Unique effective action in two dimensional induced quantum gravity

The gauge dependence of the effective action in two dimensional induced gravity with non-local action is investigated. The unique effective action in this theory on flat background is also discussed. The configuration-space metric dependence of the unique effective action is studied.On leave from Tomsk Pedagogical Inst., Tomsk, Russia Address after 1.08.92: Dept. of Physics, Hiroshima Univ., Higashi-Hiroshima 724, Japan     

Description of the algebra of infinitesimal automorphisms of quadrics of codimension two and their classification

This research was accomplished with the financial support of the Russian Foundation for Fundamental Research, Grant No. 93-011-225.     

Condensation of ketoximes with phenylacetylene

2-Methyl-5-phenyl- and 2,5-diphenylpyrrole and 2-phenyl-, Z-[1-(2-phenylvinyl)]-3-phenyl-, and 4,5,6,7-tetrahydroindole, and 2,4-diphenyl-3,3-dimethyl-5-hydroxypyrroline have been obtained from the reaction of ketoximes with phenylacetylene, catalyzed by KOH-DMSO.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 4, pp. 485–488, April, 1992.     

Thermoconductivity and thermoelasticity of thin isotropic shells heated by a moving heat pulse

The paper presents a solution to the problem of thermal conduction and thermoelasticity for a thin shallow spherical shell heated by a concentrated or local impulsive heat source moving over the shell surface. It is assumed that temperature is linearly distributed across the shell thickness and that the shell, on its sides, exchanges heat with the environment in accordance with Newton’s law of cooling. The Fourier and Laplace transforms are used to find an analytic solution. The dependence of the temperature field and stress/strain components on the type of heating and the form of heat source is studied __________ Translated from Prikladnaya Mekhanika, Vol. 42, No. 11, pp. 85–92, November 2006.     

Coating Platinum Nanoparticles with Methyl Radicals: Effects on Properties and Catalytic Implications

It was recently reported that the reaction of methyl radicals with Pt⁰ nanoparticles (NPs), prepared by the reduction of Pt(SO₄)₂ with NaBH₄, is fast and yields as the major product stable (Pt⁰‐NPs)?(CH₃)_n and as side products, in low yields, C₂H₆, C₂H₄, and some oligomers. We decided to study the effect of this coating on the properties of the Pt⁰‐NPs. The results show that the coating can cover up to 75 % of the surface Pt⁰ atoms. The rate constant of the reaction, k( ^. CH₃+Pt⁰‐NPs), decreases with the increase in the surface coverage, leading to competing reaction paths in the solution, which gradually become dominant, affecting the composition of the products. The methyl coating also affects the zeta potential, the UV spectra, and the electrocatalytic reduction of water in the presence of the NPs. Thus, the results suggest that binding alkyl radicals to Pt⁰ surfaces might poison the NPs catalytic activity. When the Pt⁰‐NPs are prepared by the reduction of a different precursor salt, PtCl₆^2?, nearly no C₂H₄ and oligomers are formed and the methyl coating covers a larger percentage of the surface Pt⁰ atoms. The difference is attributed to the morphology of the Pt⁰‐NPs: those prepared from Pt(SO₄)₂ are twinned nanocrystals, whereas those prepared from PtCl₆^2? consist mostly of single crystals. Thus, the results indicate that the side products, or most of them at least, are formed on the twinned Pt⁰ nanocrystal edges created between (111) facets. In addition, the results show that Pt⁰‐NPs react very differently compared with other noble metals, for example, Au⁰ and Ag⁰; this difference is attributed in part to the difference in the bond strength, (M⁰‐NP)?CH₃, and should be considered in heterogeneous catalytic processes involving alkyl radicals as intermediates.     

Optimal Exercise Strategies for Operational Risk Insurance via Multiple Stopping Times

In this paper we demonstrate how to develop analytic closed form solutions to optimal multiple stopping time problems arising in the setting in which the value function acts on a compound process that is modified by the actions taken at the stopping times. This class of problem is particularly relevant in insurance and risk management settings and we demonstrate this on an important application domain based on insurance strategies in Operational Risk management for financial institutions. In this area of risk management the most prevalent class of loss process models is the Loss Distribution Approach (LDA) framework which involves modelling annual losses via a compound process. Given an LDA model framework, we consider Operational Risk insurance products that mitigate the risk for such loss processes and may reduce capital requirements. In particular, we consider insurance products that grant the policy holder the right to insure k of its annual Operational losses in a horizon of T years. We consider two insurance product structures and two general model settings, the first are families of relevant LDA loss models that we can obtain closed form optimal stopping rules for under each generic insurance mitigation structure and then secondly classes of LDA models for which we can develop closed form approximations of the optimal stopping rules. In particular, for losses following a compound Poisson process with jump size given by an Inverse-Gaussian distribution and two generic types of insurance mitigation, we are able to derive analytic expressions for the loss process modified by the insurance application, as well as closed form solutions for the optimal multiple stopping rules in discrete time (annually). When the combination of insurance mitigation and jump size distribution does not lead to tractable stopping rules we develop a principled class of closed form approximations to the optimal decision rule. These approximations are developed based on a class of orthogonal Askey polynomial series basis expansion representations of the annual loss compound process distribution and functions of this annual loss.     

Linear relationship between the first invariants of the stress and strain tensors in theories of plasticity with strain hardening

Energy-coupled stress and strain measures are defined in Euler coordinates. They are used to analyze the relationship between the first invariants of the stress and strain tensors for linearity and to determine strains at which the plastic component of the first strain invariant can be neglected. It is established that this relationship remains linear within an engineering plastic-strain tolerance of 0.2% irrespective of the value of strain intensity, which depends on the type of material and its stress state __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 60–72, March 2007.