Stability of numerical methods for volterra integro-differential equations

A theory of weak stability for linear multistep methods for the numerical solution of Volterra integro-differential equations is developed, and a connection between this theory and the corresponding theory for ordinary differential equations is established. In addition, the order of such methods is discussed, and a new starting procedure is proposed and analyzed.     

Molecular self-assembly of "nanowires"and "nanospools" using active transport

Mastering supramolecular self-assembly to a similar degree as nature has achieved on a subcellular scale is critical for the efficient fabrication of complex nanoscopic and mesoscopic structures. We demonstrate that active, molecular-scale transport powered by biomolecular motors can be utilized to drive the self-assembly of mesoscopic structures that would not form in the absence of active transport. In the presented example, functionalized microtubules transported by surface-immobilized kinesin motors cross-link via biotin/streptavidin bonds and form extended linear and circular mesoscopic structures, which move in the presence of ATP. The self-assembled structures are oriented, exhibit large internal strains, and are metastable while the biomolecular motors are active. The integration of molecular motors into the self-assembly process overcomes the trade-off between stability and complexity in thermally activated molecular self-assembly.     

The CEA test and other immunological tests as disease course controls in gastrointestinal adenocarcinoma

161 patients with adenocarcinoma of the gastrointestinal tract were studied to determine the value of the CEA test and a battery of non-specific immunological tests during the course of the disease. The ability of these tests to detect a tumor recurrence in radically operated patients was evaluated. A false negative preoperative CEA value was found in 40% of the patients with gastric carcinoma and 32% with colorectal carcinoma. Patients with a negative preoperative CEA value, and those with only slightly elevated values, had a distinctly better prognosis regarding initial operability and tendency to postoperative recurrence than patients with primarily markedly elevated values. With few exceptions, the development of distant metastases was detected earlier and more easily with the CEA test than by the usual routine follow-up methods. However, in the event of isolated local recurrence the CEA test was positive in only 1 of 5 patients. This reflects the direct correlation between tumor size and CEA elevation. The CEA test is a valuable supplement in the follow-up of patients with gastrointestinal carcinoma.     

Das Ergebnis der Wassergehaltsbestimmung von Butter in Abh?ngigkeit von der Arbeitsweise mit und ohne Verteilungsmitteln

Zusammenfassung Die Frage, ob Natriumchlorid allgemein — und welcher Reinheitsgrad der geprüften 5 Salzsorten im besonderen — geeignet sei, bei der gravimetrischen Butterwasserbestimmung (Trockenschrankmethode) das üblicherweise verwendete Ver teilungsmittel Seesand mit Vorteil zu ersetzen, bzw. ob unter Umständen bei dieser Arbeitsweise — vergleichsweise zur Schnellmethode — ebenfalls auf ein Verteilungsmittel verzichtet werden kann, wurde durch statistisch ausgewertete Vergleichsuntersuchungen beantwortet.Es ergab sich, daß die geprüften Salze: Natriumehlorid zur Analyse a) — reinst, getrocknet, fein gepulvert b) — reinst, getrocknet c) — reinst, kristallisiert DAB. 6. d) sowohl im Hinblick auf die Genauigkeit der Arbeitsweise, als auch in bezug auf die statistisch gesicherte Gleichartigkeit der Ergebnisse, ferner hinsichtlich der Troeknungszeit dem Verteilungsmittel Seesandgleichwertig sind. Diese Feststellung trifft bei Verwendung eines Kochsalzes mit nicht definiertem Reinheitsgrad [Salz e)] nurmehr beschränkt zu: Trotz ausreichender Genauigkeit ergibt sich bei dessen Verwendung ein niedrigerer Wassergehalt der Butter als mit Seesand, eine Unterschiedlichkeit, die statistisch gesichert ist. Auch eine vergleichsweise fast doppelt so lange Trocknungsdauer spricht gegen dessen Verwendung.Welchem von den geeigneten Salzen der Vorzug einzuräumen ist, kann nur bei gegenseitiger Abwägung verschiedener Faktoren entschieden werden:Nicht erforderlich ist es, sich einseitig auf die Verwendung von Natriumchlorid mit dem höchsten Reinheitsgrad; NaCl pro anal., festzulegen, vielmehr scheint in bezug auf Genauigkeit, Gleichartigkeit, Troeknungszeitund Preis das Natriumchlorid reinst, getrocknet, fein gepulvert b) das Salz derWahl zu sein.Bei der gravimetrischen Methode (Trocknung in einstündigen Intervallen bei 103–105°C im Trockenschrank bis zur Gewichtskonstanz) ist der Arbeitsweise mit Verteilungsmitteln gegenüber der Arbeitsweise ohne Verteilungsmitteln in bezug auf Genauigkeit und Zeitaufwand der Vorzug zu geben.Die Notwendigkeit eines Verreibens der Butter mit dem Verteilungsmittel besteht bei der Wasserbestimmungnicht, vielmehr erwies sich — vergleichsweise dazu — die Arbeitsweise des Nichtverreibens im Hinblick auf die Genauigkeit und Zeitdauer der Bestimmunggleichwertig, arbeitstechnisch gesehen aber überlegen.     

Piecewise linear optimization: Duality and numerical results

The dual of an optimization problem with piecewise linear, convex, and continous objective function and linear restrictions is investigated. It is shown that the dual problem is of the same type as the primal and can be solved by the same methods as were proposed in a previous work of the author. Experiences arising from the application of different variants of these methods to solve a number of examples, where the primal as well as the dual version was employed, are reported.     

Inhibition of GABA metabolism in rat brain slices by halothane

Based on studies with rat cerebral cortex slices, it was previously hypothesized that halothane anesthesia may result from increased GABA (gamma-aminobutyric acid) content in the synapses. Since GABA is an inhibitory neurotransmitter, such increases may cause a reduction in synaptic activity. The increase in GABA content could arise from several possible causes which are examined in this study using rat cerebral cortex slices as a model. The effects of halothane on uptake, release, and catabolism of GABA were determined. Uptake was studied by the amounts of radioactive GABA accumulated by the slices, and release studied by that discharged into the medium from slices preloaded with radioactive GABA. Catabolism was assessed by preloading the slices with radioactive GABA and then followed by measuring the amount of radioactivity found in unmetabolized GABA or in pooled GABA metabolites. Since CO2 was established as a major metabolite, it was subsequently used alone to measure the inhibition of GABA catabolism in the presence of varying amounts of halothane. Halothane (3 per cent) did not affect the high-affinity uptake or the release of GABA but did inhibit the catabolism of GABA. Using 14CO2 production as an index of catabolism, the inhibition of GABA catabolism by halothane was dose-related (8.79 per cent inhibition/per cent halothane). Such results support the hypothesis that halothane anesthesia may result at least in part from an inhibition of GABA catabolism which, in turn, causes increased GABA level in the synapse with resultant synaptic inhibition.     

Thin films of the organic superconductor α-(BEDT-TTF)2I3

α-(BEDT-TTF)₂I₃ is a quasi-two-dimensiona1 organic metal with a metal-insulator phase transition at 135 K. Thermal treatment at about 80°C leads to the metallic system α₁-(BEDT-TTF)₂I₃ which becomes superconducting below 8 K. Thin films of the α-phase (between 500 and 3000 A thick) have been evaporated in high vacuum onto several substrates and characterised by means of X-ray diffraction, scanning electron microscopy (SEM), atomic force microscopy (AFM) and a low field microwave absorption technique. Depending on the temperature of the substrate and the evaporation rate, the films exhibit different degrees of microcristallinity, which under certain conditions can be strongly reduced and a completely covering film can be obtained. X-ray diffraction spectra reveal a high orientation with the c-axis perpendicular to the substrate and as well the successful conversion into the α₁- phase by tempering. SEM and AFM investigations prove that the conversion takes place without reducing the mechanical quality of the films. Low-field microwave-absorption experiments show that the α₁-films become superconducting with an onset at 9 K.     

Divertor IR thermography on Alcator C-Mod

Alcator C-Mod is a particularly challenging environment for thermography. It presents issues that will similarly face ITER, including low-emissivity metal targets, low-Z surface films, and closed divertor geometry. In order to make measurements of the incident divertor heat flux using IR thermography, the C-Mod divertor has been modified and instrumented. A 6° toroidal sector has been given a 2° toroidal ramp in order to eliminate magnetic field-line shadowing by imperfectly aligned divertor tiles. This sector is viewed from above by a toroidally displaced IR camera and is instrumented with thermocouples and calorimeters. The camera provides time histories of surface temperatures that are used to compute incident heat-flux profiles. The camera sensitivity is calibrated in situ using the embedded thermocouples, thus correcting for changes and nonuniformities in surface emissivity due to surface coatings.