Related papers: Introduction to exterior differential systems
This is an introduction to the subject of the differential topology of the space of smooth loops in a finite dimensional manifold. It began as the background notes to a series of seminars given at NTNU and subsequently at Sheffield. I am…
Expanded lecture notes. Preliminary version, comments are welcome.
In this review paper, we consider three kinds of systems of differential equations, which are relevant in physics, control theory and other applications in engineering and applied mathematics; namely: Hamilton equations, singular…
This paper is a summary of the theory of discrete embeddings introduced in [5]. A discrete embedding is an algebraic procedure associating a numerical scheme to a given ordinary differential equation. Lagrangian systems possess a…
Abstract separation systems provide a simple general framework in which both tree-shape and high cohesion of many combinatorial structures can be expressed, and their duality proved. Applications range from tangle-type duality and tree…
The aim of this text is to provide a linguistically accessible, but comprehensive introduction into a variety of topics in dynamical systems and its applications. Whilst preliminary knowledge of dynamical systems is useful, it is not…
The paper introduces the concept of asynchronous pseudo-system. Its purpose is to correct/generalize/continue the study of the asynchronous systems (the models of the asynchronous circuits) that has been started in [1], [2].
An elementary description of the Eightfold Way for the non-specialist is presented. This article, for publication in {\it Macmillan Encylopedia of Physics, Supplement: Elementary Particle Physics}, is being submitted to the Archive for…
Not only a review of Weintraub's Differential Forms: Theory and Practice but also a discussion of why differential forms should be taught to undergraduates and an overview of some of the other possible texts that could be used.
This is a brief introduction to the world of Noncommutative Algebra aimed at advanced undergraduate and beginning graduate students.
It is a basic introduction to differential graded Lie algebras, Maurer-Cartan equation and associated deformation functors.
The first purpose of this work is to provide a friendly introduction to the theory of nonautonomous linear systems of ordinary differential equations, the property of exponential dichotomy and its corresponding spectral theory. The second…
The bases of the theory of integrals for multidimensional differential systems are stated. The integral equivalence of total differential systems, linear homogeneous systems of partial differential equations, and Pfaff systems of equations…
The goal of this article is twofold. Firstly, nonlinear system identification is introduced to a wide audience, guiding practicing engineers and newcomers in the field to a sound solution of their data driven modeling problems for nonlinear…
These notes contain a survey of some aspects of the theory of differential modules and complexes as well as of their generalization, that is, the theory of $N$-differential modules and $N$-complexes. Several applications and examples coming…
The paper investigates exterior and symmetric (co)homologies of groups. We introduce symmetric homology of groups and compute exterior and symmetric (co)homologies of some finite groups. We also compare the classical, exterior and symmetric…
The proper handling of 3D orientations is a central element in many optimization problems in engineering. Unfortunately many researchers and engineers struggle with the formulation of such problems and often fall back to suboptimal…
We define an abstract framework called {\it discrete finite differences embedding} which can be used to obtain discrete analogue of formal functional relations in the spirit of category theory. For ordinary differential equations we exhibit…
Main purposes of the paper are followings: 1) To show examples of the calculations in domain of QFT via ``derivative rules'' of an expert system; 2) To consider advantages and disadvantage that technology of the calculations; 3) To reflect…
The goal of these notes is to provide an introduction to rough partial differential equations. For this purpose, we will present the theory of rough paths to the extend as it is required. Applications to stochastic partial differential…