Location of terror response facilities: A game between state and terrorist

We study a leader follower game with two players: a terrorist and a state where the later one installs facilities that provide support in case of a terrorist attack. While the Terrorist attacks one of the metropolitan areas to maximize his utility, the State, which acts as a leader, installs the facilities such that the metropolitan area attacked is the one that minimizes her disutility (i.e., minimizes ‘loss’). We solve the problem efficiently for one facility and we formulate it as a mathematical programming problem for a general number of facilities. We demonstrate the problem via a case study of the 20 largest metropolitan areas in the United States.     

Sparse pseudorandom distributions

The existence of sparse pseudorandom distributions is proved. These are probability distributions concentrated in a very small set of strings, yet it is infeasible for any polynomial-time algorithm to distinguish between truly random coins and coins selected according to these distributions. It is shown that such distributions can be generated by (nonpolynomial) probabilistic algorithms, while probabilistic polynomial-time algorithms cannot even approximate all the pseudorandom distributions. Moreover, we show the existence of evasive pseudorandom distributions which are not only sparse, but also have the property that no polynomial-time algorithm may find an element in their support, except for a negligible probability. All these results are proved independently of any intractability assumption.     

Simple Constructions of Almost k-wise Independent Random Variables

We present three alternative simple constructions of small probability spaces on n bits for which any k bits are almost independent. The number of bits used to specify a point in the sample space is (2 + o(1)) (log log n + k/2 + log k + log 1/?), where ? is the statistical difference between the distribution induced on any k bit locations and the uniform distribution. This is asymptotically comparable to the construction recently presented by Naor and Naor (our size bound is better as long as ? < 1/(k log n)). An additional advantage of our constructions is their simplicity.     

Divinylsiloxane‐bisbenzocyclobutene‐based polymer modified with polystyrene–polybutadiene–polystyrene triblock copolymers

Divinylsiloxane‐bisbenzocyclobutene (DVS‐bisBCB) polymer has very low dielectric constant and dissipation factor, good thermal stability, and high chemical resistance. The fracture toughness of the thermoset polymer is moderate due to its high crosslink density. A thermoplastic elastomer, polystyrene–polybutadiene–polystyrene triblock copolymer, was incorporated into the matrix to enhance its toughness. The cured thermoset matrix showed different morphology when the elastomer was added to the B‐staged prepolymer or when the elastomer was B‐staged with the DVS‐bisBCB monomer. Small and uniformly distributed elastomer domains were detected by transmission electron micrographs (TEM) in the former case, but TEM did not detect a separate domain in the latter case. A high percentage of the polystyrene–polybutadiene–polystyrene triblock copolymer could be incorporated into the DVS‐bisBCB thermoset matrix by B‐staging the triblock copolymer with the BCB monomer. The elastomer increased the fracture toughness of DVS‐bisBCB polymer as indicated by enhanced elongation at break and increased K1c values obtained by the modified edge‐lift‐off test. Elastomer modified DVS‐bisBCB maintained excellent electrical properties, high T_g and good thermal stability, but showed higher coefficient of linear thermal expansion values. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1591–1599, 2006     

Rapid liquid chromatography-ultraviolet determination of organic acids and phenolic compounds in red wine and must

A reversed-phase liquid chromatography-ultraviolet (LC-UV) method is proposed for the rapid simultaneous analysis of the main carboxylic acids and polyphenols in must and wine. Good resolution was obtained for citric, tartaric, malic, lactic, acetic, caffeic, ellagic and gallic acids, (-)-epicatechin, quercetin and resveratrol. A novel silica-based column containing ether-linked phenyl groups, with polar end-capping and suitable for low-pH aqueous mobile phases was used and found to be superior to others tested. The method employed a mixture of 0.2% TFA in water and acetonitrile as eluents, showed linearity and precision, and was applied to samples of must and wine.     

Form fluctuations of carbosilane dendrimers in dilute solution: a study using neutron spin echo spectroscopy

A series of carbosilane dendrimers with perfluorinated end groups has been prepared. The structure of these molecules in dilute solution is studied using small angle neutron scattering. For generations g<3 we find a non-spherical shape of the particles and a tendency for aggregation. This result is supported by the analysis of the diffusion coefficient obtained from photon correlation spectroscopy. The overall shape of the molecules is that of a core-shell particle. The generation 4 molecule is obtained as a compact sphere. Neutron spin echo spectroscopy reveals a relaxation time which is attributed to the form fluctuations of this particle.     

High regio-, chemo-, and stereoselectivity via low-temperature 4 + 3 cycloadditions. Convergent synthesis of multifunctionalized vinylmetals (M = Si, Sn) and S-vinyl benzenecarbothioates

A series of enantiomerically pure 8-oxabicyclo[3.2.1]oct-6-en-3-ones functionalized in the unsaturated two-carbon bridge has been prepared by the title reaction. Carbocation reactivity has been fined-tuned at -95 degrees C and adjusted to diene nucleophilicity. Conventional electrophilic substitution of 3-silylated and 3-stannylated furan is suppressed in favor of the rapid 4 + 3 cycloaddition mode. In the case of cycloadduct 13A, stereoselectivity (17:1) is perfectly matched to regioselectivity (17:1). High stereoselection as well as unprecedented regioselection and chemoselection is attributed to the low-temperature cycloaddition protocol and the design of chiral auxiliary and tether.     

Oxidation of propene in the gas phase

A series of laboratory and modelling experiments on the oxidation of propene in the gas phase has been undertaken to determine conditions which give high yields of propene oxide. The conditions under which the experiments were conducted were 505–549 K and up to 4 bar pressure. It is proposed that propene oxide is formed from propene by reaction with several peroxy radicals including HO₂ and CH₃CO₃. However, one of the more important radicals is hydroxypropylperoxy. Its reaction with propene, under these conditions is more important than concerted decomposition to formaldehyde and acetaldehyde. © 1995 John Wiley & Sons, Inc.     

Rigidity of circle domains whose boundary hasσ-finite linear measure

Summary Let be a circle domain in the Riemann sphere whose boundary has -finite linear measure. We show that is rigid in the sense that any conformal homeomorphism of onto any other circle domain is equal to the restriction of a Möbius transformation. Previously, Kaufman and Bishop have independently found examples of non-rigid circle, domains whose boundary is a Cantor set of (Hausdorff) dimension one.Oblatum 19-VI-1992 & 2-IV-1993Supported by NSF and Sloan Foundation