Applications of convex analysis within mathematics

In this paper, we study convex analysis and its theoretical applications. We first apply important tools of convex analysis to Optimization and to Analysis. We then show various deep applications of convex analysis and especially infimal convolution in Monotone Operator  Theory. Among other things, we recapture the Minty surjectivity theorem in Hilbert space, and present a new proof of the sum theorem in reflexive spaces. More technically, we also discuss autoconjugate representers for maximally monotone operators. Finally, we consider various other applications in mathematical analysis.     

Effects of particle size on the structural and hyperfine properties of tin dioxide nanoparticles

In this work, we report on the study of SnO ₂ nanoparticles prepared by a polymer precursor method. X-ray diffraction (XRD) data analysis evidenced the formation of only the tetragonal rutile-type phase for the as-grown and thermally annealed samples. A mean grain size of about 11 nm for the as-prepared sample has been determined. This mean size increases after the thermal annealing and with the annealing temperature. The room temperature M?ssbauer spectra (MS) were well fitted using a quadrupole splitting (QS) distribution. The isomer shift (IS) tends to increase when the grain size decreases. That increase has been associated to the extra s-electron density generated by the oxygen vacancies.     

Local convergence of quasi-Newton methods under metric regularity

We consider quasi-Newton methods for generalized equations in Banach spaces under metric regularity and give a sufficient condition for q-linear convergence. Then we show that the well-known Broyden update satisfies this sufficient condition in Hilbert spaces. We also establish various modes of q-superlinear convergence of the Broyden update under strong metric subregularity, metric regularity and strong metric regularity. In particular, we show that the Broyden update applied to a generalized equation in Hilbert spaces satisfies the Dennis–Moré condition for q-superlinear convergence. Simple numerical examples illustrate the results.     

Solution Thermodynamics of Triclocarban in Organic Solvents of Different Hydrogen Bonding Capability

The thermodynamic functions Gibbs energy, enthalpy and entropy for the solution of triclocarban (TCC) in four organic solvents were calculated from solubility values obtained at temperatures from 293.15 up to 313.15 K. The solubility of TCC was determined in octanol (ROH), isopropyl myristate (IPM), chloroform (CLF), and heptane (HPT). The excess Gibbs energy and the activity coefficients of the solutes were also calculated. The solubilities of TCC are higher in ROH and IPM relative to those obtained in CLF and HPT. In addition, thermodynamic quantities for the transfer of this drug from HPT to the other organic solvents were calculated in order to estimate the hydrogen-bonding contributions.     

Synthesis of 1-methyl-3-oxo-7-oxabicyclo[2.2.1]hept-5-ene-2-carboxylic acid methyl ester

A simple and efficient method for the preparation of 1-methyl-3-oxo-7- oxabicyclo[2.2.1]hept-5-en-2-carboxylic acid methyl ester (1) is described. The first step is a highly regioselective Diels-Alder reaction between 2-methylfuran and methyl-3-bromo- propiolate. A remarkably difficult ketal hydrolysis reaction was effected by treatment with HCl, a simple reagent that was shown to be more efficient, in this case, than commonly used more elaborate methods.     

Sorption of organic molecules by graphitic acid and methylated graphitic acid: A preliminary study

Summary Interlamellar sorption complexes formed by graphitic acid and methylated graphitic acid have been studied. The latter forms complexes less readily with amines, more readily with fatty acids; for nitriles and alcohols the differences are minor. We believe this is due to the reduction in the acid nature on methylation. An important rôle in sorption is also ascribed to the number of active points per unit area of substrate.A liquid-solid transition is believed to occur in the sorbed film. Evidence is presented that the states concerned are not as sharply demarcated as for the free substance, and that the transition may occur at a lower temperatue for the sorbed film than the free substance.Mixtures of similar substances (amines) give a linear variation of interlayer spacing with composition. Mixtures of dissimilar substances may give complicated curves for this variation, from which conclusions may be drawn regarding the segregation (de-mixing) of sorbed molecules.

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Zusammenfassung Sorptionskomplexe der Zwischenschicht der Graphitsäure und der methylierten Graphitsäure wurden untersucht. Letztere bildet nur ziemlich schwer Komplexe mit Aminen, dagegen viel leichter mit Fettsäuren; die beobachteten Unterschiede für Nitrile und Alkohole sind klein. Wir denken, daß dies in Verbindung mit einer Verminderung des sauren Charakters der Graphitsäure infolge der Methylierung steht. Eine wichtige Rolle bei dem Sorptionsprozeß spielt wahrscheinlich auch die Anzahl von aktiven Zentren per Flächeneinheit.Wir glauben, einen Übergang flüssig-fest in der sorbierten Schicht beobachtet zu haben. Gewisse experimentelle Tatsachen weisen darauf hin, daß der Unterschied dieser beiden Zustände weniger bemerkbar bei der sorbierten Schicht als bei der freien Substanz ist. Der Übergang tritt im letzteren Fall auch bei einer niedrigeren Temperatur auf.Mischungen gleichartiger Substanzen (Amine) ergeben eine lineare Änderung der Zwischenschichtaufweitung mit der Zusammensetzung. Mischungen ungleichartiger Substanzen dagegen zeigen kompliziertere Kurven, die gewisse Folgerungen über die Ausscheidung der Molekeln in den Schichten ermöglichen.

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Address at which this work was performed: Physics Department Queen's College, University of St. Andrews, Dundee, Scotland.     

Purification of a PHA-Like Chitin-binding Protein from Acacia farnesiana Seeds: A Time-dependent Oligomerization Protein

A lectin-like protein from the seeds of Acacia farnesiana was isolated from the albumin fraction, characterized, and sequenced by tandem mass spectrometry. The albumin fraction was extracted with 0.5 M NaCl, and the lectin-like protein of A. farnesiana (AFAL) was purified by ion-exchange chromatography (Mono-Q) followed by chromatofocusing. AFAL agglutinated rabbit erythrocytes and did not agglutinate human ABO erythrocytes either native or treated with proteolytic enzymes. In sodium dodecyl sulfate gel electrophoresis under reducing and nonreducing conditions, AFAL separated into two bands with a subunit molecular mass of 35 and 50 kDa. The homogeneity of purified protein was confirmed by chromatofocusing with a pI = 4.0 +/- 0.5. Molecular exclusion chromatography confirmed time-dependent oligomerization in AFAL, in accordance with mass spectrometry analysis, which confers an alteration in AFAL affinity for chitin. The protein sequence was obtained by a liquid chromatography quadrupole time-of-flight experiment and showed that AFAL has 68% and 63% sequence similarity with lectins of Phaseolus vulgaris and Dolichos biflorus, respectively.     

Changes in mouse Leydig cells ultrastructure and testosterone secretion after diethylcarbamazine administration

Diethylcarbamazine (DEC) has been proven to be highly effective against lymphatic filariasis, although its effect on vertebrate cells remains uncertain. Mice Leydig cells after treatment with 200mg/kg of DEC for 12 days showed numerous lipid droplets, degenerated mitochondria, residual bodies and several giant whorl-like smooth endoplasmic reticulum, some of them encircling large lipids droplets. Treatment with lower dosages showed similar alterations on Leydig cells and the morphological effects decreased directly proportional to the drug concentration. Serum testosterone levels were significantly lower only in 200 mg/kg DEC-treated group when compared to the controls. However, no significant changes were observed in the pregnancy rates and offspring number of DEC-treated male-mated female mice in any doses studied. The results obtained in the present study are consistent with the hypothesis that DEC has some effects on mice Leydig cells, although they were not sufficient enough to interfere with the rodent fertility.     

Application of Thermogravimetry in the Quality Control of Chloramphenicol Tablets

The stability and thermal behaviour of chloramphenicol and various of its mixtures were investigated. The thermogravimetric and stability constant results showed that the chloramphenicol base is thermally more stable than the tablet in the studied formulation. The reduction in stability was attributed to the presence of starch in the formulation. The thermal decompositions of the chloramphenicol base and the tablet obey first-order kinetics. This revised version was published online in August 2006 with corrections to the Cover Date.