Fonctions analytiques Cliffordiennes

We define analytic functions within Clifford Algebras CL, and study their trigonometric properties. We write the addition formulas when their arguments, A and B in CL, commute, this generalizes ordinary trigonometry. We examine in particular the case A² = 1.      

Isometric Isomorphisms Between Banach Algebras Related to a Certain Class of Clifford Topological Semigroups

In the present paper it is shown that if S₁ and S₂ are two Clifford topological semigroups satisfying certain conditions and T is an isometric isomorphism of LUC(S₁*) onto LUC(S₂*), then T maps S₁ topologically isomorphically onto S₂. Furthermore, T maps M ^l _n(S₁) (M(S₁), respectively) isometrically isomorphically onto M ^l _n(S₂) (M(S₂), respectively). Indeed, we have obtained a generalization of a well-known result of Ghahramani, Lau and Losert for locally compact groups to a more general setting of Clifford topological semigroups.     

Experiences in Expert Systems

This paper describes some work carried out in the Scientific Research and Development Branch (SRDB) of the Home Office, intended to contribute to an overall aim of building up internal expertise in the field of expert systems. This was done by carrying out a number of pilot and demonstrator projects, two of which are described in some detail. The plan, which proved successful, was to build as far as possible on the relevant skills already possessed by an OR group in the branch. The lessons learned from these are summarized in the hope that they will be of use to other groups who wish to become involved in this important area.     

Nanotechnology in the Chemical Industry – Opportunities and Challenges

The traditional chemical industry has become a largely mature industry with many commodity products based on established technologies. Therefore, new product and market opportunities will more likely come from speciality chemicals, and from new functionalities obtained from new processing technologies as well as new microstructure control methodologies. It is a well-known fact that in addition to its molecular structure, the microstructure of a material is key to determining its properties. Controlling structures at the micro- and nano-levels is therefore essential to new discoveries. For this article, we define nanotechnology as the controlled manipulation of nanomaterials with at least one dimension less than 100nm. Nanotechnology is emerging as one of the principal areas of investigation that is integrating chemistry and materials science, and in some cases integrating these with biology to create new and yet undiscovered properties that can be exploited to gain new market opportunities. In this article market opportunities for nanotechnology will be presented from an industrial perspective covering electronic, biomedical, performance materials, and consumer products. Manufacturing technology challenges will be identified, including operations ranging from particle formation, coating, dispersion, to characterization, modeling, and simulation. Finally, a nanotechnology innovation roadmap is proposed wherein the interplay between the development of nanoscale building blocks, product design, process design, and value chain integration is identified. A suggestion is made for an R&D model combining market pull and technology push as a way to quickly exploit the advantages in nanotechnology and translate these into customer benefits.     

When should you sack a football manager? Results from a simple model applied to the English Premiership

What strategy should a football (soccer, in American parlance) club adopt when deciding whether to sack its manager? This paper introduces a simple model assuming that a club's objective is to maximize the number of league points that it scores per season. The club's strategy consists of three choices: the length of the honeymoon period during which it will not consider sacking a new manager, the level of the performance trapdoor below which the manager get the sack, and the weight that it will give to more recent games compared to earlier ones. Some data from the last six seasons of the English Premiership are used to calibrate the model. At this early stage of the research, the best strategy appears to have only a short honeymoon period of eight games (much less than the actual shortest period of 12 games), to set the trapdoor at 0.74 points per game, and to put 47% of the weight on the last five games. A club adopting this strategy would obtain on average 56.8 points per season, compared to a Premiership average of 51.8 points.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

Naphthalimide-thiazoles as novel photonucleases: molecular design, synthesis, and evaluation

A new family of photonucleases, naphthalimide-thiazoles was synthesized and evaluated. These compounds intercalated into DNA efficiently and damaged DNA photochemically at concentrations as low as 5 μM. Mechanistic experiment suggests that a novel naphthalimide-thiazole radical produced via an excited triple state might be involved in the DNA photodamage. Different activity may arise from the impact of substituents at 2-phenyl ring of thiazole on the electron population of excited triple state according to AM1 semi-empirical calculation.