Related papers: Lie families: theory and applications

After introducing the concept of commutativity for continuous-time linear time-varying systems, the related literature and the results obtained so far are presented. For a simple introduction of the commutativity of discrete-time linear…

First, we point out that the present applied superposition principle is linear, it must be developed into a generality. Next, the linear operators and equations should be developed nonlinearly. They will include nonlinear Klein-Gordon…

We obtain explicit formulas for the solutions of the system of second-order difference equations of the form $x_{n+ 1} = \frac{x_n y_{n-1}}{y_n (a_n + b_n x_n y_{n - 1})}, \quad y_{n+1} = \frac{x_{n - 1} y_n}{x_n (c_n+d_n x_{n-1} y_n)}$,…

A new proof for adjoint systems of linear equations is presented. The argument is built on the principles of Algorithmic Differentiation. Application to scalar multiplication sets the base line. Generalization yields adjoint inner vector,…

We study automorphic Lie algebras and their applications to integrable systems. Automorphic Lie algebras are a natural generalisation of celebrated Kac-Moody algebras to the case when the group of automorphisms is not cyclic. They are…

We give labeled natural deduction systems for a family of tense logics extending the basic linear tense logic Kl. We prove that our systems are sound and complete with respect to the usual Kripke semantics, and that they possess a number of…

In this paper we present a uniform way to derive families of maps from the corresponding differential equations describing systems which experience periodic kicks. The families depend on a single parameter - the order of a differential…

In this work, we prove three types of results with the strategy that, together, the author believes these should imply the local version of Hilbert's Fifth problem. In a separate development, we construct a nontrivial topology for rings of…

In this set of five lectures the authors have presented techniques to analyze open classical and quantum systems using correlation matrices. For diverse reasons we shall see that random matrices play an important role to describe a null…

The recently introduced series of description logics under the common moniker DL-Lite has attracted attention of the description logic and semantic web communities due to the low computational complexity of inference, on the one hand, and…

This work represents a PhD thesis concerning three main topics. The first one deals with the study and applications of Lie systems with compatible geometric structures, e.g. symplectic, Poisson, Dirac, Jacobi, among others. Many new Lie…

Quantum theory allows for the superposition of causal orders between operations, i.e., for an indefinite causal order; an implication of the principle of quantum superposition. Since a higher theory might also admit this feature, an…

The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…

Networks play a central role in modern data analysis, enabling us to reason about systems by studying the relationships between their parts. Most often in network analysis, the edges are given. However, in many systems it is difficult or…

We generalize first-species counterpoint theory to arbitrary rings and obtain some new counting and maximization results that enrich the theory of admitted successors, pointing to a structural approach, beyond computations. The…

In a previous paper, we introduce and study formal manifolds, which generalize smooth manifolds. In this paper, we establish the basic theory of formal Lie groups, which are group objects in the category of formal manifolds. In particular,…

It was recently shown that the theory of linear stochastic systems can be viewed as a particular case of the theory of linear systems on a certain commutative ring of power series in a countable number of variables. In the present work we…

Matrix Riccati equations and other nonlinear ordinary differential equations with superposition formulas are, in the case of constant coefficients, shown to have the same exact solutions as their group theoretical discretizations. Explicit…

We pursue the study of families of functions on the natural numbers, with emphasis here on the bounded families. The situation being more complicated than the unbounded case, we attack the problem by classifying the families according to…

We provide a general condition under which e-variables in the form of a simple-vs.-simple likelihood ratio exist when the null hypothesis is a composite, multivariate exponential family. Such `simple' e-variables are easy to compute and…