Hybrid BDF methods for the numerical solutions of ordinary differential equations

In this article, we have presented the details of hybrid methods which are based on backward differentiation formula (BDF) for the numerical solutions of ordinary differential equations (ODEs). In these hybrid BDF, one additional stage point (or off-step point) has been used in the first derivative of the solution to improve the absolute stability regions. Stability domains of our presented methods have been obtained showing that all these new methods, we say HBDF, of order p, p = 2,4,..., 12, are A(α)-stable whereas they have wide stability regions comparing with those of some known methods like BDF, extended BDF (EBDF), modified EBDF (MEBDF), adaptive EBDF (A-EBDF), and second derivtive Enright methods. Numerical results are also given for five test problems.     

Spreading, evaporation, and contact line dynamics of surfactant-laden microdrops

An optical technique based on the reflectivity measurements of a thin film was used to experimentally study the spreading, evaporation, contact line motion, and thin film characteristics of drops consisting of a water-surfactant (polyalkyleneoxide-modified heptamethyltrisiloxane, called superspreader) solution on a fused silica surface. On the basis of the experimental observations, we concluded that the surfactant adsorbs primarily at the solid-liquid and liquid-vapor interfaces near the contact line region. At equilibrium, the completely wetting corner meniscus was associated with a flat adsorbed film having a thickness of approximately 31 nm. The calculated Hamaker constant, A = -4.47 x 10(-)(20) J, shows that this thin film was stable under equilibrium conditions. During a subsequent evaporation/condensation phase-change process, the thin film of the surfactant solution was unstable, and it broke into microdrops having a finite contact angle. The thickness of the adsorbed film associated with the drops was lower than that of the equilibrium meniscus. The drop profiles were experimentally measured and analyzed during the phase-change process as the contact line advanced and receded. The apparent contact angle, the maximum concave curvature near the contact line region, and the convex curvature of the drop increased as the drop grew during condensation, whereas these quantities decreased during evaporation. The position of the maximum concave curvature of the drop moved toward the center of the drop during condensation, whereas it moved away from the center during evaporation. The contact line velocity was correlated to the observed experimental results and was compared with the results of the drops of a pure alcohol. The experimentally obtained thickness profiles, contact angle profiles, and curvature profiles of the drops explain how the surfactant adsorption affects the contact line motion. We found that there was an abrupt change in the velocity of the contact line when the adsorbed film of the surfactant solution was just hydrated or desiccated during the phase-change processes. This result shows the effect of vesicles and aggregates of the surfactant on the shape evolution of the drops. For these surfactant-laden water drops, we found that the apparent contact angle increased during condensation and decreased during evaporation. However, for the drop of a pure liquid (n-butanol and 2-propanol) the apparent contact angle remained constant at a constant velocity during condensation and evaporation. The contact line was pinned during the evaporation and spreading of the surfactant-laden water drops, but it was not pinned for a drop of a pure alcohol (self-similar shape evolution).     

Studies on the thermal dissociation of some carbonate minerals

Differential thermal investigations with pure synthetic carbonate minerals revealed a general lowering of the dissociation peak for magnesite, dolomite or calcite when present together in an artificial mixture. The presence of siderite did not affect the dissociation curves of these carbonates. A systematic study of this phenomenon using pure compounds with controlled grain size and other affecting parameters may help in understanding the dissociation curves of natural carbonate aggregates.

---

Zusammenfassung Differentialthermoanalytische Untersuchungen an reinen synthetischen Karbonatgemischen von mineralischer Zusammensetzung zeigten im allgemeinen eine Verminderung in der Temperatur der Dissoziationsspitze von Magnesit, Dolomit und Kalzit, wenn sie gemeinsam zugegen waren. Siderit beeinflu\te den Verlauf der Dissoziation der Karbonate nicht. Eine systematische Untersuchung dieser Erscheinung mit Hilfe von reinen Verbindungen mit kontrollierter Korngrö\e und anderen beinflu\baren Parametern trÄgt zur KlÄrung der Dissoziationserscheinungen von natürlichen Karbonataggregaten bei.

---

Résumé L'étude par ATD de carbonates minéraux synthétiques purs a montré un abaissement du pic de dissociation de la magnésite, de la dolomie, ou de la calcite, quand ils coexistent dans le mélange artificiel. La présence de sidérite n'affecte pas le mode de dissociation de ces carbonates. L'étude systématique de ce phénomène avec des composés purs, en contrÔlant la granulométrie et les autres paramètres, a permis de comprendre le mode de dissociation des agrégats des carbonates naturels.

---

, , , , . , . Ë .

     

Determination of scandium in wolframite and in the residues obtained after the extraction of tungsten

The separation of scandium from iron and manganese by extraction with TBP from hydrochloric acid was studied in detail and this method was applied to the estimation of scandium in wolframite and its residues. The method consists of the extraction of tungsten from the wolframite with sodium carbonate, dissolution of the residue in hydrochloric acid and preferential extraction of iron and scandium from hydrochloric acid, stripping of the scandium with 8 M hydrochloric acid and re-extraction of accompanying iron with fresh TBP, precipitation of scandium with ammonia in presence of ammonium chloride, and final purification of the scandium by TBP extraction.     

Nucleosides. Part LIX. The 2-(4-nitrophenyl)ethylsulfonyl (Npes) Group: A New Type of Protection in Nucleoside Chemistry

The 2-(4-nitrophenyl)ethylsulfonyl (npes) group is developed as a new sugar OH-blocking group in the ribonucleoside series. Its cleavage can be performed in a β-eliminating process under aprotic conditions using 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU) as the most effective base. Since sulfonates do not show acyl migration, partial protection of 1,2-cis-diol moieties is possible leading to new types of oligonucleotide building blocks. A series of Markiewicz-protected ribonucleosides 1–10 is converted into their 2′-O-[2-(4-nitrophenyl)ethylsulfonyl] derivatives 29–38 in which the 5′-O? Si bond can be cleaved by acid hydrolysis forming 39–45 . Subsequent monomethoxytritylation leads to 46–50 , and desilylation affords the 5′-O-(monomethoxytrityl)-2′-O-[2-(4-nitrophenyl)ethylsulfonyl]ribonucleosides 51–55 . Acid treatment to remove trityl groups do also not harm the npes group (→ 56–58 ). Unambiguous syntheses of fully blocked 2′-O-[2-(4-nitrophenyl)ethylsulfonyl]ribonucleosides 96–102 are achieved from the corresponding 3′-O-(tert-butyl)dimethylsilyl derivatives. Furthermore, various base-protected 5′-O-(monomethoxytrityl)- and 5′-O-(dimethoxytrityl)ribonucleosides, i.e. 59–77 , are treated directly with 2-(4-nitrophenyl)ethylsulfonyl chloride forming in all cases a mixture of the 2′,3′-di-O- and the two possible 2′- and 3′-O-monosulfonates 107–148 which can be separated into the pure components by chromatographic methods. The npes group is more labile towards DBU cleavage than the corresponding base-protecting 2-(4-nitrophenyl)ethyl (npe) and 2-(4-nitrophenyl)ethoxycarbonyl (npeoc) groups allowing selective deblocking which is of great synthetic potential.     

A minimum discrimination information estimator of preliminary conjectured normal variance

For the problem of estimating the normal variance ² based on random sampleX ₁,...,X _n when a preliminary conjectured interval [C ₀ ^–1 ₀ ² ,C _{0 0} ² ] is available, the minimum discrimination information (MDI) approach is presented. This provides a simple way of specifying the prior information, and also allows to consider a shrinkage type estimator. MDI estimator and its mean square error are derived. The estimator compares favorably with the previously proposed estimators in terms of mean square error efficiency.     

A statistical approach to determine process parameter impact in Nd:YAG laser drilling of IN718 and Ti-6Al-4V sheets

The numerous unique advantages afforded by pulsed Nd:YAG laser systems have led to their increasing utility for producing high aspect ratio holes in a wide range of materials. Notwithstanding the growing industrial acceptance of the technique, the increasingly tighter geometrical tolerances and more stringent hole quality requirements of modern industrial components demand that “defects” such as taper, recast, spatter etc., in laser-drilled holes are minimized. Process parameters like pulse energy, pulse repetition rate, pulse duration, focal position, nozzle standoff, type of gas and gas pressure of the assist gas are known to significantly influence hole quality during laser drilling. The present study reports the use of Taguchi design of experiments technique to study the effects of the above process variables on the quality of the drilled holes and ascertain optimum processing conditions. Minimum taper in the drilled hole was considered as the desired target response. The entire study was conducted in three phases:(a) screening experiments, to identify process variables that critically influence taper in laser drilled holes, (b) Optimization experiments, to ascertain the set of parameters that would yield minimum taper and (c) validation trials, to assess the validity of the experimental procedures and results. Results indicate that laser drilling with focal position on the surface of the material being drilled and employing low level values of pulse duration and pulse energy represents the ideal conditions to achieve minimum taper in laser-drilled holes. Thorough assessment of results also reveals that the laser-drilling process, optimized considering taper in the drilled hole as the target response, leads to very significant improvements in respect of other hole quality attributes of interest such as spatter and recast as well.     

Mechanism and specificity of the terminal thioesterase domain from the erythromycin polyketide synthase

BACKGROUND: Polyketides are important compounds with antibiotic and anticancer activities. Several modular polyketide synthases (PKSs) contain a terminal thioesterase (TE) domain probably responsible for the release and concomitant cyclization of the fully processed polyketide chain. Because the TE domain influences qualitative aspects of product formation by engineered PKSs, its mechanism and specificity are of considerable interest. RESULTS: The TE domain of the 6-deoxyerythronolide B synthase was overexpressed in Escherichia coli. When tested against a set of N-acetyl cysteamine thioesters the TE domain did not act as a cyclase, but showed significant hydrolytic specificity towards substrates that mimic important features of its natural substrate. Also the overall rate of polyketide chain release was strongly enhanced by a covalent connection between the TE domain and the terminal PKS module (by as much as 100-fold compared with separate TE and PKS 'domains'). CONCLUSIONS: The inability of the TE domain alone to catalyze cyclization suggests that macrocycle formation results from the combined action of the TE domain and a PKS module. The chain-length and stereochemical preferences of the TE domain might be relevant in the design and engineered biosynthesis of certain novel polyketides. Our results also suggest that the TE domain might loop back to catalyze the release of polyketide chains from both terminal and pre-terminal modules, which may explain the ability of certain naturally occurring PKSs, such as the picromycin synthase, to generate both 12-membered and 14-membered macrolide antibiotics.     

Numerical computations of supersonic inlet flow

Air‐breathing propulsion systems for high‐speed space travel applications are studied. Ramjets and scramjets have been identified as potential candidates. The flow inlets of such systems are modelled with a simulation that can predict all complex inlet flow features, including shock due to forebody, multiple shock reflections, normal shock, shock–boundary layer interaction and associated separation for two‐dimensional and axisymmetric inlets. Computed values are in good agreement with experimental data. Copyright © 2001 John Wiley & Sons, Ltd.     

Protection of aspergillus niger cellulases by urea during growth on glucose or glycerol supplemented media

The cellulase enzymes ofAspergillus niger were found to undergo catabolite repression in the presence of glucose and glycerol accompanied by sudden drop in pH of the fermentation medium below 2.0. This sudden drop in pH caused inactivation of cellulolytic enzymes produced byAspergillus niger. The supplementation of nitrogen sources, especially urea, protectsA. niger cellulases from inactivation caused by a sudden drop in pH, since urea helped to maintain the pH of the fermentation medium between 3.5 and 4.5. The role of urea in the protection of cellulase was more prominent when it was used in combination with glycerol (5%).