Global dissipative solutions of the two-component Camassa-Holm system for initial data with nonvanishing asymptotics

We show existence of a global weak dissipative solution of the Cauchy problem for the two-component Camassa-Holm (2CH) system on the line with nonvanishing and distinct spatial asymptotics. The influence from the second component in the 2CH system on the regularity of the solution, and, in particular, the consequences for wave breaking, is discussed. Furthermore, the interplay between dissipative and conservative solutions is treated.Comment: arXiv admin note: text overlap with arXiv:1111.318

Dynamics of a non-autonomous incompressible non-Newtonian fluid with delay

We first study the well-posedness of a non-autonomous incompressible non-Newtonian fluid with delay. The existence of global solution is obtained by classical Galerkin approximation and the energy method. Actually, we also prove the uniqueness of solution as well as the continuous dependence on the initial value. Then we analyze the long time behavior of the dynamical system associated to the incompressible non-Newtonian fluid. Finally, we establish the existence of pullback attractors for the non-autonomous dynamical system associated to the problem.Ministerio de Economía y CompetitividadFondo Europeo de Desarrollo RegionalJunta de AndalucíaNational Natural Science Foundation of ChinaScience and Technology Commission of Shanghai MunicipalityShanghai Leading Academic Discipline Projec

Room Temperature Synthesis and Antibacterial Activity of New Sulfonamides Containing N,N -Diethyl-Substituted AmidoMoieties

Sulfonamide drugs which have brought about an antibiotic revolution in medicine are associated with a wide range of biological activities. We have synthesized a series of α-tolylsulfonamide, 1–11 and their substituted N,N-diethyl-2-(phenylmethylsulfonamido) alkanamide derivatives, 12–22 in improved and excellent yields in aqueous medium at room temperature through highly economical synthetic routes. The chemical structures of the synthesized compounds 1–22 were confirmed by analytical and spectral data such as IR, 1H- and 13C-NMR, andmass spectra. The in vitro antibacterial activity of these compounds along with standard clinical reference, streptomycin, was investigated on two key targeted organisms. It was observed that 1-(benzylsulfonyl) pyrrolidine-2-carboxylic acid, 2 emerged as the most active compound against Staphylococcus aureus at MIC value of 1.8 μg/mL while 4-(3-(diethylamino)-3-oxo-2-(phenylmethyl sulfonamido) propyl)phenyl phenylmethanesulfonate, 22 was the most active sulfonamide scaffold on Escherichia coli at MIC value of 12.5 μg/mL

A simple mean field model for social interactions: dynamics, fluctuations, criticality

We study the dynamics of a spin-flip model with a mean field interaction. The system is non reversible, spacially inhomogeneous, and it is designed to model social interactions. We obtain the limiting behavior of the empirical averages in the limit of infinitely many interacting individuals, and show that phase transition occurs. Then, after having obtained the dynamics of normal fluctuations around this limit, we analize long time fluctuations for critical values of the parameters. We show that random inhomogeneities produce critical fluctuations at a shorter time scale compared to the homogeneous system.Comment: 37 pages, 2 figure

On the capacity of information processing systems

We propose and analyze a family of information processing systems, where a finite set of experts or servers are employed to extract information about a stream of incoming jobs. Each job is associated with a hidden label drawn from some prior distribution. An inspection by an expert produces a noisy outcome that depends both on the job's hidden label and the type of the expert, and occupies the expert for a finite time duration. A decision maker's task is to dynamically assign inspections so that the resulting outcomes can be used to accurately recover the labels of all jobs, while keeping the system stable. Among our chief motivations are applications in crowd-sourcing, diagnostics, and experiment designs, where one wishes to efficiently learn the nature of a large number of items, using a finite pool of computational resources or human agents. We focus on the capacity of such an information processing system. Given a level of accuracy guarantee, we ask how many experts are needed in order to stabilize the system, and through what inspection architecture. Our main result provides an adaptive inspection policy that is asymptotically optimal in the following sense: the ratio between the required number of experts under our policy and the theoretical optimal converges to one, as the probability of error in label recovery tends to zero