Microstructural evolution of decagonal quasicrystal in the undercooled Al72Ni12Co16 alloy melts

The microstructure evolution of decagonal quasicrystals in Al₇₂Ni₁₂Co₁₆ alloy was investigated by the electromagnetic melting and cyclic superheating method. Single-phase decagonal quasicrystals have been obtained when the undercoolings were larger than 60 K. The decagonal quasicrystals formed at various undercoolings show different microstructural morphologies. Furthermore, grain refinement was found near the undercooling of 120 K. Based on current thermodynamic and dendrite growth theories, a dimensionless superheating parameter was adopted to explain the effect of processing conditions on the microstructure of Al₇₂Ni₁₂Co₁₆ alloy. The result indicate that the fine equiaxied microstructure of decagonal quasicrystal (D-phase) formed near on undercooling of 120 K originates from the break-up of dendrites.     

Chemical analysis and distribution investigation of trace elements in indium matrix by spark source mass spectrometry

Summary High-purity indium was analysed by spark source mass spectrometry, using electrical and photoplate detection. For the calibration of the differences in elemental sensitivity, a standard sample was prepared in which 10 impurities were determined by graphite furnace atomic absorption spectrometry. In this way accuracies of less than 40% were obtained for relatively homogeneous elements at ppm and sub-ppm level. About 40 elements could be determined with detection limits of 10 to 30 ppb. Two pattern recognition methods, principal component analysis and clustering analysis, were applied to obtain information on trace element distribution, which indicated that a number of elements were strongly spatially correlated in the analysed sample.

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Chemische Analyse und Verteilungsbestimmung von Spurenelementen in Indium-Matrix durch Funkenquellen-Massenspektrometrie

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On leave from: Department of Chemistry, Nanjing Normal University, Nanjing, People's Republic of China     

Microwave‐improved polymerization of ϵ‐caprolactone initiated by carboxylic acids

The ring‐opening polymerization of ε‐caprolactone (ε‐CL), initiated by carboxylic acids such as benzoic acid and chlorinated acetic acids under microwave irradiation, was investigated; with this method, no metal catalyst was necessary. The product was characterized as poly(ε‐caprolactone) (PCL) by ¹H NMR spectroscopy, Fourier transform infrared spectroscopy, ultraviolet spectroscopy, and gel permeation chromatography. The polymerization was significantly improved under microwave irradiation. The weight‐average molecular weight (M_w) of PCL reached 44,800 g/mol, with a polydispersity index [weight‐average molecular weight/number‐average molecular weight (M_w/M_n)] of 1.6, when a mixture of ε‐CL and benzoic acid (25/1 molar ratio) was irradiated at 680 W for 240 min, whereas PCL with M_w = 12,100 and M_w/M_n = 4.2 was obtained from the same mixture by a conventional heating method at 210 °C for 240 min. A degradation of the resultant PCL was observed during microwave polymerization with chlorinated acetic acids as initiators, and this induced a decrease in M_w of PCL. However, the degradation was hindered by benzoic acid at low concentrations. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 13–21, 2003     

Lower bounds for sums of Barban-Davenport-Halberstam type (supplement)

This article was processed by the author using the IATEX style filecljourl from Springer-Verlag.     

A modified method of characteristics incorporating streamline diffusion

A hybrid finite-element method, combining ideas from a modified method of characteristics and the streamline diffusion method, delivers accurate solutions to the advection–diffusion equation. An error analysis for the case of tensorial diffusion shows that the lowest-order version of the scheme, which allows one to use a symmetric linear solvers at each time step, possesses first-order accuracy in time and space. Numerical experiments demonstrate the scheme's ability to model advection-dominated transport of solute plumes without distorting sharp fronts. © 1995 John Wiley & Sons, Inc.     

Temperature‐modulated differential scanning calorimetry studies on the origin of double melting peaks in isothermally melt‐crystallized poly(L‐lactic acid)

In this work, the melting behaviors of nonisothermally and isothermally melt‐crystallized poly(L ‐lactic acid) (PLLA) from the melt were investigated with differential scanning calorimetry (DSC) and temperature‐modulated differential scanning calorimetry (TMDSC). The isothermal melt crystallizations of PLLA at a temperature in the range of 100–110 °C for 120 min or at 110 °C for a time in the range of 10–180 min appeared to exhibit double melting peaks in the DSC heating curves of 10 °C/min. TMDSC analysis revealed that the melting–recrystallization mechanism dominated the formation of the double melting peaks in PLLA samples following melt crystallizations at 110 °C for a shorter time (≤30 min) or at a lower temperature (100, 103, or 105 °C) for 120 min, whereas the double lamellar thickness model dominated the formation of the double melting peaks in those PLLA samples crystallized at a higher temperature (108 or 110 °C) for 120 min or at 110 °C for a longer time (≥45 min). © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 466–474, 2007     

A new generalized algebra method and its application in the (2 + 1) dimensional Boiti–Leon–Pempinelli equation

In the present paper, some types of general solutions of a first-order nonlinear ordinary differential equation with six degree are given and a new generalized algebra method is presented to find more exact solutions of nonlinear differential equations. As an application of the method and the solutions of this equation, we choose the (2 + 1) dimensional Boiti Leon Pempinelli equation to illustrate the validity and advantages of the method. As a consequence, more new types and general solutions are found which include rational solutions and irrational solutions and so on. The new method can also be applied to other nonlinear differential equations in mathematical physics.     

Constraints on the number of maximal independent sets in graphs

A maximal independent set of a graph G is an independent set that is not contained properly in any other independent set of G. Let i(G) denote the number of maximal independent sets of G. Here, we prove two conjectures, suggested by P. Erdös, that the maximum number of maximal independent sets among all graphs of order n in a family Φ is o(3^n/3) if Φ is either a family of connected graphs such that the largest value of maximum degrees among all graphs of order n in Φ is o(n) or a family of graphs such that the approaches infinity as n → ∞.     

Synthesis,characterization, and micellization of an epoxy‐based amphiphilic diblock copolymer of ϵ‐caprolactone and glycidyl methacrylate by enzymatic ring‐opening polymerization and atom transfer radical polymerization

Amphiphilic diblock copolymer polycaprolactone‐block‐poly(glycidyl methacrylate) (PCL‐b‐PGMA) was synthesized via enzymatic ring‐opening polymerization (eROP) and atom transfer radical polymerization (ATRP). Methanol first initiated eROP of ?‐caprolactone (?‐CL) in the presence of biocatalyst Novozyme‐435 under anhydrous conditions. The resulting monohydroxyl‐terminated polycaprolactone (PCL–OH) was subsequently converted to a bromine‐ended macroinitiator (PCL–Br) for ATRP by esterification with α‐bromopropionyl bromide. PCL‐b‐PGMA diblock copolymers were synthesized in a subsequent ATRP of glycidyl methacrylate (GMA). A kinetic analysis of ATRP indicated a living/controlled radical process. The macromolecular structures were characterized for PCL–OH, PCL–Br, and the block copolymers by means of nuclear magnetic resonance, gel permeation chromatography, and infrared spectroscopy. Differential scanning calorimetry and wide‐angle X‐ray diffraction analyses indicated that the copolymer composition (?‐CL/GMA) had a great influence on the thermal properties. The well‐defined, amphiphilic diblock copolymer PCL‐b‐PGMA self‐assembled into nanoscale micelles in aqueous solutions, as investigated by dynamic light scattering and transmission electron microscopy. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 5037–5049, 2007