Extensions of the Borsuk-Ulam Theorem by Timothy Prescott

We show that there exists a closed non-σ-porous set of extended uniqueness. We also give a new proof of Lyons’ theorem, which shows that the class of H(n)-sets is not large in U0.

Let X and Y be two real normed vector spaces. A mapping /: X —► Y preserves unit distance in both directions iff for all x, y e X with ||jc — y|| = l it follows that ||/(jc) /0>)|| = 1 and conversely. In this paper we shall study, instead of isometries, mappings satisfying the weaker assumption that they preserve unit distance in both directions. We shall prove that such mappings are not very f...

A condition for the synchronizability of a pair of extended systems governed by partial differential equations (PDEs), coupled through a finite set of variables, is commonly the existence of internal synchronization or internal coherence in each system separately. The condition was previously illustrated in a forced-dissipative system and is here extended to Hamiltonian systems using an example...

This paper is a companion to [2]. We give short proofs of Gromov’s theorem on directed embeddings [1; 2.4.5 (C′)] and of the Normal Deformation Theorem [2; 4.7]. AMS Classification 57R40, 57R42; 57A05

The Mordell-Lang conjecture and its variants assert subvarieties of algebraic groups can meet certain subgroups only in a finite set of translates of subgroups. In most cases the number of such translates is unknown and it is not even known whether this number may be bounded by a function of the geometric data. In this note we show that some uniformity follows immediately from the finiteness re...

Abstract This chapter introduces the model-state- and parameter estimation problem from basic principles starting with Bayes’ theorem. We define general formulation introduce concept of theorem solved recursively over a sequence assimilation time windows.

The Bayesian interpretation of probability is one of two broad categories of interpretations. Bayesian inference updates knowledge about unknowns, parameters, with information from data. The LaplacesDemon package in R enables Bayesian inference, and this vignette provides an introduction to the topic. This article introduces Bayes’ theorem, model-based Bayesian inference, components of Bayesian...