Asking that the metric of a complex Finsler space should be strong convex, Abate and Patrizio ([1]) associate to the real tangent bundle a real Finsler metric for which they analyze the relation between Cartan (real) connection of the obtained space and the real image of Chern-Finsler complex connection. Following the same ideas, in the present paper we shall deal with the more general case of ...

The complex analytic methods have found a wide range of applications in the study of multiplicity-free representations. This article discusses, in particular, its applications to the question of restricting highest weight modules with respect to reductive symmetric pairs. We present a number of multiplicity-free branching theorems that include the multiplicity-free property of some of known res...

In recent years, discrete wavelet transform (DWT) provides an useful platform for digital information hiding and copyright protection. Many DWT-based algorithms for this aim are proposed. The performance of these algorithms is in term of signal-to-noise ratio (SNR) and bit-error-rate (BER) which are used to measure the quality and the robustness of an embedded audio. However, there is a tradeof...

We analyze the relation of notion a pluri-Lagrangian system, which recently emerged in theory integrable systems, to classical variational symmetry, due E. Noether. treat mechanical systems and show that, for any Lagrangian system with $m$ commuting symmetries, one can construct 1-form $(m+1)$-dimensional time, whose multi-time Euler-Lagrange equations coincide original supplied evolutionary fl...

In this paper we give a classification of simple stable singularities of Lagrange projections of the first open Whitney umbrella, the simplest singularity of Lagrange varieties. Our classification extends the ADE-classification, due to Arnold, of simple stable singularities of Lagrange projections of smooth Lagrange submanifolds. We also prove a criterion of equivalence of stable Lagrange proje...

Charged particle optics, the description of trajectories in vicinity some optical axis, describe imaging properties optics devices. Here, we present a complete and compact charged employing perturbative expansion Hamiltonian mechanics. The derived framework allows straightforward computation transversal longitudinal (chromatic) static dynamic devices with straight curved axes. It furthermore gi...

Let F be a family of finite loops closed under subloops and factor loops. Then every loop in F has the strong Lagrange property if and only if every simple loop in F has the weak Lagrange property. We exhibit several such families, and indicate how the Lagrange property enters into the problem of existence of finite simple loops. The two most important open problems in loop theory, namely the e...

In this paper, we are interested in new versions of Farkas lemmas for systems involving convex and DC-inequalities. These versions extend well-known Farkas-type results published recently, which were used as main tools in the study of convex optimization problems. The results are used to derive several strong duality results such as: Lagrange, Fenchel-Lagrange or Toland-Fenchel-Lagrange duality...