1 We develop the method of anholonomic frames with associated nonlinear connection (in brief, N–connection) structure and show explicitly how geometries with local anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton spaces) can be modelled on the metric–affine spaces. There are formulated the criteria when such generalized Finsler metrics are effectively defined in the Einstein, telepa...

Distance metric learning is of fundamental interest in machine learning because the distance metric employed can significantly affect the performance of many learning methods. Quadratic Mahalanobis metric learning is a popular approach to the problem, but typically requires solving a semidefinite programming (SDP) problem, which is computationally expensive. Standard interior-point SDP solvers ...

Fitting Hyperbolic pants to a three-body problem. Abstract. Consider the three-body problem with an attractive 1/r 2 potential. Modulo symmetries, the dynamics of the bounded zero-angular momentum solutions is equivalent to a geodesic flow on the thrice-punctured sphere, or " pair of pants ". The sphere is the shape sphere. The punctures are the binary collisions. The metric generating the geod...

In this article, we review the current status of Finsler–Lagrange geometry and generalizations. The goal is to aid non–experts on Finsler spaces, but physicists and geometers skilled in general relativity and particle theories, to understand the crucial importance of such geometric methods for applications in modern physics. We also would like to orient mathematicians working in generalized Fin...

We study the variational principle and derivation of field equations for different classes teleparallel gravity theories, using both their metric-affine covariant tetrad formulations. These theories have in common that addition to or metric, they employ a flat connection as additional variable, but differ by presence absence torsion nonmetricity this independent connection. Besides underlying g...

In the framework of first-order differential structure introduced by Gigli, we obtain a Gauss–Green formula on regular bounded open sets in doubling metric measure spaces supporting weak Poincaré inequality, valid for BV functions and vector fields with integrable divergence. Then, study least gradient provide an Euler–Lagrange-type formulation problem, using this as main tool.

We develop the method of anholonomic frames with associated nonlinear connec-tion (in brief, N–connection) structure and show explicitly how geometries with lo-cal anisotropy (various type of Finsler–Lagrange–Cartan–Hamilton geometry) can bemodeled in the metric–affine spaces. There are formulated the criteria when such gen-eralized Finsler metrics are effectively induced in the...

Recently it has been shown that the conventional notions of stability in the sense of Lyapunov and asymptotic stability can be used to characterize the stability properties of a class of “logical” discrete event systems (DES). Moreover, it has been shown that stability analysis via the choice of appropriate Lyapunov functions can be used for DES and can be applied to several DES applications in...

When implementing a nonlinear constraint in quantum field theory by means of Lagrange multiplier, $\ensuremath{\lambda}(x)$, it is often the case that dynamics induce quadratic and even higher-order terms which then does not enforce anymore. This illustrated unimodular gravity, where metric tensor has to be ($g(x)\ensuremath{\equiv}\mathrm{det}\text{ }{g}_{\ensuremath{\mu}\ensuremath{\nu}}(x)=\...