Some new classes of stochastic order relations among arithmetic random variables, with applications in actuarial sciences

Recently, Fishbum and Lavalle (1995) and Lefèvre and Utev (1996) have considered some stochastic order relations specific for arithmetic random variables. The present work is concerned with these orderings, together with two other classes of stochastic order relations closely related. First, attention is paid to characterizations and various properties of all these orderings. Then, sufficient conditions of crossing-type for the two new classes of orderings are derived and extrema among discrete random variables are deduced. This is applied in actuarial sciences to obtain new bounds for the classical single life premiums as well as for the probability of ruin in the compound binomial risk model.     

Automorphisms of Green Orders and Their Derived Categories

In an earlier paper, Raphaël Rouquier and the author introduced the group of self-equivalences of a derived category. In the case of a Brauer tree algebra, we determined a nontrivial homomorphism of the Artin braid group to this group of self-equivalences. The class of Brauer tree algebras include blocks of finite group rings over a large enough field with cyclic defect groups. In the present paper we give an integral version of this homomorphism. Moreover, we identify some interesting arithmetic subgroups with natural groups of self-equivalences of the derived category.     

凸度量空间中单值和集值映象的公共不动点定理

§ 1.　Introduction　　Anecessaryandsufficientconditionandasufficientconditiontoensurethataset valuedmappingandasingle valuedmappinginacompletemetricspaceandacompleteconvexmetricspacehavingacommonfixedpointarerespectivelygivenin [1 ] .Meanwhilethemainresultsin[2 ]— [5]areimprovedandextendedin [1 ] .Inthispaper ,theexistenceatcommonfixedpointsoftwoset valuedmappingandasing valuedmappingwerestudied ,andthecorrespond ingresultsin [1 ]— [5]wereextendedandimproved .Let(X ,d)beanon emptymetricspa…     

Compatible Lie Brackets and Integrable Equations of the Principal Chiral Model Type

We consider two classes of integrable nonlinear hyperbolic systems on Lie algebras. These systems generalize the principal chiral model. Each system is related to a pair of compatible Lie brackets and has a Lax representation, which is determined by the direct sum decomposition of the Lie algebra of Laurent series into the subalgebra of Taylor series and the complementary subalgebra corresponding to the pair. New examples of compatible Lie brackets are given.     

Pure quantitative characterization of finite simple groups

Let G be a finite group, and let π _e (G) be the set of all element orders of G. In this short paper we prove that π _e (B _n (q)) ≠ π _e (C _n (q)) for all odd q.      

Lax Pairs for Equations Describing Compatible Nonlocal Poisson Brackets of Hydrodynamic Type and Integrable Reductions of the Lamé Equations

We solve the problem of describing compatible nonlocal Poisson brackets of hydrodynamic type. We prove that for nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type, there exist special local coordinates such that the metrics and the Weingarten operators of both brackets are diagonal. The nonlinear evolution equations describing all nonsingular pairs of compatible nonlocal Poisson brackets of hydrodynamic type are derived in these special coordinates, and the integrability of these equations is proved using the inverse scattering transform. The Lax pairs with a spectral parameter for these equations are found. We construct various classes of integrable reductions of the derived equations. These classes of reductions are of an independent differential-geometric and applied interest. In particular, if one of the compatible Poisson brackets is local, we obtain integrable reductions of the classical Lamé equations describing all orthogonal curvilinear coordinate systems in a flat space; if one of the compatible brackets is generated by a constant-curvature metric, the corresponding equations describe integrable reductions of the equations for orthogonal curvilinear coordinate systems in a space of constant curvature.     

All-solid-state potentiometric sensors for ascorbic acid by using a screen-printed compatible solid contact

The development of all-solid-state potentiometric ion selective electrodes for monitoring of ascorbic acid, by using a screen-printed compatible solid contact is described. The applied methodology is based on the use of PVC membrane modified with some firstly-tested ionophores (triphenyltin(IV)chloride, triphenyltin(IV)hydroxide and palmitoyl-l-ascorbic acid) and a novel one synthesized in our laboratory (dibutyltin(IV) diascorbate). Synthesis protocol and some preliminary identification studies are given. A conductive graphite-based polymer thick film ink was used as an internal solid contact between the graphite electrode and the PVC membrane. The presence and the nature of the solid contact (plain or doped with lanthanum 2,6-dichlorophenolindophenol (DCPI)) seem to enhance the analytical performance of the electrodes in terms of sensitivity, dynamic range, and response time. The analytical performance of the constructed electrodes was evaluated with potentiometry, constant-current chronopotentiometry and electrochemical impedance spectroscopy (EIS). The interference effect of various compounds was also tested. The potential response of the optimized Ph₃SnCl-based electrode was linear against ascorbic acid concentration range 0.005-5.0 mM. The applicability of the proposed sensors in real samples was also tested. The detection limit was 0.002 mM ascorbic acid (50 mM phosphate, pH 5 in 50 mM KCl). The slope of the electrodes was super-Nernstian and pH dependent, indicating a mechanism involving a combination of charge transfer and ion exchange processes. Fabrication of screen-printed ascorbate ISEs has also been demonstrated.     

CHARACTERIZATION OF AMPHIPHILIC AND MICROPHASE SEPARATED GRAFT COPOLYMERS Ⅱ SURFACE CHARACTERIZATION AND IN VITRO BLOOD-COMPATIBILITY ASSESSMENT OF POLYSTYRENE-GRAFT-ω-STEARYLPOLY (ETHYLENE OXIDE)*

This paper reported the research results concerning the surface characterization ofpolystyrene-graft-w-stearyl poly(ethylene oxide) (PS-g-SPEO) by means of XPS,contactangle measurement and TEM, and its in vitro blood compatibility assessment by measuringthe plasma recalcification time (RT) and partial thromboplastin time (PTT). The XPSresults demonstrated that the surface and bulk composition of the PS-g-SPEO graftcopolymers differ remarkably from each other,and that SPEO component was constantlyenriched at the copolymer/air interface. Contact angle studies indicated that the surfacewater wettability can be adjusted effectively by changing the composition of the copolymer.PS-g-SPEO graft copolymers can undergo microphase separation as clearly illustrated byTEM photographs. The relationship between the surface properties of PS-g-SPEO graftcopolymer and its blood compatibility was also discussed.     

DETERMINATION OF DEGREE OF CRYSTALLINITY OF NYLON 1212 BY WIDE-ANGLE X-RAY DIFFRACTION

Based on the X-ray scattering intensity theory and using the approximate expression for the atomic scattering factor, the correction factors for three crystalline peaks and an amorphous peak of Nylon 1212 were calculated and the formula of degree of crystallinity of Nylon 1212 was derived by a graphic multipeak resolution method. The degree of crystallinity calculated from the WAXD method is compatible with those obtained by density and calorimetry methods.     

A simple method for the calculation of π-bond orders in alternant hydrocarbons

A new method for the calculation of bond orders in alternant hydrocarbons is presented. The method requires a summation over the contributions of various superposition diagrams. Quantitatively, the method is almost as reliable as PPP, and due to its simplicity it can be used for fast and relatively accurate calculation of bond orders. In addition some simple rules are derived, which in many cases can be used to predict the signs of bond orders between nonbonded atoms.Dedicated to Professor J. Koutecký on the occasion of his 65th birthdayResearch supported by the Robert A. Welch Foundation of Houston, Texas