A Geometric Intrepertation for the Hans Lewy Operator
A geometric solution to the dynamic disturbance decoupling for discrete-time nonlinear systems
The notion of controlled invariance under quasi-static state feedback for discrete-time nonlinear systems has been recently introduced and shown to provide a geometric solution to the dynamic disturbance decoupling problem (DDDP). However, the proof relies heavily on the inversion (structure) algorithm. This paper presents an intrinsic, algorithm-independent, proof of the solvability conditions to the DDDP.
A global characterization of jet bundles of -velocities and covelocities
A Hodge type decomposition for spinor valued forms
A Homotopy Classification οf Symplectic Immersions
A lossless reduction of geodesics on supermanifolds to non-graded differential geometry
Let be a smooth supermanifold with connection and Batchelor model . From we construct a connection on the total space of the vector bundle . This reduction of is well-defined independently of the isomorphism . It erases information, but however it turns out that the natural identification of supercurves in (as maps from to ) with curves in restricts to a 1 to 1 correspondence on geodesics. This bijection is induced by a natural identification of initial conditions for geodesics...
A map associated to the Lepagian forms on the calculus of variations in fibred manifolds
A metric tangential calculus.
A natural graded Lie algebra sheaf over Riemann surfaces
A necessary and sufficient condition for the existence of a bundle in differential spaces
A new class of almost complex structures on tangent bundle of a Riemannian manifold
In this paper, the standard almost complex structure on the tangent bunle of a Riemannian manifold will be generalized. We will generalize the standard one to the new ones such that the induced -tensor on the tangent bundle using these structures and Liouville -form will be a Riemannian metric. Moreover, under the integrability condition, the curvature operator of the base manifold will be classified.
A new infinite order formulation of variational sequences
The theory of variational bicomplexes is a natural geometrical setting for the calculus of variations on a fibred manifold. It is a well–established theory although not spread out very much among theoretical and mathematical physicists. Here, we present a new approach to infinite order variational bicomplexes based upon the finite order approach due to Krupka. In this approach the information related to the order of jets is lost, but we have a considerable simplification both in the exposition...
A new Taylor type formula and extensions for asymptotically developable functions
The paper studies the relation between asymptotically developable functions in several complex variables and their extensions as functions of real variables. A new Taylor type formula with integral remainder in several variables is an essential tool. We prove that strongly asymptotically developable functions defined on polysectors have extensions from any subpolysector; the Gevrey case is included.
A Nijenhuis-type tensor on the quotient of a distribution
A non-linear version of Swan's theorem.
A note on global Nash subvarieties and Artin-Mazur theorem
It is shown that every connected global Nash subvariety of is Nash isomorphic to a connected component of an algebraic variety that, in the compact case, can be chosen with only two connected components arbitrarily near each other. Some examples which state the limits of the given results and of the used tools are provided.
A Note on Sufficiency of Jets.
A note on tangent bundles in a category with a ring object.
A note on the holonomy of connections in twisted bundles
A note to the unipotency of the identity component of the group of algebra automorphisms.