Synthesis of a protected keto-lysidine analogue via improved preparation of arabino-isocytosine nucleosides

Anhydrouridines react with aliphatic amines to give N-alkyl isocytosines, but reported procedures often demand very long reaction times and can be low yielding, with narrow scope. A modified procedure for such reactions has been developed, using microwave irradiation, significantly reducing reaction time and allowing facile access to a diverse range of novel nucleosides on the gram scale. The method has been used to prepare a precursor to a novel analogue of lysidine, a naturally occurring iminonucleoside found in (t)RNA

On a stochastic partial differential equation with non-local diffusion

In this paper, we prove existence, uniqueness and regularity for a class of stochastic partial differential equations with a fractional Laplacian driven by a space-time white noise in dimension one. The equation we consider may also include a reaction term

The Continuum Directed Random Polymer

Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white noise. The strength of the interaction is determined by an inverse temperature parameter beta, and for a given beta and realization of the noise the path evolves in a Markovian way. The transition probabilities are determined by solutions to the one-dimensional stochastic heat equation. We show that for all beta > 0 and for almost all realizations of the white noise the path measure has the same Holder continuity and quadratic variation properties as Brownian motion, but that it is actually singular with respect to the standard Wiener measure on C([0,1]).Comment: 21 page

Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise II. Fully discrete schemes

We present an abstract framework for analyzing the weak error of fully discrete approximation schemes for linear evolution equations driven by additive Gaussian noise. First, an abstract representation formula is derived for sufficiently smooth test functions. The formula is then applied to the wave equation, where the spatial approximation is done via the standard continuous finite element method and the time discretization via an I-stable rational approximation to the exponential function. It is found that the rate of weak convergence is twice that of strong convergence. Furthermore, in contrast to the parabolic case, higher order schemes in time, such as the Crank-Nicolson scheme, are worthwhile to use if the solution is not very regular. Finally we apply the theory to parabolic equations and detail a weak error estimate for the linearized Cahn-Hilliard-Cook equation as well as comment on the stochastic heat equation

Large Deviations for Stochastic Evolution Equations with Small Multiplicative Noise

The Freidlin-Wentzell large deviation principle is established for the distributions of stochastic evolution equations with general monotone drift and small multiplicative noise. As examples, the main results are applied to derive the large deviation principle for different types of SPDE such as stochastic reaction-diffusion equations, stochastic porous media equations and fast diffusion equations, and the stochastic p-Laplace equation in Hilbert space. The weak convergence approach is employed in the proof to establish the Laplace principle, which is equivalent to the large deviation principle in our framework.Comment: 31 pages, published in Appl. Math. Opti

Transport in rough self-affine fractures

Transport properties of three-dimensional self-affine rough fractures are studied by means of an effective-medium analysis and numerical simulations using the Lattice-Boltzmann method. The numerical results show that the effective-medium approximation predicts the right scaling behavior of the permeability and of the velocity fluctuations, in terms of the aperture of the fracture, the roughness exponent and the characteristic length of the fracture surfaces, in the limit of small separation between surfaces. The permeability of the fractures is also investigated as a function of the normal and lateral relative displacements between surfaces, and is shown that it can be bounded by the permeability of two-dimensional fractures. The development of channel-like structures in the velocity field is also numerically investigated for different relative displacements between surfaces. Finally, the dispersion of tracer particles in the velocity field of the fractures is investigated by analytic and numerical methods. The asymptotic dominant role of the geometric dispersion, due to velocity fluctuations and their spatial correlations, is shown in the limit of very small separation between fracture surfaces.Comment: submitted to PR

Gravitationally lensed QSOs in the ISSIS/WSO-UV era

Gravitationally lensed QSOs (GLQs) at redshift z = 1-2 play a key role in understanding the cosmic evolution of the innermost parts of active galaxies (black holes, accretion disks, coronas and internal jets), as well as the structure of galaxies at intermediate redshifts. With respect to studies of normal QSOs, GLQ programmes have several advantages. For example, a monitoring of GLQs may lead to unambiguous detections of intrinsic and extrinsic variations. Both kinds of variations can be used to discuss central engines in distant QSOs, and mass distributions and compositions of lensing galaxies. In this context, UV data are of particular interest, since they correspond to emissions from the immediate surroundings of the supermassive black hole. We describe some observation strategies to analyse optically bright GLQs at z of about 1.5, using ISSIS (CfS) on board World Space Observatory-Ultraviolet.Comment: 7 pages, 4 figures, Accepted for publication in Astrophysics & Space Scienc