A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Discrete Lagrange problems solved with Lie group constraints.
Paper derives invariantised Euler-Lagrange equations for Herglotz problems.
New statistical biharmonic maps derived from a variation problem.
The article concerns the problem if a~given system of differential equations is identical with the Euler--Lagrange system of an~appropriate variational integral. Elementary approach is applied. The main results involve the determination of the first--order variational integrals related to the second--order Euler--Lagra…
Study nonholonomic systems with collisions using variational principles.
Researchers use Gaussian processes to approximate Lagrange multipliers for Maximum-Entropy distributions.
Schwarzian derivative connects to Euler-Lagrange equations in variational calculus.
If a Lagrangian defining a variational problem has order then its Euler-Lagrange equations generically have order . This paper considers the case where the Euler-Lagrange equations have order strictly less than , and shows that in such a case the Lagrangian must be a polynomial in the highest-order derivati…
The goal of this paper is to encode equivalently the fractional Lagrange dynamics as a nonholonomic almost Kahler geometry. We use the fractional Caputo derivative generalized for nontrivial nonlinear connections (N-connections) originally introduced in Finsler geometry, with further developments in Lagrange and Hamilt…
A solution for the Weinstein's Problem in the general framework of generalized Lie algebroids is the target of this paper. We present the mechanical systems called by use, mechanical (?; ?)-systems, Lagrange mechanical (?; ?)-systems or Finsler mechanical (?; ?)-systems and we develop their geometries. We obtain the ca…
Curves in Lagrange Grassmannians appear naturally in the intrinsic study of geometric structures on manifolds. By a smooth geometric structure on a manifold we mean any submanifold of its tangent bundle, transversal to the fibers. One can consider the time-optimal problem naturally associate with a geometric structure.…
For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange struc…
Optimization with inequality constraints using embedded gradient vector field method
We use methods from exterior differential systems (EDS) to develop a geometric theory of scalar, first-order Lagrangian functionals and their associated Euler-Lagrange PDEs, subject to contact transformations. The first chapter contains an introduction of the classical Poincare-Cartan form in the context of EDS, follow…
In this paper are studied the harmonic maps between two generalized Lagrange spaces. At the same time, it is proved that the solutions of class of certain ODEs or PDEs are harmonic maps between certain convenient generalized Lagrange spaces.
Extends Newton's minimal resistance problem to Lorentz-Minkowski space.
Curves in Lagrange Grassmannians naturally appear when one studies intrinsically "the Jacobi equations for extremals", associated with control systems and geometric structures. In this way one reduces the problem of construction of the curvature-type invariants for these objects to the much more concrete problem of fin…
Develops Lagrange-Hamilton geometry for COVID-19 disease dynamics.
Lagrange's map construction ideas influenced later mathematicians.
We extend the correspondence between Hessian and Kähler metrics and curvatures to Lagrange spaces.
Sum of Lagrange numbers equals a specific formula.
Paper shows geometric frequency and Lagrange derivative equivalence for electric and fluid systems.
Dirac structures on tangent bundles provide a unified framework for Lagrange--Dirac dynamical systems.
Study variational problems for integral invariants of maps between pseudo-Riemannian manifolds.
Lagrange geometry is the geometry of the tensor field defined by the fiberwise Hessian of a non degenerate Lagrangian function on the total space of a tangent bundle. Finsler geometry is the geometrically most interesting case of Lagrange geometry. In this paper we study a generalization, which consists of replacing th…
Geometric framework for dissipative systems on Lie algebroids.
This paper extends invariant Euler-Lagrange equations to higher dimensions and groups.
L3Ms fine-tune LLMs with constraints for tailored applications.
The paper introduces discrete Dirac structures for mechanics, simplifying dynamics.
This article is concerned with the question: For which pairs of hyperbolic Euler-Lagrange systems in the plane does there exist a rank- Bäcklund transformation relating them? We express some obstructions to such existence in terms of the local invariants of the Euler-Lagrange systems. In addition, we discover a clas…
A class of metrizable vector bundles in the general framework of generalized Lie algebroids have been presented in the eight reference. Using a generalized Lie algebroid we obtain the Lie algebroid generalized tangent bundle of a vector bundle. This Lie algebroid is a new example of metrizable vector bundle. A new clas…
A new method solves variational inequality problems with multiple constraints without needing optimal Lagrange multipliers.
Study S-shaped utility maximization with VaR constraint and unobservable drift.
The paper constructs a generalized metrical multi-time Lagrange space, which allows a natural development of relativistic geometrical optics theories, in a general setting.
The aim of this paper is to write explicit expression in terms of a given principal connection of the Lagrange-d'Alembert-Poincarè equations in several stages. This is obtained by using a reduced Lagrange-d'Alembert's Principle in several stages, extending methods introduced for the case of two stages by one of the aut…
In this paper, we will give a rigorous construction of the exact discrete Lagrangian formulation associated to a continuous Lagrangian problem. Moreover, we work in the setting of Lie groupoids and Lie algebroids which is enough general to simultaneously cover several cases of interest in discrete and continuous descri…
In this paper we investigate the following question: under what conditions can a second-order homogeneous ordinary differential equation (spray) be the geodesic equation of a Finsler space. We show that the Euler-Lagrange partial differential system on the energy function can be reduced to a first order system on this …
The purpose of this paper is to describe geometrically discrete Lagrangian and Hamiltonian Mechanics on Lie groupoids. From a variational principle we derive the discrete Euler-Lagrange equations and we introduce a symplectic 2-section, which is preserved by the Lagrange evolution operator. In terms of the discrete Leg…
The approach to nonholonomic Ricci flows and geometric evolution of regular Lagrange systems [S. Vacaru: J. Math. Phys. \textbf{49} (2008) 043504 \& Rep. Math. Phys. \textbf{63} (2009) 95] is extended to include geometric mechanics and gravity models on Lie algebroids. We prove that such evolution scenarios of geometri…
We prove a version of the variational Euler-Lagrange equations valid for functionals defined on Fréchet manifolds, such as the spaces of sections of differentiable vector bundles appearing in various physical theories.
We relate certain universal curvature identities for Kaehler manifolds to the Euler-Lagrange equations of the scalar invariants which are defined by pairing characteristic forms with powers of the Kaehler form.
Perfect tracking control for real-world Euler-Lagrange systems is challenging due to uncertainties in the system model and external disturbances. The magnitude of the tracking error can be reduced either by increasing the feedback gains or improving the model of the system. The latter is clearly preferable as it allows…
Inspired by the question of identifying the start time of financial bubbles, we address the calibration of time series in which the inception of the latest regime of interest is unknown. By taking into account the tendency of a given model to overfit data, we introduce the Lagrange regularisation of the normalised …
Variational calculus on a vector bundle E equipped with a structure of a general algebroid is developed, together with the corresponding analogs of Euler-Lagrange equations. Constrained systems are introduced in the variational and in the geometrical setting. The constrained Euler-Lagrange equations are derived for ana…
We deal with Lagrangian systems that are invariant under the action of a symmetry group. The mechanical connection is a principal connection that is associated to Lagrangians which have a kinetic energy function that is defined by a Riemannian metric. In this paper we extend this notion to arbitrary Lagrangians. We the…
For For a given PDE system, or an exterior differential system possessing a Lie group of internal symmetries the orbit reduction procedure is introduced. It is proved that the solutions of the reduced exterior differential system are in one-to-one correspondence with the moduli space of regular solutions of the prolong…
Develops geometry for Lotka-Volterra model of species competition.
Generalized Lagrange-Weyl structures and compatible connections are introduced as a natural generalization of similar notions from Riemannian geometry. Exactly as in Riemannian case, the compatible connection is unique if certain symmetry conditions with respect to vertical and horizontal Christoffel symbols are impose…