Quadrics on Riemannian spaces of constant curvature. Separation of variables and connection with the Gaudin magnet

Integrable systems associated with separation of the variables in real Riemannian spaces of constant curvature are considered. An isomorphism between all such systems and the hyperbolic Gaudin magnet is established. This isomorphism is used in a classification of all coordinate systems that admit separation of the variables, the basis of which is the classification of the correspondingL operators of the Gaudin magnet.Leningrad State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 91, No. 1, pp. 83–111, April, 1992.     

A Faster Deterministic Maximum Flow Algorithm

Cheriyan and Hagerup developed a randomized algorithm to compute the maximum flow in a graph with n nodes and m edges in O(mn + n² log²n) expected time. The randomization is used to efficiently play a certain combinatorial game that arises during the computation. We give a version of their algorithm where a general version of their game arises. Then we give a strategy for the game that yields a deterministic algorithm for computing the maximum flow in a directed graph with n nodes and m edges that runs in time O(mn(log_{m/n log n}n)). Our algorithm gives an O(mn) deterministic algorithm for all m/n = Ω(n^ε) for any positive constant ε, and is currently the fastest deterministic algorithm for computing maximum flow as long as m/n = ω(log n).     

Silver nitrate-acetonitrile and iodine-benzene complexes as studied by NMR in thermotropic liquid crystals

Silver nitrate-acetonitrile and π iodine-benzene complexes in thermotropic liquid crystals have been studied by ¹H, ²H, and ¹³C NMR spectroscopy and by optical microscopy. Evidence for at least two silver complexes in each liquid crystal is presented.     

Properties of neodymium-doped aluminophosphate laser glasses

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 56, No. 1, pp. 90–95, January, 1992.     

The elastoplastic stressed state of a half-plane under local nonstationary heating

We solve the thermoplastic problem for a semi-infinite plate under local nonstationary heating by heat sources. The physical equations are taken to be the relations of the nonisothermic theory of plastic flow associated with the Mises fluidity condition. The solution of the problem is constructed by the method of integral equations and the self-correcting method of sequential loading, where time is taken as the loading parameter. We carry out numerical computations of the stresses in the case of heating a plate with heat output by normal-circular heat sources. We study the problem of optimization of heating regimes in order to introduce favorable residual compressive stresses (from the point of view of hardness) in a given region of a half-plane. Two figures.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 29–34.     

Universality in some classical Coulomb systems of restricted dimension

Coulomb systems in which the particles interact through thed-dimensional Coulomb potential but are confined in a flat manifold of dimensiond–1 are considered. The actual Coulomb potential acting is defined by particular boundary conditions involving a characteristic macroscopic distanceW in the direction perpendicular to the manifold: either it is periodic of periodW in that direction, or it vanishes on one ideal conductor wall parallel to the manifold at a distanceW from it, or it vanishes on two parallel walls at a distanceW from each other with the manifold equidistant from them. Under the assumptions that classical equilibrium statistical mechanics is applicable and that the system has the macroscopic properties of a conductor, it is shown that the suitably smoothed charge correlation function is universal, and that the free energy and the grand potential have universal dependences onW (universal means independent of the microscopic detail). The casesd=2 are discussed in detail, and the generic results are checked on an exactly solvable model. The cased=3 of a plane parallel to an ideal conductor is also explicitly worked out.Laboratoire associé au Centre National de la Recherche Scientifique-URA D0063.     

On practical metrology and chemical analysis: etalons and traceability systems

 National measurement systems are infrastructures to ensure, for each nation, a consistent and internationally recognised basis for measurement. Such complex systems have historical, technical, legal, organisational and institutional aspects to connect scientific metrology with practical measurements. Underlying any valid measurement is a chain of comparisons linking the measurement to an accepted standard. The ways the links are forged and the etalons (measurement standards) to which they connect are defining characteristics of all measurement systems. This is often referred to as traceability which aims at basing measurements in common measurement units – a key issue for the integration of quantitative chemical analysis with the evolving physical and engineering measurement systems. Adequate traceability and metrological control make possible new technical capabilities and new levels of quality assurance and confidence by users in the accuracy and integrity of quantitative analytical results. Traceability for chemical measurements is difficult to achieve and harder to demonstrate. The supply of appropriate etalons is critical to the development of metrology systems for chemical analysis. An approach is suggested that involves the development of networks of specialised reference laboratories able to make matrix-independent reference measurements on submitted samples, which may then be used as reference materials by an originating laboratory using its practical measurement procedures. Received: 31 July 1995 Accepted: 19 August 1995     

Existence of black hole solutions for the Einstein-Yang/Mills equations

This paper provides a rigorous proof of the existence of an infinite number of black hole solutions to the Einstein-Yang/Mills equations with gauge groupSU(2), for any event horizon. It is also demonstrated that the ADM mass of each solutions is finite, and that the corresponding Einstein metric tends to the associated Schwarzschild metric at a rate 1/r ², asr tends to infinity.Research supported in part by the NSF, Contract No. DMS-89-05205Research supported in part by the DE, Contract No. De-FG 02-88 EF 25065     

Hybrid free radical/cationic frontal photopolymerizations

The irradiation of hybrid photopolymer systems consisting of a free radically polymerizable multifunctional acrylate monomer and a cationically polymerizable epoxide or oxetane monomer was conducted under conditions where only the free radical polymerization takes place. This results in the formation of a free‐standing polyacrylate network film containing quiescent oxonium ions along with the unreacted cyclic ether monomer. The subsequent application of a point source of heat to the film ignites a cationic ring‐opening frontal polymerization that emanates from that site and propagates to all portions of the irradiated sample. This article examines the impact of various molecular structural and experimental parameters on these novel hybrid frontal polymerizations that produce interpenetrating network polymers. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 4331–4340, 2007