Multicriteria Goal Games

In this paper, we deal with multicriteria matrix games. Different solution concepts have been proposed to cope with these games. Recently, the concept of Pareto-optimal security strategy which assures the property of security in the individual criteria against an opponent's deviation in strategy has been introduced. However, the idea of security behind this concept is based on expected values, so that this security might be violated by mixed strategies when replications are not allowed. To avoid this inconvenience, we propose in this paper a new concept of solution for these games: the G-goal security strategy, which includes as part of the solution the probability of obtaining prespecified values in the payoff functions. Thus, attitude toward risk together with payoff values are considered jointly in the solution analysis.     

A simple Markov chain structure for the evolution of credit ratings

We focus on continuous Markov chains as a model to describe the evolution of credit ratings. In this work it is checked whether a simple, tridiagonal type of generator provides a good approximation to a general one. Three different tridiagonal approximations are proposed and their performance is checked against two generators, corresponding to a volatile and a stable period, respectively. Copyright © 2007 John Wiley & Sons, Ltd.     

Influence of Temperature and Time on the Stability of Silver in Silica Sol-Gel Glasses

The darkening of silica sol-gel glasses doped with 0.05 mol% silver was studied. Six sols were prepared from TEOS and silver nitrate. Different additives were used, to influence the chemical and physical states of silver: oxidizing or reducing agents (H₂O₂, As₂O₅), colloid stabilizer (sodium citrate) and network modifiers (Li₂O, CaO). Sols were gelified at 60°C and densified at 600°C. The samples without additives and those prepared with H₂O₂ at room temperature even if they were protected from light. With increased temperature, the darkening became samples were heated above, 400°C, reversible bleaching took place. This darkening-bleaching is of thermal nature (“thermochromic effect”) and seems to be determined by a reversible aggregation-disaggregation of tiny silver particles. The presence of sodium citrate, as an additive delayed the darkening effect and the presence of CaO delayed it even further. Lithium oxide inhibited it totally.     

The existence of ferrous ferricyanide

Evidence in the literature on the synthesis of ferrous ferricyanide is critically discussed. Pyrolysis and pressure effects on Prussian Blue lead to ferrous ferrocyanide together with decomposition by-products, and not to ferrous ferricyanide. The latter compound could be a precursor in the formation of Turnbull's Blue or an excited state of Prussian Blue, but it is not a stable chemical species.     

On the critical behavior of the magnetization in high-dimensional Ising models

We derive rigorously general results on the critical behavior of the magnetization in Ising models, as a function of the temperature and the external field. For the nearest-neighbor models it is shown that ind4 dimensions the magnetization is continuous atT _c and its critical exponents take the classical values=3 and=1/2, with possible logarithmic corrections atd=4. The continuity, and other explicit bounds, formally extend tod>3 1/2. Other systems to which the results apply include long-range models ind=1 dimension, with 1/|x–y| couplings, for which 2/(–1) replacesd in the above summary. The results are obtained by means of differential inequalities derived here using the random current representation, which is discussed in detail for the case of a nonvanishing magnetic field.Research supported in part by NSF grant PHY-8301493 A02, and by a John S. Guggenheim Foundation fellowship (M.A.).     

Accurate intermolecular ground state potential of the Ar-N2 van der Waals complex

After carrying out a systematic basis set convergence study, we evaluate several ground state potential energy surfaces of the Ar-N(2) van der Waals complex at the coupled cluster singles and doubles model including connected triples corrections. We use the aug-cc-pVXZ (X=5,Q,D) and the daug-cc-pVQZ basis sets augmented with a set of 3s3p2d1f1g (denoted 33211) and 3s3p2d2f1g (denoted 33221) midbond functions, respectively. aug-cc-pVTZ-33211 results were available in the literature. The aug-cc-pV5Z-33211 (daug-cc-pVQZ-33221) surface is characterized by a T-shaped minimum at R(e)=3.709 (3.701) A and of 99.01 (102.50) cm(-1), and a linear saddle point at 4.260 (4.257) A and D(e)=75.28 (79.73) cm(-1). These results are compared with the values provided by the semiempirical potentials available, and those of previous theoretical studies. The basis set convergence of the intermolecular potentials is also analyzed. From the potentials the rovibronic spectroscopic properties are determined. We study the basis set convergence of the rotational frequencies. The binding parameters that characterized the aug-cc-pVTZ-33211 surface are reasonable, but the surface is not good enough to evaluate the microwave spectra. The aug-cc-pVQZ-33211 basis set results considerably improve the triple zeta and are close to the aug-cc-pV5Z-33211. Considering the small differences between the quadruple and the quintuple zeta surfaces, the latter results can be expected to be close to convergence. At this level the differences with respect to the accurate experimental frequencies are in the order of 0.7%. In the case of the daug-cc-pVXZ-33211,33221 (X=5,Q,T,D) series, the convergence of the interaction energies with respect to basis set improvement is not so smooth. The errors in the frequencies obtained with the daug-cc-pVQZ-33221 basis set with respect to experiment are in the order of 0.4%.     

Reaction of allylsilanes and allylstannanes with alkynes catalyzed by electrophilic late transition metal chlorides

The intramolecular reaction of allylsilanes and allylstannanes with alkynes proceeds catalytically in the presence of Pt(II), Pd(II), Ru(II), and Au(III) chlorides. Although more limited, AgOTf also catalyzes the cyclization. Usually, PtCl2 as the catalyst in methanol or acetone gives the best results. The reaction proceeds by exo attack of the allyl nucleophile on the alkyne to form five- or six-membered ring carbocycles. The reaction generally proceeds with anti stereoselectivity. However, a terminally substituted trimethylsilyl derivative reacts by a syn-type addition. The intermediate alkenylpalladium complex has been trapped with allyl chloride to form an allylated derivative with an additional carbon-carbon bond.