Collective Strategy Condensation: When Envy Splits Societies

Human societies are characterized by three constituent features, besides others. (A) Options, as for jobs and societal positions, differ with respect to their associated monetary and non-monetary payoffs. (B) Competition leads to reduced payoffs when individuals compete for the same option as others. (C) People care about how they are doing relatively to others. The latter trait—the propensity to compare one’s own success with that of others—expresses itself as envy. It is shown that the combination of (A)–(C) leads to spontaneous class stratification. Societies of agents split endogenously into two social classes, an upper and a lower class, when envy becomes relevant. A comprehensive analysis of the Nash equilibria characterizing a basic reference game is presented. Class separation is due to the condensation of the strategies of lower-class agents, which play an identical mixed strategy. Upper-class agents do not condense, following individualist pure strategies. The model and results are size-consistent, holding for arbitrary large numbers of agents and options. Analytic results are confirmed by extensive numerical simulations. An analogy to interacting confined classical particles is discussed.     

Unions of three starshaped sets in R2

LetS be a compact, simply connected set inR ². If every boundary point ofS is clearly visible viaS from at least one of the three pointsa, b, c, thenS is a union of three starshaped sets whose kernels containa, b, c, respectively. The result fails when the number three is replaced by four.As a partial converse, ifS is a union of three starshaped sets whose kernels containa, b, c, respectively, then the set of points in the boundary ofS clearly visible from at least one ofa, b, orc is dense in the boundary ofS.Supported in part by NSF grant DMS-8705336.     

Three chiral vinyldioxaza­borocanes

The structures of three chiral vinyldioxaza­borocanes are reported, namely (2E)‐ and (2Z)‐6‐benzyl‐2‐buten‐2‐yl‐1,3,6,2‐dioxaza­borocane, C₂₇H₃₀BNO₂, (II) and (III), respectively, and (2Z)‐2‐buten‐2‐yl‐6‐isobutyl‐1,3,6,2‐dioxaza­boro­cane, C₂₄H₃₂BNO₂, (IV). These compounds may be useful in asymmetric reactions. In the structures reported here, the N—B donor–acceptor bond is longer than in any previously reported analogous compounds.     

Degradation of epoxy polymers: 2—Mechanism of thermal degradation of bisphenol-A diglycidyl ether

In a previous paper, some 15 compounds were positively identified among the products of thermal degradation of bisphenol-A diglycidyl ether. The structures of an additional 22 compounds, all aromatic, were speculated upon on the basis of mass spectral analysis. In the present paper, mechanisms are proposed to account for all these products and the characteristics of their formation in the overall degradation process.     

Activation of alkenes and H2 by [Fe]-H2ase model complexes

The established ability of the Fe(II) bridging hydride species (micro-H)(micro-pdt)[Fe(CO)2(PMe3)]2+, 1-H+, to take-up and heterolytically activate dihydrogen, resulting in H/D scrambling of H2/D2 and H2/D2O mixtures (Zhao et al. Inorg. Chem. 2002, 41, 3917) has prompted a study of simultaneous alkene/H2 activation by such [Fe]H2ase model complexes. That the required photolysis produced an open site was substantiated by substitution of CO in 1-H+ by CH3CN with formation of structurally characterized [(micro-H)(micro-pdt)[Fe(CO)2(PMe3)][Fe(CO)(CH3CN)(PMe3)]]+[PF6]-. Under similar photolytic conditions, H/D exchange reactions between D2 and terminal alkenes (ethylene, propene and 1-butene), but not bulkier alkenes such as 2-butene or cyclohexene, were catalyzed by 1-H+ and the edt (SCH2CH2S) analogue, 2-H+. Substantial regioselectivity for H/D exchange at the internal vinylic hydrogen was observed. The extent to which the olefins were deuterium enriched vs deuterated was catalyst dependent. The stabilizing effect of the binuclear chelating ligands, SCH2CH2CH2S, pdt, and SCH2CH2S, edt, is required for the activity of binuclear catalysts, as the mono-dentate micro-SEt analogue decomposed to inactive products under the photolytic conditions of the catalysis. Reactions of 1 and 2 with EtOSO2CF3 yielded the S-alkylated products, [(micro-SCH2CH2CH2SEt)[Fe(CO)2(PMe3)]2]+[SO3CF3]- (1-Et+), and 2-Et+, rather than micro-C2H5 analogues to the micro-H of 1-H+. The stability and lack of reactivity toward H2 of 1-Et+ and 2-Et+, indicates they are not on the reaction path of the olefin/D2 H/D exchange process. A mechanism with olefin binding to an open site created by CO loss and formation of an Fe-(CH2CHDR) intermediate is indicated. A likely role of a binuclear chelate effect is implicated for the unique S-XXX-S cofactor in the active site of [Fe]H2ase.     

Multiresidue determination of fluoroquinolones in shrimp by liquid chromatography-fluorescence-mass spectrometry

An efficient multiresidue method for analysis of fluoroquinolones in shrimp has been developed in which quantitation by fluorescence and confirmation by Multiple Stage Mass Spectrometry (MS) is achieved simultaneously. In this method, shrimp tissue is extracted with ammoniacal acetonitrile and the extract is defatted and then evaporated. After dissolution in basic phosphate buffer, fluoroquinolones in the extract are separated by liquid chromatography and quantitated, taking advantage of their intense fluorescence. Eluate from the fluorescence detector enters the MS, which allows for confirmation by monitoring ratios of 2 prominent product ions in the MS3 or MS2 spectrum. Using this method, 8 fluoroquinolones have been analyzed in shrimp samples fortified at 10, 25, 50, or 100 ppb levels. Recoveries for desethyleneciprofloxacin, norfloxacin, ciprofloxacin, danofloxacin, enrofloxacin, orbifloxacin, sarafloxacin, and difloxacin ranged from 75 to 92%, with relative standard deviation values of <6%. The limits of quantitation ranged from 0.1 to 1 ng/g. Enrofloxacin and ciprofloxacin were also successfully determined in enrofloxacin-incurred shrimp using this method.     

Synthesis of spiro-fused (C5)-isoxazolino-(C4)-pyrazolones (1-oxa-2,7,8-triazaspiro[4,4]-2,8-dien-6-ones) via 1,3-dipolar cycloaddition and cycloelimination

An efficient and selective method for the synthesis of spiro-fused (C5)-isoxazolino-(C4)-pyrazolones (C) is reported. The process consists of utilizing the Baylis-Hillman reaction-or a quicker, stepwise MAC procedure-to give I followed by 1,3-dipolar cycloaddition and Swern oxidation to give beta-ketoesters H, which were condensed with hydrazine derivatives to provide hydrazones that underwent cycloelimination. These novel spiro-fused (C5)-isoxazolino-(C4)-pyrazolones were confirmed by spectroscopic analysis as well as single-crystal X-ray of 5. We also concluded that all condensations/cycloeliminations, except with hydrazine itself, were more effective with catalysts or higher reaction temperatures. For example, TiCl(4) was an efficient catalyst for hydrazone formation and cycloelimination with methylhydrazine, while phenyl-, benzyl-, and (4-methoxyphenyl)hydrazine reacted effectively without catalyst in refluxing xylene.     

Synthesis and characterization of the non-Kekulé, singlet biradicaloid Ar'Ge(micro-NSiMe(3))(2)GeAr' (Ar' = 2,6-Dipp(2)C(6)H(3), Dipp = 2,6-i-Pr(2)C(6)H(3))

Reaction of Ar'GeGeAr' (1) with an excess of Me3SiN3 gives the non-Kekulé, biradicaloid Ar'Ge(mu-NSiMe3)2GeAr' (3, Ar' = 2,6-Dipp2C6H3, Dipp = 2,6-i-Pr2C6H3) which has a planar Ge2N2Si2 array and pyramidal geometry at the germaniums. DFT calculations for the model MeGe(mu-NSiH3)2GeMe indicate no Ge-Ge bonding and a singlet ground state. The calculated energy difference between the optimized singlet and triplet states is 17.51 kcal/mol.     

Synthesis of β-ketoenamine donors having O, N, Se/Te donor functionalities and their reaction chemistry with Pd(II) and Pt(II) metal ions

Monoanionic tridentate ligands LH_a and LH_b containing ONSe and ONTe donor sequences and their Pd²⁺ and Pt²⁺ derivatives were synthesized and characterized. The formation of a five- and a six-membered ring around the central metal atom and associative phenomena in solutions provide extra stability to the metal complexes.