Sieving for rational points on hyperelliptic curves

We give a new and efficient method of sieving for rational points on hyperelliptic curves. This method is often successful in proving that a given hyperelliptic curve, suspected to have no rational points, does in fact have no rational points; we have often found this to be the case even when our curve has points over all localizations . We illustrate the practicality of the method with some examples of hyperelliptic curves of genus .

     

Synthesis and structural characterisation of CdS nanoparticles prepared in a four-components "water-in-oil" microemulsion

Nanostructured semiconductor particles are currently under intense investigation because of their enhanced photoreactivity and photocatalytic properties due to the quantum-size effect and the dependence of the photophysical and photochemical properties on their size as it approaches the exciton diameter. This increasing interest has led to the development of several synthetic procedures to prepare and stabilise uniform crystallites. In this paper, we report a novel synthetic pathway to obtain cadmium sulphide (CdS) nanoparticles in a quaternary "water-in-oil" microemulsion formed by a cationic surfactant cetyltrimethylammonium bromide (CTAB), pentanol, n-hexane and water. The synthesis of CdS in this system is achieved by mixing two microemulsions containing Cd(NO3)2 and Na2S, respectively. The nanocrystals have been characterised by using UV--visible spectroscopy and Transmission Electron Microscopy to investigate the influence of various parameters of the particles' formation and stability in solution. Capping of nanoparticles with suitable organic molecules has been performed in order to increase their stability and afford solubility in a wide range of solvents.     

Hydrodynamic and thermal interactions of a cluster of solid particles in a pool of liquid of different Prandtl numbers using two-fluid model

The knowledge of thermal interaction between hot particles and liquid is essential for many engineering applications. The main focus of the present study is to understand the underlying phenomena of transient interaction between the hot particles and the liquid of varying Prandtl number under different parametric conditions. Analysis is carried out numerically using in-house multiphase code based on Eulerian two-fluid laminar model. The code is validated against existing results. The dispersion and penetration characteristics of the particles are observed to be a strong function of Prandtl number as well as volume fraction and particle diameter, with a stronger mushrooming observed for lower particle size or high Prandtl number liquid. The thermal interaction is observed to be between the particles and the narrow thermal envelope surrounding the particles. The particles cooling rate are observed to be several orders faster in a liquid with lower Prandtl number.     

The development of an integrated platform to identify breast cancer glycoproteome changes in human serum

Protein glycosylation represents one of the major post-translational modifications and can have significant effects on protein function. Moreover, changes in the carbohydrate structure are increasingly being recognized as an important modification associated with cancer etiology. In this report, we describe the development of a proteomics approach to identify breast cancer related changes in either concentration and/or the carbohydrate structures of glycoprotein(s) present in blood samples. Diseased and healthy serum samples were processed by an optimized sample preparation protocol using multiple lectin affinity chromatography (M-LAC) that partitions serum proteins based on glycan characteristics. Subsequently, three separate procedures, 1D SDS-PAGE, isoelectric focusing and an antibody microarray, were applied to identify potential candidate markers for future study. The combination of these three platforms is illustrated in this report with the analysis of control and cancer glycoproteomic fractions. Firstly, a molecular weight based separation of glycoproteins by 1D SDS-PAGE was performed, followed by protein, glycoprotein staining, lectin blotting and LC–MS analysis. To refine or confirm the list of interesting glycoproteins, isoelectric focusing (targeting sialic acid changes) and an antibody microarray (used to detect neutral glycan shifts) were selected as the orthogonal methods. As a result, several glycoproteins including alpha-1B-glycoprotein, complement C3, alpha-1-antitrypsin and transferrin were identified as potential candidates for further study.     

Some New Radical Reactions of Xanthates

Xanthates are convenient precursors of a variety of radicals that can be captured in an inter- or intramolecular fashion. Overall, the process involves rupture of the sulfide C-S bond and addition of the elements of the xanthate to the olefinic trap. The xanthate in the product can be used in another radical sequence or ionically modified in a great variety of ways. S-Propargyl xanthates exhibit a special but interesting behaviour which involves a sigmatropic rearrangement to the corresponding allene and ring closure to a novel betaine.     

Exact solution of a class of nonlinear knapsack problems

We consider a class of nonlinear knapsack problems with applications in service systems design and facility location problems with congestion. We provide two linearizations and their respective solution approaches. The first is solved directly using a commercial solver. The second is a piecewise linearization that is solved by a cutting plane method.     

Analysis of Ti:LiNbO3 zero-gap directional coupler for wavelength division multiplexer/demultiplexer

For the purpose of multichannel integrated-optical wavelength division MUX/DEMUX design, the wavelength tuning method of Ti:LiNbO₃ zero-gap directional coupler is analysed by effective-index based matrix method (EIMM). In this method, first, the 2D refractive index profile of the Ti:LiNbO₃ zero-gap directional coupler is transformed into lateral 1D effective-index profile by WKB method. Finally, matrix method is applied to this effective-index profile and the propagation constants are computed from the resonance peaks of the excitation efficiency versus propagation constant characteristics. It has been shown that the channel wavelength tuning can be achieved by varying the Y-branching angle at the input and output of the device or by a slight variation of two-mode-section length. The method of electro-optic fine tuning of the channel wavelength and channel separation of the device has also been investigated. A cascaded structure with proper parameters for four-channel application is also simulated and the results are presented.     

Simultaneous Spectrophotometric Determination of Imipramine Hydrochloride with Chlordiazepoxide and Nortriptyline Hydrochloride with Fluphenazine Hydrochloride

Spectrophotometry was used with multivariate calibration to simultaneously determine compounds in mixtures. Two antidepressant mixtures were investigated: imipramine hydrochloride and chlordiazepoxide and nortriptyline hydrochloride and fluphenazine hydrochloride. Considerable spectral overlap and large differences in component concentrations were challenges. Since this type of analysis is often performed using complex algorithms, a simple strategy was used here for the simultaneous determination of both mixture components by classical least squares, principal component regression, and partial least squares. Experimental design was used to select the optimum parameters including the wavelength range, sampling interval, software, and derivative order. Accuracy was enhanced by proper wavelength selection. In addition, derivatives of the raw spectra improved the selectivity. The standard deviation, deviation of mean recovery from 100%, and prediction ability of the models were used as the responses. In respect to these terms, first-order derivatization of the spectra and a sampling interval of 1?nm provided the best results. In particular, the low concentration compounds in the mixtures (chlordiazepoxide and fluphenazine) were determined more accurately with precision lower than 3%. The strategy was used for the quality control of pharmaceuticals containing the mixtures without chemical pretreatment.     

Chemical and Photochemical Water Oxidation Catalyzed by Mononuclear Ruthenium Complexes with a Negatively Charged Tridentate Ligand

Two mononuclear ruthenium complexes [RuL(pic)₃] ( 1 ) and [RuL(bpy)(pic)] ( 2 ) (H₂L=2,6‐pyridinedicarboxylic acid, pic=4‐picoline, bpy=2,2′‐bipyridine) have been synthesized and fully characterized. Both complexes could promote water oxidation chemically and photochemically. Compared with other known ruthenium‐based water oxidation catalysts using [Ce(NH₄)₂(NO₃)₆] (Ce^IV) as the oxidant in solution at pH 1.0, complex 1 is one of the most active catalysts yet reported with an initial rate of 0.23 turnover s^?1. Under acidic conditions, the equatorial 4‐picoline in complex 1 dissociates first. In addition, ligand exchange in 1 occurs when the Ru^III state is reached. Based on the above observations and MS measurements of the intermediates during water oxidation by 1 using Ce^IV as oxidant, [RuL(pic)₂(H₂O)]⁺ is proposed as the real water oxidation catalyst.