Large Deviations from a Stationary Measure for a Class of Dissipative PDEs with Random Kicks

We study a class of dissipative PDEs perturbed by a bounded random kick force. It is assumed that the random force is nondegenerate, so that the Markov process obtained by the restriction of solutions to integer times has a unique stationary measure. The main result of the paper is a large deviations principle for occupation measures of the Markov process in question. The proof is based on Kifer's large‐deviation criterion, a coupling argument for Markov processes, and an abstract result on large‐time asymptotic for generalized Markov semigroups.© 2015 Wiley Periodicals, Inc.     

An approach to the imine ring system of pinnatoxins

[reaction: see text] A concise stereoselective approach to the spirobicyclic imine fragment of pinnatoxins and pteriatoxins is described. The approach relies on a tandem reaction sequence involving consecutive sigmatropic rearrangements to build the quaternary chiral center at the core of the spirobicyclic ring system.     

Ultrasonic assessment of tissue hydration status

Tissue water content is an important diagnostic parameter that can be used for estimation of water loss in muscles such as common dehydration during high endurance exercises. It could be also applied for evaluation of the increased fluids content in the tissue caused by the variety of pathological conditions or edemas. Ultrasonic method for tissue water content monitoring is based on the premise that the speed of a bulk or compression sound wave is determined mainly by the molecular content of the tissue. Most soft tissues, including muscles that consist of about 70-80% water, exhibit shift of the ultrasound velocity associated with the change in their water content. In the present paper, we tested the feasibility of assessing changes in tissue water content by measurements of ultrasound velocity in ex vivo animal muscle tissues. An increase in the ultrasound velocity correlated with the volumetric water loss in the tissue was observed when other tissue components (proteins, fat) remained constant. Possibility to assess muscle dehydration with 1% accuracy was confirmed in model dehydration experiments, where ultrasound velocity slope of about 3 m/s per 1% of water loss was revealed at measurement error less than 2 m/s. Hence, the ultrasonic approach can provide basis for a convenient, lightweight system in sports medicine for monitoring total body hydration during long-term endurance exercise in hot conditions, as well as for edemas monitoring and other medical applications.     

Graphs that are not complete pluripolar

Let be domains in . Under very mild conditions on we show that there exist holomorphic functions , defined on with the property that is nowhere extendible across , while the graph of over is not complete pluripolar in . This refutes a conjecture of Levenberg, Martin and Poletsky (1992).

     

Harmonic maps into loop spaces of compact Lie groups

We study harmonic maps from Riemann surfaces M to the loop spaces ΩG of compact Lie groups G, using the twistor approach. We conjecture that harmonic maps of the Riemann sphere ℂℙ¹ into ΩG are related to Yang-Mills G-fields on ℝ⁴. This work was partly supported by the RFBR (Grant Nos. 04-01-00236, 06-02-04012), by the program of Support of Scientific Schools (Grant No. 1542.2003.1), and by the Scientific Program of RAS “Nonlinear Dynamics”     

Operating Points in Infinite Nonlinear Networks Approximated by Finite Networks

Given a nonlinear infinite resistive network, an operating point can be determined by approximating the network by finite networks obtained by shorting together various infinite sets of nodes, and then taking a limit of the nodal potential functions of the finite networks. Initially, by taking a completion of the node set of the infinite network under a metric given by the resistances, limit points are obtained that represent generalized ends, which we call ``terminals,' of the infinite network. These terminals can be shorted together to obtain a generalized kind of node, a special case of a 1-node. An operating point will involve Kirchhoff's current law holding at 1-nodes, and so the flow of current into these terminals is studied. We give existence and bounds for an operating point that also has a nodal potential function, which is continuous at the 1-nodes. The existence is derived from the said approximations.

     

Freudenthal duality and generalized special geometry

Freudenthal duality, introduced in Borsten et al. (2009) [1] and defined as an anti-involution on the dyonic charge vector in d=4 space-time dimensions for those dualities admitting a quartic invariant, is proved to be a symmetry not only of the classical Bekenstein-Hawking entropy but also of the critical points of the black hole potential.Furthermore, Freudenthal duality is extended to any generalized special geometry, thus encompassing all N>2 supergravities, as well as N=2 generic special geometry, not necessarily having a coset space structure.     

10‐Step Asymmetric Total Synthesis and Stereochemical Elucidation of (+)‐Dragmacidin D

The asymmetric synthesis of dragmacidin D ( 1 ) was completed in 10 steps. Its sole stereocenter was set by using direct asymmetric alkylation enabled by a C₂‐symmetric tetramine and lithium N‐(trimethylsilyl)‐tert‐butylamide as the enolization reagent. A central Larock indole synthesis was employed in a convergent assembly of the heterocyclic subunits. The stereochemical evidence from this work strongly supports the predicted S configuration at the 6′′′ position, which is consistent with other members of the dragmacidin family of natural products.     

A Coupling Approach to Randomly Forced Nonlinear PDE's. II

 We consider a class of discrete time random dynamical systems and establish the exponential convergence of its trajectories to a unique stationary measure. The result obtained applies, in particular, to the 2D Navier–Stokes system and multidimensional complex Ginzburg–Landau equation with random kick-force. Received: 7 February 2002 / Accepted: 29 April 2002 Published online: 12 August 2002