors defined in this work.
One studies the flow prolongation of projectable vector fields with respect to a bundle functor of order on the category of fibered manifolds. As a result, one constructs an operator transforming connections on a fibered manifold into connections on an arbitrary vertical bundle over . It is deduced that this operator is the only natural one of finite order and one presents a condition on vertical bundles over under which every natural operator in question has finite order.
Let be a -dimensional foliation on an -manifold , and the -tangent bundle of . The purpose of this paper is to present some reltionship between the foliation and a natural lifting of to the bundle . Let
The authors study some geometrical constructions on the cotangent bundle from the viewpoint of natural operations. First they deduce that all natural operators transforming functions on into vector fields on are linearly generated by the Hamiltonian vector field with respect to the canonical symplectic structure of and by the Liouville vector field of . Then they determine all natural operators transforming pairs of functions on into functions on . In this case, the main generator is...
[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.