Synthesis and properties of N-[ω-(p-toluenesulfonoxyl)alkyl]uracils

Conclusions The possibility of N-(-hydroxyalkyl)uracil tosylates undergoing intramolecular cyclization to give bicyclic pyrimidinium salts was studied.Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 10, pp. 2349–2356, October, 1980.     

A NEW FINITE ELEMENT APPROXIMATION OF A STATE-CONSTRAINED OPTIMAL CONTROL PROBLEM

In this paper, we study numerical methods for an optimal control problem with pointwise state constraints. The traditional approaches often need to deal with the deltasingularity in the dual equation, which causes many difficulties in its theoretical analysis and numerical approximation. In our new approach we reformulate the state-constrained optimal control as a constrained minimization problems only involving the state, whose optimality condition is characterized by a fourth order elliptic variational inequality. Then direct numerical algorithms （nonconforming finite element approximation） are proposed for the inequality, and error estimates of the finite element approximation are derived. Numerical experiments illustrate the effectiveness of the new approach.     

Local observations of phase singularities in optical fields in waveguide structures

A linear copolymer made of two reciprocally attracting N-monomer blocks collapses to a compact phase through a novel transition, whose exponents are determined with extensive Monte Carlo simulations in two and three dimensions. In the former case, an identification with the statistical geometry of suitable percolation paths allows one to predict that the number of contacts between the blocks grows like N9/16. In the compact phase the blocks are mixed and, in two dimensions, also zipped, in such a way to form a spiral, double chain structure.     

Influencing the angular emission of a single molecule

We present the first experimental proof for the influence of a nearby nanosized metal object on the angular photon emission by a single molecule. Using a novel angular sensitive detection scheme, we directly quantify the redirection of angular emission for different molecular dipole orientations as an object is scanned laterally over the molecule at different heights. An excellent agreement between experiments and 2D-numerical simulations is found for molecules oriented perpendicular to the sample, whereas, for parallel orientations, the observed behavior contradicts the calculated behavior.     

The sorting direct method for stochastic simulation of biochemical systems with varying reaction execution behavior

A key to advancing the understanding of molecular biology in the post-genomic age is the development of accurate predictive models for genetic regulation, protein interaction, metabolism, and other biochemical processes. To facilitate model development, simulation algorithms must provide an accurate representation of the system, while performing the simulation in a reasonable amount of time. Gillespie's stochastic simulation algorithm (SSA) accurately depicts spatially homogeneous models with small populations of chemical species and properly represents noise, but it is often abandoned when modeling larger systems because of its computational complexity. In this work, we examine the performance of different versions of the SSA when applied to several biochemical models. Through our analysis, we discover that transient changes in reaction execution frequencies, which are typical of biochemical models with gene induction and repression, can dramatically affect simulator performance. To account for these shifts, we propose a new algorithm called the sorting direct method that maintains a loosely sorted order of the reactions as the simulation executes. Our measurements show that the sorting direct method performs favorably when compared to other well-known exact stochastic simulation algorithms.