There Are No Algebraically Integrable Ovals in Even-dimensional Spaces

Some Results on TVS-cone Normed Spaces and Algebraic Cone Metric Spaces

In this paper we introduce the cone bounded linear mapping and demonstrate a proof to show that the cone norm is continuous. Among other things, we prove the open mapping theorem and the closed graph theorem in TVS-cone normed spaces. We also show that under some restrictions on the cone, two cone norms are equivalent if and only if the topologies induced by them are the same. In the sequel, we...

Determination of subrepresentations of the standard higher dimensional shearlet group

‎This paper is devoted to definition standard higher dimension shearlet group $ mathbb{S} = mathbb{R}^{+} times mathbb {R}^{n-1} times mathbb {R}^{n} $ and determination of square integrable subrepresentations of this group‎. ‎Also we give a characterisation of admissible vectors associated to the Hilbert spaces corresponding to each su brepresentations‎.

ar X iv : q ua nt - p h / 04 09 18 4 v 1 2 7 Se p 20 04 Sets of Mutually Unbiased Bases as Arcs in Finite Projective Planes ?

This note is a short elaboration of the conjecture of Saniga et al (J. Opt. B: Quantum Semiclass. 6 (2004) L19-L20) by regarding a set of mutually unbiased bases (MUBs) in a d-dimensional Hilbert space, d being a power of a prime, as an analogue of an arc in a (Desarguesian) projective plane of order d. Complete sets of MUBs thus correspond to (d+1)-arcs, i.e., ovals. The existence of two princ...

On Limit Cycles Appearing by Polynomial Perturbation of Darbouxian Integrable Systems

We prove an existential finiteness result for integrals of rational 1-forms over the level curves of Darbouxian integrals. 1. Limit cycles born by perturbation of integrable systems 1.1. Poincaré–Pontryagin integral. Limit cycles (isolated periodic trajectories) of polynomial planar vector fields can be produced by perturbing integrable systems which have nested continuous families of non-isola...

Convolution and Homogeneous Spaces