Related papers: Linearised Higher Variational Equations
We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…
Gauge-invariant treatments of general-relativistic higher-order perturbations on generic background spacetime is proposed. We show the fact that the linear-order metric perturbation is decomposed into gauge-invariant and gauge-variant…
We examine the variational and conformal structures of higher order theories of gravity which are derived from a metric-connection Lagrangian that is an arbitrary function of the curvature invariants. We show that the constrained first…
We introduce an algorithm to solve linear inverse problems regularized with the total (gradient) variation in a gridless manner. Contrary to most existing methods, that produce an approximate solution which is piecewise constant on a fixed…
This work develops a procedure to find classes of Lagrangian densities that describe generalizations of the Abelian Maxwell-Higgs, the Chern-Simons-Higgs and the Maxwell-Chern-Simons-Higgs models. The investigation focuses on the…
Some positive answers to the problem of endowing a dynamical system with a Hamiltonian formulation are presented within the class of Poisson structures in a geometric framework. We address this problem on orientable manifolds and by using…
In this study, firstly, the k-th order extension of complex product manifold is consid- ered. Then the higher order vertical, complete lifts of geometric structures on product manifold to its extended spaces are given. Also higher order…
We consider the iterative solution of large linear systems of equations in which the coefficient matrix is the sum of two terms, a sparse matrix $A$ and a possibly dense, rank deficient matrix of the form $\gamma UU^T$, where $\gamma > 0$…
This paper explores some sufficient conditions for the enhanced solvability of strong vector equilibrium problems, which can be established via a variational approach. Enhanced solvability here means existence of solutions, which are strong…
We investigate finite-dimensional constrained structured optimization problems, featuring composite objective functions and set-membership constraints. Offering an expressive yet simple language, this problem class provides a modeling…
A generalization of the already studied transformations of the linear differential equation into a system of the first order equations is given. The proposed transformation gives possibility to get new forms of the N-dimensional system of…
This mini-course provides a presentation of the method of characteristics to initial/boundary-value problems for systems of first-order partial differential equations and to Hamilton-Jacobi variational inequalities. In particular, these…
This paper is concerned with solving some structured multi-linear systems, which are called tensor absolute value equations. This kind of absolute value equations is closely related to tensor complementarity problems and is a generalization…
This work builds on an existing model of discrete canonical evolution and applies it to the general case of a linear dynamical system, i.e., a finite-dimensional system with configuration space isomorphic to $ \mathbb{R}^{q} $ and linear…
The generalized Maxwell equations are considered which include an additional gradient term. Such equations describe massless particles possessing spins one and zero. We find and investigate the matrix formulation of the first order of…
In this paper we will be considering a basic geometric problem, the extension problem of classical Hamilton-Cartan variational theory to higher jet prolongations on fibered manifolds.
Many physical systems are well described on domains which are relatively large in some directions but relatively thin in other directions. In this scenario we typically expect the system to have emergent structures that vary slowly over the…
Most of the engineering and physical systems are generally characterized by differential and difference equations based on their continuous-time and discrete-time dynamics, respectively. Moreover, these dynamical models are analyzed using…
Latent factor models that integrate data from multiple sources/studies or modalities have garnered considerable attention across various disciplines. However, existing methods predominantly focus either on multi-study integration or…
An algebraic criterion that is sufficient to establish the existence of certain a priori estimates for the solution of first-order homogeneous linear characteristic problems is derived. Estimates of such kind ensure the stability of the…