Related papers: Valuative lattices and spectra
In this article, a concept of implicit methods for scalar conservation laws in one or more spatial dimensions allowing also for source terms of various types is presented. This material is a significant extension of previous work of the…
There is knowledge. There is belief. And there is tacit agreement.' 'We may talk about objects. We may talk about attributes of the objects. Or we may talk both about objects and their attributes.' This work inspects tacit agreements on…
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
A set of algorithms is presented for efficient numerical calculation of the time evolution of classical dynamical systems. Starting with a first approximation for solving the differential equations that has a "reversible" character, we show…
Just as for non-abelian gauge theories at strong coupling, discrete lattice methods are a natural tool in the study of non-perturbative quantum gravity. They have to reflect the fact that the geometric degrees of freedom are dynamical, and…
This is the first part of a series of articles where we are going to develop theory of valuations on manifolds generalizing the classical theory of continuous valuations on convex subsets of a linear space. In this article we still work…
Classification and invariants, with respect to basis changes, of finite dimensional algebras are considered. An invariant open, dense (in the Zariscki topology) subset of the space of structural constants is defined. The algebras with…
In this note we describe how some objects from generalized geometry appear in the qualitative analysis and numerical simulation of mechanical systems. In particular we discuss double vector bundles and Dirac structures. It turns out that…
Formal verification has been successfully developed in computer science for verifying combinatorial classes of models and specifications. In like manner, formal verification methods have been developed for dynamical systems. However, the…
We introduce two new operations (compositional products and implication) on Weihrauch degrees, and investigate the overall algebraic structure. The validity of the various distributivity laws is studied and forms the basis for a comparison…
We reinterpret a result of Pop and Stix on the $p$-adic section conjecture in terms of Berkovich spaces and fixed points. In doing this, we see a version of the result extends to larger classes of fields, which in turn allows us to prove a…
In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines…
A survey of some recent and important results which have to do with integrable equations and their relationship with the theory of surfaces is given. Some new results are also presented. The concept of the moving frame is examined, and it…
Smooth parametrization consists in a subdivision of the mathematical objects under consideration into simple pieces, and then parametric representation of each piece, while keeping control of high order derivatives. The main goal of the…
In 20th century mathematics, the field of topology, which concerns the properties of geometric objects under continuous transformation, has proved surprisingly useful in application to the study of discrete mathematics, such as…
The dynamical analysis of vibrational systems of masses interconnected by restitution elements each with a single degree of freedom, and different configurations between masses and spring constants, is presented. Finite circular and linear…
The novel proposal to invoke the split of the Ricci scalar into bulk and boundary terms in the gravitational action, opens up a new avenue of investigation into stellar dynamics. The Lagrangian contains functional forms of the bulk term…
A method is discussed to analyze the dynamics of a dissipative quantum system. The method hinges upon the definition of an alternative (time-dependent) product among the observables of the system. In the long time limit this yields a…
We exhibit differential geometric structures that arise in numerical methods, based on the construction of Cauchy sequences, that are currently used to prove explicitly the existence of weak solutions to functional equations. We describe…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…