Collocation Methods for Weakly Singular Second-kind Volterra Integral Equations with Non-smooth Solution

Collocation type methods are studied for the numerical solutionof the weakly singular Volterra integral equation of the secondkind: where the solution (t) is assumedto have the form f(t) = x(t)+r^?(t), x and being sufficientlysmooth. The solution is approximated near zero by a linear combinationof powers of t?, and away from zero by the usual polynomialrepresentation. Convergence is proved and many numerical experimentsare carried out with examples from the literature. A comparisonis made with a method of Brunner & Norsett (1981), originallydeveloped for (1) with a smooth solution. Special attentionis paid to the numerical approximation of the so-called momentintegrals which emerge in the collocation scheme.     

Rhodium-Catalyzed Enantioselective Radical Addition of CX4 Reagents to Olefins

We describe the synthetically useful enantioselective addition of Br−CX₃ (X=Cl or Br) to terminal olefins to introduce a trihalomethyl group and generate optically active secondary bromides. Computational and experimental evidence supports an asymmetric atom-transfer radical addition (ATRA) mechanism in which the stereodetermining step involves outer-sphere bromine abstraction from a [(bisphosphine)Rh^IIBrCl] complex by a benzylic radical intermediate. This mechanism appears unprecedented in asymmetric catalysis.     

Enantioselective total synthesis of (-)-kibdelone C

The kibdelones are aromatic polyketide natural products featuring isoquinolinone and tetrahydroxanthone ring systems. They display potent cytotoxicity toward a range of human cancer cell lines. Here, we present an enantioselective total synthesis of kibdelone C that utilizes a Shi epoxidation to establish the absolute and relative stereochemistry, an acid-catalyzed cyclization to form the tetrahydroxanthone, and a C-H arylation to complete the hexacyclic skeleton.     

A thin film triode type carbon nanotube field emission cathode

The field electron emission of carbon nanotubes has been heavily studied over the past two decades for various applications, such as in display technologies, microwave amplifiers, and spacecraft propulsion. However, a commercializable lightweight and internally gated electron source has yet to be realized. This work presents the fabrication and testing of a novel internally gated carbon nanotube field electron emitter. Several specific methods are used to prevent electrical shorting of the gate layer, a common failure for internally gated devices. A unique design is explored where the etch pits extend into the silicon substrate and isotropic etching is used to create a lateral buffer zone between the gate and carbon nanotubes. Carbon nanotubes are self-aligned to and within 10 microns from the gate, which creates large electric fields at low potential inputs. Initial tests confirm high field emission performance with an anode current density (based on total area of the device) of 293 μA?cm^?2 and a gate current density of 1.68 mA?cm^?2 at 250 V.     

无机酸洗脱对胜利褐煤微晶结构及其自燃倾向性的影响

利用XRD、Raman、XPS和FT-IR表征技术,研究无机酸洗脱(HCl、H2SO4、HCl-HF)处理的胜利褐煤微晶结构的变化,采用自行设计的表面吸附仪-GC联用装置,对样品进行不同温度的低温脉冲氧化实验,考察了煤样在不同温度下氧吸附量的变化规律,通过低温脉冲氧吸附规律与TG/DTG和固定床燃烧实验关联,考察了煤样的自燃倾向。结果表明,无机酸洗脱对矿物质的脱除使得煤结构的有序度增加,石墨化程度提高,无机酸洗脱煤样与原煤相比吸氧量明显下降。随着吸附温度的升高,各煤样吸氧量明显增加,且随着脱除矿物质程度的增加,吸氧量呈减小的趋势,导致自燃倾向降低。     

Enantioselective total synthesis of (+)- and (-)-nigellamine A2

The nigellamine alkaloids are dolabellane diterpenes displaying potent lipid metabolism-promoting activity. Total synthesis of (+)- and (-)-nigellamine A2 has been accomplished. Absolute stereochemistry of synthetic nigellamine A2 was established through an intramolecular asymmetric allylic alkylation using a Pd(phosphinooxazoline) catalyst. Other notable transformations include a radical alkynylation, a diastereoselective Nozaki-Hiyama-Kishi cyclization, and a regio- and stereoselective catalytic epoxidation. On the basis of X-ray crystallographic analysis of an optically active intermediate, we have confirmed the assigned absolute stereochemistry of the natural product. Minor modifications of the synthetic sequence outlined here should provide access to the other nigellamine alkaloids.     

The kinetics of the thermal degradation of calcium carbonate

The decomposition of calcium carbonate fine powder in a flowing nitrogen atmosphere has been investigated by non-isothermal thermogravimetry at heating rates in the range, 10–50 deg min^–1. The analog percentage weight change record was digitized at 1 deg intervals. The resulting data, transformed into dimensionless extents of reaction and calculated rates of reaction, was then subjected to the Arrhenius, Friedman and Generalized Kissinger analyses, using a recently developed FORTRAN program system. The value ofn namely 0.39 ±0.04, resulting when the data is analyzed assuming an nth order reaction, strongly indicates that the most probable rate controlling step is a three-dimensional diffusion process (D4 mechanism), withE=172.4 kJ·mol^–1 andA=1.97·10⁴ K^–1·min^–1. Reasons for the wide disparity in previously reported kinetic data are discussed.

---

Zusammenfassung Die Zersetzung von feinpulvrigem Calciumcarbonat im Stickstoffstrom wurde durch nicht-isotherme Thermogravimetrie bei Aufheizgeschwindigkeiten von 10–50 °C/min untersucht. Die analoge prozentuale Gewichtsverlustregistrierung wurde in Intervallen von einem Grad digitalisiert. Die erhaltenen, in solche eines dimensionslosen Reaktionsgradcs überführten Daten und berechnete Reaktionsgeschwindigkeiten wurden der Arrhenius-, der Friedmann- und einer verallgemeinerten Kissinger-Analyse unterzogen, wobei ein kürzlich aufgestelltes FORTRAN-Programm benutzt wurde. Der unter der Annahme einer Reaktion n-ter Ordnung fürn erhaltene Wert von 0.39 ±0.04 ist ein nachdrücklicher Hinweis darauf, daß der geschwindigkeitsbestimmende Schritt höchstwahrscheinlich ein dreidimensionaler Diffusionsprozeß (D4-Mechanismus) mitE=172.4 kJ·mol^–1 undA=1.97·10⁴ K^–1·min^–1 ist. Gründe für die weitreichende Verschiedenheit der bisher mitgeteilten kinetischen Daten werden diskutirt.

---

10–50° . , , 1. , , , , , . n- , =0,39 ±0,04 , , e (4 ) E=172, 4 · ^–1 =1,97·10^{4 –1}·^–1. .

---

---

To be presented at the 14th North American Thermal Analysis Society Conference, San Francisco, CA, September 15–18, 1985.