Existence of Pulsating Roll-Waves for the Saint Venant System

The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic travelling waves) follows from a classical work due to DRESSLER [6]. The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation. Following JIN and KATSOULAKIS [15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions.     

Feasibility study for the preparation of certified reference materials part I – mineral oil contaminated soils

The international joint project HYCREF (Contract No. G6RD-CT-2002-00854), funded by the European Commission in the 5th Framework programme, aimed to develop methods to prepare homogeneous and stable reference materials of water, soil, and waste contaminated with mineral oil hydrocarbons and to certify the mineral oil content by gas chromatographic methods. The results of a feasibility study for the preparation of three soil reference materials are discussed in this paper, and for the preparation of three waste reference materials in the second part (Koch et al., Accred Qual Assur submitted for publication). The soil materials were selected to represent different soil types and contamination levels. The project plan set three requirements for these reference materials: uncertainty in the mineral oil content resulting from the certification exercise <5%, a sample inhomogeneity of <3% and a minimum long-term stability of 5 years. For the most part, these requirements were met within this project.     

Learning to See: Making Sense of the Mathematics of Change in Middle School

In this article, we will describe the results of a study of 6th grade students learning about the mathematics of change. The students in this study worked with software environments for the computer and the graphing calculator that included a simulation of a moving elevator, linked to a graph of its velocity vs. time. We will describe how the students and their teacher negotiated the mathematical meanings of these representations, in interaction with the software and other representational tools available in the classroom. The class developed ways of selectively attending to specific features of stacks of centimeter cubes, hand-drawn graphs, and graphs (labeled velocity vs. time) on the computer screen. In addition, the class became adept at imagining the motions that corresponded to various velocity vs. time graphs. In this article, we describe this development as a process of learning to see mathematical representations of motion. The main question this article addresses is: How do students learn to see mathematical representations in ways that are consistent with the discipline of mathematics? This revised version was published online in July 2006 with corrections to the Cover Date.     

Peptides-XXXXVI: Studies in the synthesis of an analogue of hen egg white lysozyme

The previously synthesised (1–37), (38–75), (76–93), (94–104), (105–117) and (118–129) fragments of the analogue were combined making extensive use of the DCCI/HONSu method. The final coupling involved the (1–75) and (76–129) sub-fragments. Aggregation of the latter fragment caused problems in purification by routine gel filtration methods employing Enzacryl K2 or Sephadex LH60. The fully protected (1–129) product was partially purified by washing, then deprotectcd and purified by gel filtration and ion exchange chromatography. Satisfactory removal of the acetamidomethyl group used for cysteine protection could not be achieved.     

REALISIS: a medicinal chemistry-oriented reagent selection, library design, and profiling platform

REALISIS is a software system for reagent selection, library design, and profiling, developed to fit the workflow of bench chemists and medicinal chemists. Designed to be portable, the software offers a comprehensive graphical user interface and rapid, integrated functionalities required for reagent retrieval and filtering, product enumeration, and library profiling. REALISIS is component-based, consisting of four main modules: reagent searching; reagent filtering; library enumeration; and library profiling. Each module allows the chemist to access specific functionalities and diverse filtering and profiling mechanisms. By implementing the entire process of reagent selection, library design, and profiling and by integrating all the necessary functionalities for this process, REALISIS cuts the time required to design combinatorial and noncombinatorial libraries from several days to a few hours.     

E-Beam—a new transfer system for isolator technology

In every aseptic filling application, the sterile transfer of goods into the aseptic area is a challenge, and there are many different ways to do it.

With isolator technology a higher sterility assurance level (SAL) is achieved. This SAL is only as good as the weakest segment in the chain of manufacturing. The transfer of goods into and out of the isolator is one of these critical segments.

Today different techniques, some already well established, others still very new, are available on the market like: dry heat tunnel, autoclave, pulsed light, rapid transfer systems (RTP), H₂O₂ tunnel, UV light, etc. all these systems are either not applicable for continuous transfer, only good for heat-compatible materials like glass, or do not guarantee a 6 log spore reduction.

E-Beam opens new perspectives in this field. With E-beam technology it is possible to transfer heat-sensitive (plastic), pre-sterilised materials at high speed, continuously into an aseptic area.

E-Beam unifies three different technologies, that result in a very efficient and high-speed decontamination machine designed for the pharmaceutical industry. First, there is the electron beam that decontaminates the goods and an accurate shielding that protects the surrounding from this beam. Second, there is the conveyor system that guarantees the output and the correct exposure time underneath the beam. And third, there is the isolator interface to provide correct differential pressure and clean air inside the tunnel as well as the decontamination of the tunnel with H₂O₂ prior to production.

The E-beam is a low-energy electron beam, capable of decontaminating any kind of surface. It penetrates only a few micrometers into the material and therefore does not deform the packaging media.

Currently, machines are being built to transfer pre-sterilised syringes, packed in plastic tubs with a Tyvek cover into an aseptic filling isolator with the following data: decontamination efficiency of 10⁶ (6 log spore reduction), decontamination speed of 6 tubs (600 syringes) per minute.

This is just one of many applications for this new technology.     

On the limiting law solution of the cylindrical Poisson-Boltzmann equation for polyelectrolytes

Upper and lower bounds are given for the behaviour of the Poisson-Boltzmann potential of a highly charged, cylindrical polyelectrolyte in excess salt solution as the salt correntration or cylinder radius tends to zero. The exact singular behaviour of the potential very close to the cylinder is given in terms of a delta function.