On the classification of oriented vector bundles over 9-complexes
On the conformal relation between twistors and Killing spinors
[For the entire collection see Zbl 0699.00032.] The author considers the conformal relation between twistors and spinors on a Riemannian spin manifold of dimension . A first integral is constructed for a twistor spinor and various geometric properties of the spin manifold are deduced. The notions of a conformal deformation and a Killing spinor are considered and such a deformation of a twistor spinor into a Killing spinor and conditions for the equivalence of these quantities is indicated.
On the formality of products and wedges
On the geodesic flow of a foliation of a compact manifold of negative constant curvature
On the geometric functors on manifolds
On the horizontal cohomology with general coefficients
[For the entire collection see Zbl 0699.00032.] A new cohomology theory suitable for understanding of nonlinear partial differential equations is presented. This paper is a continuation of the following paper of the author [Differ. geometry and its appl., Proc. Conf., Brno/Czech. 1986, Commun., 235-244 (1987; Zbl 0629.58033)].
On the meaning of Bell's inequalities violation
On the -deformed Heisenberg uncertainty relations and discrete time
The opportunity for verifying the basic principles of quantum theory and possible -deformation appears in quantum cryptography (QC) – a new discipline of physics and information theory.The author, member of the group of cryptology of Praha, presents in this paper the possibility to verify the -deformation of Heisenberg uncertainty relation -deformed QM and possible discretization on the base of a model presented in the fourth section.In the seven sections, the author discusses these problems....
On Vassiliev's knot invariants
Ornstein-Uhlenbeck process in quantum mechanics and the sub-quantum coherence effect
Poisson geometry of certain moduli spaces
Pontryagin algebra of a transitive Lie algebroid
[For the entire collection see Zbl 0699.00032.] It was previously known that for every principal fibre bundle P there is some corresponding transitive Lie algebroid A(P) - a vector bundle equipped with some structure like the structure of a Lie algebra in the module of sections. The author of this article shows that the Chern-Weil homomorphism of P is a notion of the Lie algebroid of P, i.e. knowing only A(P) of P one can uniquely reproduce the ring of invariant polynomials and the Chern-Weil...
Pradines-type groupoids
Prolongation of vector fields to jet bundles
[For the entire collection see Zbl 0699.00032.] In this interesting paper the authors show that all natural operators transforming every projectable vector field on a fibered manifold Y into a vector field on its r-th prolongation are the constant multiples of the flow operator. Then they deduce an analogous result for the natural operators transforming every vector field on a manifold M into a vector field on any bundle of contact elements over M.
Properties of product preserving functors
A product preserving functor is a covariant functor from the category of all manifolds and smooth mappings into the category of fibered manifolds satisfying a list of axioms the main of which is product preserving: . It is known that any product preserving functor is equivalent to a Weil functor . Here is the set of equivalence classes of smooth maps and are equivalent if and only if for every smooth function the formal Taylor series at 0 of and are equal in . In this paper all...
-deformed inverse scattering problem
Summary: Starting from the physical point of view on the Miura transformation as reflectionless potential and its connection with supersymmetry we define a scaling -deformation of this to obtain -deformed supersymmetric quantum mechanics. An application to an inverse scattering problem is given.
-difference conformal invariant operators and equations
QCD at the hadron scale and non-local Thirring model
Quantum deformation of relativistic supersymmetry
From the text: The author reviews recent research on quantum deformations of the Poincaré supergroup and superalgebra. It is based on a series of papers (coauthored by P. Kosiński, J. Lukierski, P. Maślanka and A. Nowicki) and is motivated by both mathematics and physics. On the mathematical side, some new examples of noncommutative and noncocommutative Hopf superalgebras have been discovered. Moreover, it turns out that they have an interesting internal structure of graded bicrossproduct. As far...
Rational homotopy type of nilpotent and complete spaces