Evaluating Individual Market Power in Electricity Markets via Agent-Based Simulation

We use agent-based simulation in a coordination game to analyse the possibility of market power abuse in a competitive electricity market. The context of this was a real application to the England and Wales electricity market as part of a Competition Commission Inquiry into whether two particular generators could profitably influence wholesale prices. The research contributions of this paper are both in the areas of market power and market design policy issues for electricity markets, and in the methodological use of large industry-wide evolutionary simulation models.     

Asymptotics of periodic subelliptic operators

We establish that heat diffusion with periodic conductivity is governed by two scales. The small time diffusion is described by the geodesic distance but the large time behaviour is dictated by the distance associated with an homogenized system obtained by a suitable averaging process. Our methods are quite general and apply to diffusion on a stratified Lie group.     

A matrix method for modelling liquid crystal textures

A simple method for modelling the textures of liquid-crystalline phases, recently proposed by Bedford et al., is here rewritten in matrix form. A formal similarity is found between their method and the continuum theory of liquid crystals. Disclination patterns are simulated by solving a modified matrix equation.     

Relative locality of derivations

Let H and K be symmetric linear operators on a C¹-algebra $\text{U}$ with domains D(H) and D(K). H is defined to be strongly K-local if $\text{ω(K(A)}{}^1\text{K(A)) = 0}$ implies $\text{ω(H(A)}{}^1\text{H(A)) = 0}$ for A?D(H) ∩ D(K) and ω in the state space of $\text{U}$, and H is completely strongly K-local if $\text{Ω(K(A)}{}^1\text{K(A))=0}$ implies $\text{Ω(H(A)}{}^1\text{H(A))=0}$ for A ∈ D(H) ∩ D(K) and Ω in the state of $\text{U}$, and H is cpmpletely strongly K-local if $\text{H??}{}_{\mathrm{n}}$ is $\text{K??}{}_{\mathrm{n}}$-local on U?M_n for all n ? 1, where $\text{1}$_n is the identity on the n × n matrices M_n. If $\text{U}$ is abelian then strong locality and complete strong locality are equivalent. The main result states that if τ is a strongly continuous one-parameter group of ¹-automorphisms of $\text{U}$ with generator δ₀ and δ is a derivation which commutes with τ and is completely strongly δ₀-local then δ generates a group α of ¹-automorphisms of $\text{U}$. Various characterizations of α are given and the particular case of periodic τ is discussed.     

The graph isomorphism disease

The graph isomorphism problem—to devise a good algorithm for determining if two graphs are isomorphic—is of considerable practical importance, and is also of theoretical interest due to its relationship to the concept of NP-completeness. No efficient (i.e., polynomial-bound) algorithm for graph isomorphism is known, and it has been conjectured that no such algorithm can exist. Many papers on the subject have appeared, but progress has been slight; in fact, the intractable nature of the problem and the way that many graph theorists have been led to devote much time to it, recall those aspects of the four-color conjecture which prompted Harary to rechristen it the “four-color disease.” This paper surveys the present state of the art of isomorphism testing, discusses its relationship to NP-completeness, and indicates some of the difficulties inherent in this particularly elusive and challenging problem. A comprehensive bibliography of papers relating to the graph isomorphism problem is given.     

A versatile approach to analogues of the cannabinoid-like anti-emetic nonabine (BRL 4664)

Analogues of the cannabinoid-like anti-emetic nonabine (BRL 4664), in which the 4-pyridinyl and 1,2-dimethylheptyl groups have been replaced by other aryl and alky groups respectively, have been synthesised from the appropriate resorcinol by a novel procedure. The route has been shown to be of general applicability, although in the case of nonabine itself the procedure does not represent a viable alternative to that previously published.     

A serendipitous route to the benzidene nucleus. Structural elucidation by noeds.

The epimeric indenones (3) and (4) are readily synthesised and rapidly formed by treating bis(p-methoxyphenylcyclopropyl) ketone (2) with stannic chloride in nitromethane. The structure of (3) was determined by X-ray crystallography and that of (4) by NOEDS.     

A mild reduction of aliphatic nitro compounds to imines for further in situ reactions : A simple synthesis of pyrroles

Tributylphosphine-diphenyldisulphide reduces nitroalkanes to imines which can be trapped intramolecularly to give pyrroles.     

A non-factorial algorithm for canonical numbering of a graph

A graph certificate or canonical form is a short unique (up to isomorphism) representation of the graph. Thus two graphs are isomorphic iff their certificates are identical. In this paper an O(cⁿ) graph isomorphism algorithm which also yields a certificate of the graph is presented. The certificate produced by this algorithm is a canonical numbering of the vertices of the graph.     

On the existence of hydrodynamic fluctuation forces

The form of fluctuating hydrodynamic forces has been derived recently [R.B. Jones, Physica 105A (1981) 395] from the stochastic fluid equations of Landau and Lifshitz. We show by general physical arguments as well as by a direct calculation that such forces do not exist in the classical limit.