Flammability Limits of an Oxidation Reaction in a Batch Reactor. II. The Rychlý Mechanism

It is often numerically convenient to reduce models in two-dimensions to one-dimension. This can be done formally through the use of centre manifold techniques, or informally using physical reasoning. We investigate the extent to which flammability limits in a two-dimensional slab are accurately represented by the values in the corresponding one-dimensional slab. We use a simple chemical mechanism containing exothermic and endothermic reactions that has been used to model the combustion of hydrocarbon fragments produced by polymer pyrolysis.     

An extension of the method of least squares

The standard method of least squares assumes that there is a linear relationship relating two variables, only one of which has an error in it. A discussion of the validity of this assumption leads to the desirability of a technique which applies to the more general situation where both variables are subject to error. This includes relating the relevant statistical distance to be minimized to the Euclidean distance. The corresponding statistical formulae are derived, and simple comparisons are then made for various ranges of the statistical parameters.     

Continuum limits for classical sequential growth models

A random graph order, also known as a transitive percolation process, is defined by taking a random graph on the vertex set {0,…,n ? 1} and putting i below j if there is a path i = i₁…i_k = j in the graph with i₁ < … < i_k. Rideout and Sorkin 14 provide computational evidence that suitably normalized sequences of random graph orders have a “continuum limit.” We confirm that this is the case and show that the continuum limit is always a semiorder. Transitive percolation processes are a special case of a more general class called classical sequential growth models. We give a number of results describing the large‐scale structure of a general classical sequential growth model. We show that for any sufficiently large n, and any classical sequential growth model, there is a semiorder S on {0,…,n ‐ 1} such that the random partial order on {0,…,n ‐ 1} generated according to the model differs from S on an arbitrarily small proportion of pairs. We also show that, if any sequence of classical sequential growth models has a continuum limit, then this limit is (essentially) a semiorder. We give some examples of continuum limits that can occur. Classical sequential growth models were introduced as the only models satisfying certain properties making them suitable as discrete models for spacetime. Our results indicate that this class of models does not contain any that are good approximations to Minkowski space in any dimension ≥ 2. © 2009 Wiley Periodicals, Inc. Random Struct. Alg., 2010     

Estimating the limits for statistical process control charts: A direct method improving upon the bootstrap

This paper considers the problem of finding limits for a statistical process control (SPC) chart for the process mean, when the process distribution is unknown. The bootstrap method estimates these limits relying on Monte Carlo methods, which are subject to simulation errors. Therefore this paper develops a computationally efficient enumeration method for exact calculations of the control limits.     

Fast Reaction Limit and Large Time Behavior of Solutions to a Nonlinear Model of Sulphation Phenomena

We investigate the qualitative behavior of solutions to the initial-boundary value problem on the half-line for a nonlinear system of parabolic equations, which arises to describe the evolution of the chemical reaction of sulphur dioxide with the surface of calcium carbonate stones. We show that, both in the fast reaction limit and for large times, the solutions of this problem are well described in terms of the solutions to a suitable one phase Stefan problem on the same domain.     

关于极限的讲法

众所周知,极限是高等数学所有重要概念的基础,又是教学的公认难点,特别是用"ε-δ"语言证明极限的题目.本文是作者在新疆大学讲授这一内容时所做的一些探索性工作,主要方法是:提前引入无穷小概念,以特殊无穷小为标准尺对极限证明题进行论证,使得证明思路清晰、论述简单、易于掌握.     

Delta shocks and vacuum states in vanishing pressure limits of solutions to the relativistic Euler equations for polytropic gases

The Riemann solutions for the Euler system of conservation laws of energy and momentum in special relativity for polytropic gases are considered. It is rigorously proved that, as pressure vanishes, they tend to the two kinds of Riemann solutions to the corresponding pressureless relativistic Euler equations: the one includes a delta shock, which is formed by a weighted δ-measure, and the other involves vacuum state.     

A foundation for real recursive function theory

The class of recursive functions over the reals, denoted by , was introduced by Cristopher Moore in his seminal paper written in 1995. Since then many subsequent investigations brought new results: the class was put in relation with the class of functions generated by the General Purpose Analogue Computer of Claude Shannon; classical digital computation was embedded in several ways into the new model of computation; restrictions of were proved to represent different classes of recursive functions, e.g., recursive, primitive recursive and elementary functions, and structures such as the Ritchie and the Grzergorczyk hierarchies.The class of real recursive functions was then stratified in a natural way, and and the analytic hierarchy were recently recognised as two faces of the same mathematical concept.In this new article, we bring a strong foundational support to the Real Recursive Function Theory, rooted in Mathematical Analysis, in a way that the reader can easily recognise both its intrinsic mathematical beauty and its extreme simplicity. The new paradigm is now robust and smooth enough to be taught. To achieve such a result some concepts had to change and some new results were added.     

Iterated function systems, Ruelle operators, and invariant projective measures

We introduce a Fourier-based harmonic analysis for a class of discrete dynamical systems which arise from Iterated Function Systems. Our starting point is the following pair of special features of these systems. (1) We assume that a measurable space comes with a finite-to-one endomorphism which is onto but not one-to-one. (2) In the case of affine Iterated Function Systems (IFSs) in , this harmonic analysis arises naturally as a spectral duality defined from a given pair of finite subsets in of the same cardinality which generate complex Hadamard matrices.

Our harmonic analysis for these iterated function systems (IFS) is based on a Markov process on certain paths. The probabilities are determined by a weight function on . From we define a transition operator acting on functions on , and a corresponding class of continuous -harmonic functions. The properties of the functions in are analyzed, and they determine the spectral theory of . For affine IFSs we establish orthogonal bases in . These bases are generated by paths with infinite repetition of finite words. We use this in the last section to analyze tiles in .