Related papers: Differential Reductions and Cosmological Correlati…
We investigate the problem of recovering coefficients in scalar nonlinear ordinary differential equations that can be exactly linearized. This contribution builds upon prior work by Lyakhov, Gerdt, and Michels, which focused on obtaining a…
The reduction of dynamical systems has a rich history, with many important applications related to stability, control and verification. Reduction of nonlinear systems is typically performed in an exact manner - as is the case with…
It has been recently pointed out that dynamical systems depending on future values of the unknowns may be useful in different areas of knowledge. We explore in this context the extension of the concept of order reduction that has been…
We completely characterize all nonlinear partial differential equations leaving a given finite-dimensional vector space of analytic functions invariant. Existence of an invariant subspace leads to a re duction of the associated dynamical…
Multidimensional cosmological models with factorizable geometry and their dimensional reduction to effective four-dimensional theories are analyzed on sensitivity to different scalings. It is shown that a non-correct gauging of the…
We propose an approach to quantum cosmology of integrable models. To analyze the models with two dynamical variables, we introduce equivalent Hamiltonians in reduced phase spaces, which are obtained with the aid of the Faddeev--Jackiw…
In his seminal paper published in 2000 Kenyon developed a method to study the height function of the planar dimer model via discrete complex analysis tools. The core of this method is a set of identities representing height correlations…
In this paper we show how almost cosymplectic structures are a natural framework to study thermodynamical systems. Indeed, we are able to obtain the same evolution equations obtained previously by Gay-Balmaz and Yoshimura (see Entropy,…
A numerical framework is proposed for identifying partial differential equations (PDEs) governing dynamical systems directly from their observation data using Chebyshev polynomial approximation. In contrast to data-driven approaches such as…
Euclidean conformal integrals for an arbitrary number of points in any dimension are evaluated. Conformal transformations in the Euclidean space can be formulated as the Moebius group in terms of Clifford algebras. This is used to interpret…
It is well known that using high-order numerical algorithms to solve fractional differential equations leads to almost the same computational cost with low-order ones but the accuracy (or convergence order) is greatly improved, due to the…
Higher-order diagrams required for radiative corrections to mixed electroweak and QCD processes at the LHC and anticipated future colliders will require numerically stable representations of the associated Feynman diagrams. The…
The T and Y-systems are ubiquitous structures in classical and quantum integrable systems. They are difference equations having a variety of aspects related to commuting transfer matrices in solvable lattice models, q-characters of…
We study a quantization via fractional derivative of a nonminimal derivative coupling cosmological theory, namely, the Fab Four John theory. Its Hamiltonian version presents the issue of fractional powers in the momenta. That problem is…
In this paper we exploit factorisation properties of Picard-Fuchs operators to decouple differential equations for multi-scale Feynman integrals. The algorithm reduces the differential equations to blocks of the size of the order of the…
We give a unified interpretation of confluences, contiguity relations and Katz's middle convolutions for linear ordinary differential equations with polynomial coefficients and their generalization to partial differential equations. The…
A possibility to detect correlations between two quantum mechanical systems only from the information of a subsystem is investigated. For generic cases, we prove that there exist correlations between two quantum systems if the…
Let C be an algebraically closed field and X a projective curve over C. Consider an ordinary linear differential equation, or a linear differ- ence equation, with coefficients in the field of rational functions of X, and assume that its…
We consider reduction of dimension for nonlinear dynamical systems. We demonstrate that in some cases, one can reduce a nonlinear system of equations into a single equation for one of the state variables, and this can be useful for…
We study a version of the randomized Kaczmarz algorithm for solving systems of linear equations where the iterates are confined to the solution space of a selected subsystem. We show that the subspace constraint leads to an accelerated…