Our first aim is to provide an analog of the Gabriel-Quillen embedding theorem for n-exact categories. Also we give example category that in not n-cluster tilting subcategory, a...

It is shown that the number of pages required for a book embedding of a graph is the maximum of the numbers needed for any of the maximal nonseparable subgraphs and that a plane graph in which every triangle bounds a face has a two-page book embedding. The latter extends a theorem of H. Whitney and gives two-page book embeddings for X-trees and square grids.

A notion of quantified conditional logics is provided that includes quantification over individual and propositional variables. The former is supported with respect to constant and variable domain semantics. In addition, a sound and complete embedding of this framework in classical higherorder logic is presented. Using prominent examples from the literature it is demonstrated how this embedding...

It is shown that for every K > 0 and ε ∈ (0, 1/2) there exist N = N(K) ∈ N and D = D(K, ε) ∈ (1,∞) with the following properties. For every metric space (X, d) with doubling constant at most K, the metric space (X, d1−ε) admits a bi-Lipschitz embedding into R with distortion at most D. The classical Assouad embedding theorem makes the same assertion, but with N →∞ as ε→ 0.

The Temporal Logic of Actions is a formalism for reasoning about concurrent and reactive systems. In this paper I present a formulation of TLA in the Isabelle theorem prover, in which I make extensive use of facilities in the Isabelle system for embedding diierent logics, particularly the syntax for easy axiomatisation of logics and the existence of parsing and printing facilities. I show how t...

We give a new semantics for Nuprl's constructive type theory that justiies a useful embedding of the logic of the HOL theorem prover inside Nuprl. The embedding gives Nuprl eeective access to most of the large body of formalized mathematics that the HOL community has amassed over the last decade. The new semantics is dramatically simpler than the old, and gives a novel and general way of adding...

The method of reconstruction for an n-dimensional system from observations is to form vectors of m consecutive observations, which for m > 2n, is generically an embedding. This is Takens’ result. Our analytical examples show that it is possible to obtain spurious Lyapunov exponents that are even larger than the largest Lyapunov exponent of the original system. Therefore, we present examples whe...

Introduction. A general question which is of interest is the following. Suppose that ƒ is a mapping of a compact metric continuum X onto a metric space F. Under what conditions is there an embedding of X and Y in E (Euclidean n-space) or H (Hubert space) so that ƒ is topologically equivalent to a projection onto Y defined by some collection of parallel hyperplanes? Theorem 1 below provides an a...

Recall the notion due to W. Browder of a Poincaré embedding [Br1, Br3, Br2, Br4, Wa, Ra, Wi1, Wi2], which is the homotopy analogue of a smooth embedding of manifolds. Let (M,A) be a simply connected m-dimensional (finite) Poincaré pair. A Poincaré embedding of (M,A) in the sphere S will mean a finite CW-complex W and a map f : A −→ W , such that the homotopy pushout M ∪ι A× [0, 1] ∪f W is homot...