Properties of Entire Functions Over Polynomial Rings via Gröbner Bases

 In this paper it is shown that the extension ideals of polynomial prime and primary ideals in the corresponding ring of entire functions remain prime or primary, respectively. Moreover, we will prove that a primary decomposition of a polynomial ideal can be extended componentwise to a primary decomposition of the extended ideal. In order to show this we first prove the flatness of the ring of entire functions over the corresponding polynomial ring by use of Gr?bner basis techniques. As an application we give an elementary proof of a generalization of Hilbert's Nullstellensatz for entire functions (cf. [10]). Received: August 8, 2002; revised version: January 29, 2003 Keywords: Flat module, Gr?bner basis, Entire function, Hilbert's Nullstellensatz.     

High-level expression of a viscotoxin in Arabidopsis thaliana gives enhanced resistance against Plasmodiophora brassicae

PURPOSE: Primary open-angle glaucoma (POAG) is associated with a decreased content of hyaluronan in the trabecular meshwork and in the juxtacanalicular connective tissue. In this study, the authors examined selected regions of the anterior segment to localize and determine the content of CD44H, a transmembrane multifunctional glycoprotein and the principal receptor of hyaluronan. METHODS: Sections of ethanol-fixed anterior segments of six POAG and six normal postmortem eyes were analyzed by immunostaining with and without the nonionic detergent Triton X-100, using the CD44H monoclonal antibody, and the avidin/biotin complex. They were visualized by Vector VIP substrate and were quantitated by computer-aided color image analysis. RESULTS: CD44H was expressed in all regions. Statistically significant decreased content of CD44H was observed in the POAG regions compared with normal regions--ciliary muscle (P < 0.001), ciliary stroma (P < 0.001), anterior iris (P < 0.05), iris root (P < 0.05), and trabecular meshwork (P < 0.05)--and in a subgroup of nonlaser POAG juxtacanalicular connective tissue (P < 0.05) and trabecular meshwork (P < 0.01). In sections treated with Triton X-100 a further increase in immunostaining was observed in normal eyes. As evidenced by scattergram plots of the ciliary body stroma region of the change in the optical density of CD44H between pretreatment with Triton X-100 and without Triton X-100 (y axis) versus the optical density of CD44H without Triton X-100 (x axis), individual cases of POAG were separated from normals. CONCLUSIONS: These results indicate that CD44H may represent a marker of POAG and an etiologic factor in the POAG disease process.     

Influence of dike breaches on flood frequency estimation

Many river floodplains and their assets are protected by dikes. In case of extreme flood events, dikes may breach and floodwater may spill over into the dike hinterland. Depending on the specific situation, e.g. time and location of breach, and the capacity of the hinterland to contain the floodwater, dike breaches may lead to significant reductions of flood peaks downstream of breach locations. However, the influence of dike breaches on flood frequency distributions along rivers has not been systematically analysed. In order to quantify this influence, a dynamic–probabilistic model is developed. This model combines simplified flood process modules in a Monte Carlo framework. The simplifications allow for the simulation of a large number of different scenarios, taking into account the main physical processes. By using a Monte Carlo approach, frequency distributions can be derived from the simulations. In this way, process understanding and the characteristics of the river–dike–floodplain system are included in the derivation of flood frequency statements. The dynamic–probabilistic model is applied to the Lower Rhine in Germany and compared to the usually used flood frequency analysis. For extreme floods, the model simulates significant retention effects due to dike breaches, which lead to significant modifications of the flood frequency curve downstream of breach locations. The resulting probabilistic statements are much more realistic than those of the flood frequency approach, since the dynamic–probabilistic model incorporates an important flood process, i.e. dike breaching, that only occurs when a certain threshold is reached. Beyond this point, the behaviour of the flood frequency curve is dominated by this process.     

Investigation of nanopore evolution in ion track-etched polycarbonate membranes

Single heavy ion tracks in polycarbonate foils were chemically etched in an electrolytical cell under various conditions (different temperatures, etchant concentrations, and applied potentials), and the pore evolution was monitored by measuring the current through the membrane. Different zones of the latent tracks could be identified via changes in the radial etching rate with time. Further it was found that the shape of the radial etching rate versus time curves depends on temperature, etchant concentration, and applied voltage. The functionalities are attributed to etching products (double-charged diphenylol-propane anions), which are adsorbed on the pore walls and, thus, affect the further etching process.     

Multireflection pumping concept for miniaturized diode-pumped solid-state lasers

An innovative pump concept for diode-pumped, solid-state lasers is introduced as an example for an Er:YSGG laser, permitting its miniaturization. Embedded in a multireflective pump cavity, the laser crystal is simultaneously side and end pumped. Specially calculated and shaped deflecting optics distribute the coaxially input pumping light homogeneously over the lateral surface of the crystal, therefore reducing the size of the laser head, including the optical resonator, to a length of 27.5 mm and an outside diameter of 12.5 mm. The differential efficiency achieved is between 8.7% and 24%. The laser emits energy of 15.7 mJ at an absolute efficiency of 9.1% and a repetition rate of 4 Hz.     

Formation of the reaction zone between tin‐copper brazing fillers and aluminum‐silicon‐magnesium alloys: Experiments and thermodynamic analysis

A primary challenge in brazing is the controlled formation of phases resulting from interactions of elements of the liquid filler metal with those of the base material. The morphology of the brazed joint, which is decisive for the mechanical properties of the joint, is influenced by present elements and process parameters such as brazing temperature and time. Furthermore, the wetting of the base material is a crucial factor in joining of aluminum because of the low wettability of the alumina layer by molten brazing filler metals. In order to remove the alumina and prevent reoxidation of the substrate surface, the brazing process can be conducted in vacuum or inert gas atmosphere. Again, selection of process parameters is crucial for the quality of the brazed seam. In this work, we focus on the influence of the process parameters on the wetting behavior and the formation of aluminum‐copper phases theoretically by means of thermodynamic calculations using a CALPHAD database as well as by means of in‐situ observations in the large‐chamber scanning electron microscope (LC‐SEM) and by brazing experiments. Both the critical temperatures with respect to the wetting and the reaction kinetics as well as the crucial stages of the brazing process and the resulting phases were determined.     

SPL Conqueror: Toward optimization of non-functional properties in software product lines

A software product line (SPL) is a family of related programs of a domain. The programs of an SPL are distinguished in terms of features, which are end-user visible characteristics of programs. Based on a selection of features, stakeholders can derive tailor-made programs that satisfy functional requirements. Besides functional requirements, different application scenarios raise the need for optimizing non-functional properties of a variant. The diversity of application scenarios leads to heterogeneous optimization goals with respect to non-functional properties (e.g., performance vs. footprint vs. energy optimized variants). Hence, an SPL has to satisfy different and sometimes contradicting requirements regarding non-functional properties. Usually, the actually required non-functional properties are not known before product derivation and can vary for each application scenario and customer. Allowing stakeholders to derive optimized variants requires us to measure non-functional properties after the SPL is developed. Unfortunately, the high variability provided by SPLs complicates measurement and optimization of non-functional properties due to a large variant space. With SPL Conqueror, we provide a holistic approach to optimize non-functional properties in SPL engineering. We show how non-functional properties can be qualitatively specified and quantitatively measured in the context of SPLs. Furthermore, we discuss the variant-derivation process in SPL Conqueror that reduces the effort of computing an optimal variant. We demonstrate the applicability of our approach by means of nine case studies of a broad range of application domains (e.g., database management and operating systems). Moreover, we show that SPL Conqueror is implementation and language independent by using SPLs that are implemented with different mechanisms, such as conditional compilation and feature-oriented programming.