The Iyengar Type Inequalities with Exact Estimations and the Chebyshev Central Algorithms of Integrals

In this paper, both low order and high order extensions of the Iyengar type inequality are obtained. Such extensions are the best possible in the same sense as that of the Iyengar inequality. hzrthermore, the Chebyshev central algorithms of integrals for some function classes and some related problems are also considered and investigated.     

The effects of crystal structure on optical absorption/photoluminescence of bis(8-hydroxyquinoline)zinc

In this paper, the transformation processes of two types of bis(8-hydroxyquinoline)zinc: Znq₂ dihydrate and anhydrous (Znq₂)₄ were investigated by X-ray diffraction (XRD), infrared spectra (IR), scanning electron microscope (SEM), differential scanning calorimetry (DSC) and thermogravimetry (TG). The effects of crystal structure on optical properties of bis(8-hydroxyquinoiline)zinc were analyzed. Znq₂ dihydrate can be transformed into anhydrous (Znq₂)₄ during heating under vacuum. Reversal transformation occurs by the interaction between chloroform and (Znq₂)₄. But (Znq₂)₄ was partially transformed into Znq₂ dihydrate by the interaction between ethanol and (Znq₂)₄. The different molecular structure results in different crystal stacking and electronic structure, thereby affect its optical properties.     

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.     

Solid-state Electrochemistry of Gadolinium Hexacyanoferrate Modified Electrode and Electrocatalytic Properties of Gadolinium Hexacyanoferrate

A new electroactive polynuclear inorganic compound of rare earth metal, gadolinium hexacyanoferrate (GdHCF), was prepared and characterized using the techniques of FTIR spectroscopy, thermogravimetric analysis (TG), UV-Vis spectrometry, X-ray photoelectron spectroscopy (XPS), ICP atomic emission spectroscopy, and EDX. The results of ICP atomic emission spectroscopy, EDX, and TGA indicated that the prepared GdHCF sample had a stoichiometry of NaGdFe(CN)₆·12H₂O (when GdHCF was prepared in NaCl solution). The FTIR spectrum of GdHCF showed that there were two types of water molecules in the structure of GdHCF: one was the interstitial water (5 H₂O), which resulted from the association of water due to H-bonding, and the other was water coordinated with Gd (7 H₂O). The results obtained using XPS showed that the oxidation state of Fe and Gd in the GdHCF sample was +2 and +3, respectively. GdHCF was immobilized on the surface of spectroscopically pure graphite (SG) electrode forming the GdHCF/SG electrode, and the solid-state electrochemistry of the resultant electrode was studied using cyclic voltammetry. The cyclic voltammetric results indicated that the GdHCF/SG electrode exhibited a pair of well-defined and stable redox peaks with the formal potential of E^0′=(197±3) mV. The effects of the concentration of the supporting electrolyte on the electrochemical characteristics of GdHCF were studied, and the results showed that the value of E^0′ increased linearly with the activity of the cationic ion of the supporting electrolyte (lga_Na⁺), with a slope of 54.1 mV, which may become a novel method for determining the activity of Na⁺ in solution. Further experimental results indicated that GdHCF had electrocatalytic activities toward the oxidation of dopamine (DA) and ascorbic acid (AA), and the electrocatalytic current increased linearly with the concentration of DA (or AA) in the range of 1.0–10.0 mmol·L^?1 (for DA) or 0.5–20.0 mmol·L^?1 (for AA).     

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.