Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

${?}_{t}u?\mathrm{?}?({(u?z)}^{\alpha }|\mathrm{?}u{|}^{\gamma ?1}\mathrm{?}u)=f$

are locally bounded. Here, u describes the height of the water, z is a given function that represents the land elevation and f is a source term accounting for evaporation, infiltration or rainfall.     

Flat Curves

We characterize the sextic trefoil among plane curves of low degree: first as a complex curve with compact, flat geometry; and then as a curve with meromorphic arc length parameterization.     

Effect of sequence of combined loading on buckling of stiffened shells

The vibration-correlation technique, VCT for definition of real boundary conditions, and the method of repeated buckling were employed for nondestructive generation of improved interaction curves for buckling of stringer-stiffened circular-cylindrical shells subjected to a combined axial compression and external-pressure state of loading. Thirteen shells were tested, five on clamped boundary conditions and eight on norminal simple supports. The study also included an assessment of the influence of the order of loading on the behavior of the shells before and at buckling as a result of the nonlinear interaction. It has been shown that the VCT and repeated buckling approach are feasible for closely stiffened shells and are adequate tools for the derivation of more realistic buckling interaction curves. It appears that the sequence of loading, constant axial compression first and then increasing the external pressure until buckling occurs, or the reverse order of loading, does not influence the buckling loads.     

Expedient synthesis of novel β-ketoesters from the Mizoroki–Heck coupling of ethyl 3-ethoxyacrylate with aryl and pyridyl halides

It is well known that β-ketoesters are useful intermediates for the synthesis of a range of heterocyclic templates. While there are many useful synthetic methods available to access these intermediates, there are still opportunities for the discovery of useful methodologies for their construction from novel starting materials. In this regard, we report on the discovery of a facile Pd-catalyzed Mizoroki–Heck coupling of ethyl 3-ethoxyacrylate with aryl and heteroaryl halides to form substituted alkoxyacrylates which can be hydrolyzed to form novel aryl and heteroaryl β-ketoesters.     

The aliasing‐phenomenon in visual terms

In a recent paper it was shown that the aliasing phenomenon, which leads to a severe identification problem in the estimation of stochastic differential equations, can be overcome by using a polygonal (or higher) approximation for the time paths of the exogenous variables. This work attempts to visualize the problem and presents several simulated trajectories of a continuous time AR(2)‐process (Ornstein‐Uhlenbeck‐process) together with the observationally equivalent structures. Furthermore it is shown that aliasing can even change the analytical properties of the time paths of the system: whereas the first component of the Ornstein‐Uhlenbeck‐process is differentiable, the trajectories of the aliasing structures are continuous, but not differentiable any more.     

A GPU-based hyperbolic SVD algorithm

A one-sided Jacobi hyperbolic singular value decomposition (HSVD) algorithm, using a massively parallel graphics processing unit (GPU), is developed. The algorithm also serves as the final stage of solving a symmetric indefinite eigenvalue problem. Numerical testing demonstrates the gains in speed and accuracy over sequential and MPI-parallelized variants of similar Jacobi-type HSVD algorithms. Finally, possibilities of hybrid CPU–GPU parallelism are discussed.     

Use of ion chromatography with post-column reaction for the measurement of tribromide to evaluate bromate levels in drinking water

A user-friendly ion chromatography method in conjunction with a post-column reaction (PCR) achieves practical quantitation limits for the oxyhalides bromate and chlorite of 0.05 μg/l and 0.10 μg/l, respectively. This level of measurement allows for the accurate assessment of bromate contributed to finished drinking waters that have been chlorinated using sodium hypochlorite. The target sensitivity of oxyhalides in the presence of other major ion species typically found in drinking water is achieved by PCR using excess bromide under acidic conditions to form a tribromide species that is detected by ultraviolet spectrometry. The method setup involves non-hazardous materials, as opposed to other recently developed methods that employ somewhat hazardous chemicals for generating the reaction necessary for the detection of bromate at sub-μg/l levels. No pretreatment of the samples is required, other than filtration and quenching of oxidant residual.