Bromination of 1,3,5-trimethyl-4-chloropyrazole

The bromination of 1,3,5-trimethyl-4-chloropyrazole with N-bromosuccinimide (NBS) in the presence of benzoyl peroxide leads to 5-bromomethyl-1,3-dimethyl-4-chloropyrazole, whereas 3,5-bis(bromomethyl)-1-methyl-4-chloropyrazole predominates in the case of a twofold excess of NBS. Products of subsequent substitution in the 3- and 5-bromomethyl groups of the 3,5-bis(bromomethyl) compound in a ratio of 31 were detected in small amounts; this is evidently associated with the syn orientation of the bromine atom in the 5-bromomethyl group, which hinders attack by the bromine radical.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 1, pp. 40–42, January, 1988.     

Cellular automata modelling of hantarvirus infection

Hantaviruses are a group of viruses which have been identified as being responsible for the outbreak of diseases such as the hantavirus pulmonary syndrome. In an effort to understand the characteristics and dynamics of hantavirus infection, mathematical models based on differential equations have been developed and widely studied. However, such models neglect the local characteristics of the spreading process and do not include variable susceptibility of individuals. In this paper, we develop an alternative approach based on cellular automata to analyze and study the spatiotemporal patterns of hantavirus infection.     

Fast local searches and updates in bounded universes

Given a bounded universe $\{0,1,\dots ,U?1\}$, we show how to perform predecessor searches in $O(\log \log \mathrm{\Delta })$ expected time, where Δ is the difference between the element being searched for and its predecessor in the structure, while supporting updates in $O(\log \log \mathrm{\Delta })$ expected amortized time, as well. This unifies the results of traditional bounded universe structures (which support predecessor searches in $O(\log \log U)$ time) and hashing (which supports membership queries in $O(1)$ time). We also show how these results can be applied to approximate nearest neighbour queries and range searching.     

Circularly Symmetric Static Metric in Three Dimensions and Its Killing Symmetry

In this note we consider a general three-dimensional circularly symmetric static metric and investigate possible Killing symmetries it possesses.We then summarize the work by addressing Einstein equations and briefly discuss their implications on the energy momentum content of some of the metrics that arise in the process.     

Nonresonance between the first two eigenvalues for a Steklov problem

In this paper, we study the solvability of the Steklov problem Δ_pu=|u|^p−2u in Ω, on ∂Ω, under assumptions on the asymptotic behaviour of the quotients f(x,s)/|s|^p−2s and pF(x,s)/|s|^p which extends the classical results with Dirichlet boundary conditions that for a.e. x∈∂Ω, the limits at the infinity of these quotients lie between the first two eigenvalues.     

Rheological properties of carboxymethyl cellulose (CMC) solutions

In this study, we investigated the way of predicting two critical concentrations of sodium carboxymethyl cellulose (CMC) solutions using simple experimental procedures with a rotational rheometer. It was found that, above a critical shear rate, all CMC solutions (0.2 to 7 wt.%) exhibit shear-thinning behavior and the flow curves could be described by the Cross model. A first critical CMC concentration c*, transition to semidilute network solution, was determined using the following methods (1) study of the flow curve shapes, (2) Cross model parameters, (3) plot of the specific viscosity vs the overlap parameter, and (4) empirical structure–properties relationships. Furthermore, both creep and frequency-sweep measurements showed that the solutions behaved as viscoelastic materials above a second critical CMC concentration c** (transition to concentrated solution). The characterization of CMC solutions was completed with a time-dependent viscosity study that showed that the CMC solutions exhibited strong thixotropic behavior, especially at the highest CMC concentrations.     

Decomposability for division algebras of exponent two and associated forms

This article investigates the structure of quadratic forms and of division algebras of exponent two over fields of characteristic different from two with the property that the third power of the fundamental ideal in the associated Witt ring is torsion free.      

Stabilization of the nonlinear damped wave equation via linear weak observability

We consider the problem of energy decay rates for nonlinearly damped abstract infinite dimensional systems. We prove sharp, simple and quasi-optimal energy decay rates through an indirect method, namely a weak observability estimate for the corresponding undamped system. One of the main advantage of these results is that they allow to combine the optimal-weight convexity method of Alabau-Boussouira (Appl Math Optim 51:61–105, 2005) and a methodology of Ammari and Tucsnak (ESAIM COCV 6:361–386, 2001) for weak stabilization by observability. Our results extend to nonlinearly damped systems, those of Ammari and Tucsnak (ESAIM COCV 6:361–386, 2001). At the end, we give an appendix on the weak stabilization of linear evolution systems.