2,205 research outputs found
Lagrange-Fedosov Nonholonomic Manifolds
We outline an unified approach to geometrization of Lagrange mechanics,
Finsler geometry and geometric methods of constructing exact solutions with
generic off-diagonal terms and nonholonomic variables in gravity theories. Such
geometries with induced almost symplectic structure are modelled on
nonholonomic manifolds provided with nonintegrable distributions defining
nonlinear connections. We introduce the concept of Lagrange-Fedosov spaces and
Fedosov nonholonomic manifolds provided with almost symplectic connection
adapted to the nonlinear connection structure.
We investigate the main properties of generalized Fedosov nonholonomic
manifolds and analyze exact solutions defining almost symplectic Einstein
spaces.Comment: latex2e, v3, published variant, with new S.V. affiliatio
Feature Selection with the Boruta Package
This article describes a R package Boruta, implementing a novel feature selection algorithm for finding \emph{all relevant variables}. The algorithm is designed as a wrapper around a Random Forest classification algorithm. It iteratively removes the features which are proved by a statistical test to be less relevant than random probes. The Boruta package provides a convenient interface to the algorithm. The short description of the algorithm and examples of its application are presented.
Deformation Quantization of Almost Kahler Models and Lagrange-Finsler Spaces
Finsler and Lagrange spaces can be equivalently represented as almost Kahler
manifolds enabled with a metric compatible canonical distinguished connection
structure generalizing the Levi Civita connection. The goal of this paper is to
perform a natural Fedosov-type deformation quantization of such geometries. All
constructions are canonically derived for regular Lagrangians and/or
fundamental Finsler functions on tangent bundles.Comment: the latex 2e variant of the manuscript accepted for JMP, 11pt, 23
page
The Entropy of Lagrange-Finsler Spaces and Ricci Flows
We formulate a statistical analogy of regular Lagrange mechanics and Finsler
geometry derived from Grisha Perelman's functionals generalized for
nonholonomic Ricci flows. There are elaborated explicit constructions when
nonholonomically constrained flows of Riemann metrics result in Finsler like
configurations, and inversely, and geometric mechanics is modelled on Riemann
spaces with preferred nonholonomic frame structure.Comment: latex2e, 20 pages, v3, the variant accepted to Rep. Math. Phy
Fedosov Quantization of Lagrange-Finsler and Hamilton-Cartan Spaces and Einstein Gravity Lifts on (Co) Tangent Bundles
We provide a method of converting Lagrange and Finsler spaces and their
Legendre transforms to Hamilton and Cartan spaces into almost Kaehler
structures on tangent and cotangent bundles. In particular cases, the Hamilton
spaces contain nonholonomic lifts of (pseudo) Riemannian / Einstein metrics on
effective phase spaces. This allows us to define the corresponding Fedosov
operators and develop deformation quantization schemes for nonlinear mechanical
and gravity models on Lagrange- and Hamilton-Fedosov manifolds.Comment: latex2e, 11pt, 35 pages, v3, accepted to J. Math. Phys. (2009
Research of Gravitation in Flat Minkowski Space
In this paper it is introduced and studied an alternative theory of
gravitation in flat Minkowski space. Using an antisymmetric tensor, which is
analogous to the tensor of electromagnetic field, a non-linear connection is
introduced. It is very convenient for studying the perihelion/periastron shift,
deflection of the light rays near the Sun and the frame dragging together with
geodetic precession, i.e. effects where angles are involved. Although the
corresponding results are obtained in rather different way, they are the same
as in the General Relativity. The results about the barycenter of two bodies
are also the same as in the General Relativity. Comparing the derived equations
of motion for the -body problem with the Einstein-Infeld-Hoffmann equations,
it is found that they differ from the EIH equations by Lorentz invariant terms
of order .Comment: 28 page
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