A Bayesian Decision Theory Approach to Classification Problems

We address the classification problem where an item is declared to be from populationπ_jif certain of its characteristicsvare assumed to be sampled from the distribution with pdf f_j(vθ_j), wherej=1, 2, …, m. We first solve the two population classification problem and then extend the results to the generalmpopulation classification problem. Usually only the form of the pdf's is known. To use the classical classification rule the parameters,θ_j, must be replaced by their estimates. In this paper we allow the parameters of the underlying distributions to be generated from prior distributions. With this added structure, we obtain Bayes rules based on predictive distributions and these are completely determined. Using the first-order expansion of the predictive density, where the coefficients of powers ofn⁻¹remain uniformly bounded innwhen integrated, we obtain an asymptotic bound for the Bayes risk.     

Isolation of a Reactive Tricoordinate α‐Oxo Gold Carbene Complex

The [(P,P)Au=C(Ph)CO₂Et]⁺ complex 3 [where (P,P) is an o‐carboranyl diphosphine ligand] was prepared by diazo decomposition at ?40 °C. It is the first α‐oxo gold carbene complex to be characterized. Its crystallographic structure was determined and DFT calculations have been performed, unraveling the key influence of the chelating (P,P) ligand. The gold center is tricoordinate and the electrophilicity of the carbene center is decreased. Complex 3 mimics transient α‐oxo gold carbenes in a series of catalytic transformations, and provides support for the critical role of electrophilicity in the chemoselectivity of phenol functionalization (O?H vs. C?H insertion).     

A new tetrapyrazolic macrocycle. Synthesis and its use in extraction and transport of K, Na and Li

The synthesis of a new tetrapyrazolic macrocyclic structure with a functionalised arm is described. The complexing properties of this new compound towards alkali metal ions (K⁺, Na⁺, Li⁺) were studied by liquid-liquid extraction and liquid membrane transport processes. The extracted and the transport cation percentage were determined by atomic absorption measurements and UV spectroscopy.     

Incentive equilibrium in an overlapping-generations environmental game

We consider two overlapping generations that want to coordinate their strategies of working, consuming and controlling pollution. Since the cooperative solution is not an equilibrium, and hence is not a self-enforcing contract, a mechanism is required to sustain it. We show how incentive strategies, and the resulting incentive equilibrium, could provide such a mechanism. We also derive the conditions that ensure the credibility of these strategies.     

A new generalization of the KMOV cryptosystem

The KMOV scheme is a public key cryptosystem based on an RSA modulus \(n=pq\) where p and q are large prime numbers with \(p\equiv q\equiv 2\pmod 3\). It uses the points of an elliptic curve with equation \(y^2\equiv x^3+b\pmod n\). In this paper, we propose a generalization of the KMOV cryptosystem with a prime power modulus of the form \(n=p^{r}q^{s}\) and study its resistance to the known attacks.     

Characterization of v-sufficiency from the Newton filtration

The aim of this paper is to study the germ mappings : (ⁿ, 0)(^p, 0), more precisely, we formulate certain criteria for the v-sufficiency related to the Newton polyhedron. Our result implies in particular the criteria for v-sufficiency due to Kuo and Paunescu.This research was supported by the Japan Society for the Promotion of Science.Mathematics Subject Classification (2000): 14B05;58A35     

Reactivity of Gold Complexes towards Elementary Organometallic Reactions

For a while, the reactivity of gold complexes was largely dominated by their Lewis acid behavior. In contrast to the other transition metals, the elementary steps of organometallic chemistry—oxidative addition, reductive elimination, transmetallation, migratory insertion—have scarcely been studied in the case of gold or even remained unprecedented until recently. However, within the last few years, the ability of gold complexes to undergo these fundamental reactions has been unambiguously demonstrated, and the reactivity of gold complexes was shown to extend well beyond π‐activation. In this Review, the main achievements described in this area are presented in a historical context. Particular emphasis is set on mechanistic studies and structure determination of key intermediates. The electronic and structural parameters delineating the reactivity of gold complexes are discussed, as well as the remaining challenges.     

σ-Acceptor, Z-type ligands for transition metals

The ability of Lewis acids to coordinate to transition metals as σ-acceptor ligands was recognized as early as in the 1970's, but so-called Z-type ligands remained curiosities until the early 2000's. Over the last decade, significant progress has been made in this area, especially via the incorporation of Lewis acid moieties into multidentate, ambiphilic ligands. Our understanding of the nature and influence of TM → Z interactions has considerably improved and the scope of Lewis acids susceptible to behave as σ-acceptor ligands has been significantly extended. This feature article summarizes these recent achievements.