Unconstrained Optimization Reformulations of Variational Inequality Problems

Recently, Peng considered a merit function for the variational inequality problem (VIP), which constitutes an unconstrained differentiable optimization reformulation of VIP. In this paper, we generalize the merit function proposed by Peng and study various properties of the generalized function. We call this function the D-gap function. We give conditions under which any stationary point of the D-gap function is a solution of VIP and conditions under which it provides a global error bound for VIP. We also present a descent method for solving VIP based on the D-gap function.     

Another new application of standard-addition technique in flame spectrophotometry

Summary A new flame-photometric method of determination, the Double-Coefficient Method, based upon the standard-addition technique has been proposed.The method is found to be useful for samples where a concomitant may seriously interfere with the radiation intensity of the specified substance. No knowledge about sample composition is needed and the only prerequisite to the method is the log-log translation rule which has been generally valid when alkali metals are specified and concomitants cause multiplicative interference. In other words, the method is generally applicable where the concomitant C–I curve is expressed in a formI ^* = n· f_(m·c) in which I^* is the intensity recorded,C is the concentration of specified substance,I = f_(C) is the expression for the specifiedC- I curve andm andn are constants which need not be known.Many determinations of NaCl have been carried out with various interfering concomitants. In only exceptional cases did the relative error exceed 10% no matter how much interference there was from concomitants.It is suggested that some investigation into the dependence of the logC– logI relation on various excitation conditions, and some method of controlling theC-I function would be of great interest and practical value. In some special case the Double-Coefficient Method needs only a very simplified procedure.

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Zusammenfassung Eine neue flammenphotometrische Bestimmungsmethode wird vorgeschlagen. Diese Doppel-Koeffizient-Methode beruht auf der Zugabe von Standard-Substanzen und erwies sich als geeignet für Proben, in denen eine Begleitsubstanz die Strahlungsintensität des zu bestimmenden Elementes wesentlich beeinflußt. Keinerlei Kenntnis der Zusammensetzung der Probe ist nötig. Die einzige Vorbedingung des Verfahrens ist das Gesetz der log-log-Übertragung, das allgemein für die Bestimmung von Alkalimetallen neben multiplikativ störenden Begleitsubstanzen gültig ist. Mit anderen Worten, die Methode ist allgemein dort anwendbar, wo dieC-I-Kurve der Begleitstoffe durch die BeziehungI ^* =n · f_(m·.C) ausdrückbar ist; darin steht I^* für die beobachtete Intensität,C für die Konzentration des zu bestimmenden Elementes,I = f_(C) gilt für dieC-I-Kurve des zu bestimmen- den Elementes, m undn stellen Konstanten dar, deren Wert nicht bekannt zu sein braucht.Zahlreiche Bestimmungen von NaCl wurden neben verschiedenen störenden Begleitstoffen ausgeführt. Nur in Ausnahmefällen und unabhängig von dem Ausmaß deren störender Wirkung überschritt der Fehler 10%.Die Untersuchung der Abhängigkeit des logC - logI-Verhältnisses unter verschiedenen Anregungsbedingungen sowie eine Überprüfung derC- I-Funktion wäre von großem Interesse und praktischem Wert. In einzelnen, besonders gelagerten Fällen bedarf die Doppel-Koeffizient-Methode nur einer sehr vereinfachten Arbeitsweise.

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Résumé On a proposé une nouvelle méthode de dosage par photométrie de flamme, la méthode du double coefficient, fondée sur la technique d'addition d'un échantillon-type. On a trouvé que cette méthode était utile pour l'analyse des échantillons dans lesquels la présence d'une substance concomitante était susceptible d'altérer de façon importante l'intensité de radiation de la substance étudiée. Il n'est pas nécessaire de connaître la composition de l'échantillon, il suffit de connaître au préalable la règle de translation log-log qui est généralement valable lorsque la substance étudiée est un métal alcalin et que les substances concomitantes donnent lieu à des erreurs multiples. En d'autres termes, la méthode est généralement applicable lorsque la courbeC-I de la substance concomitante s'exprime sous la forme I^* =n · f_(m·.C) dans laquelle I^* est l'intensité enregistrée,C est la concentration de la substance étudiée,I = f_(C) est l'expression de la courbeC-I pour la substance étudiée etm etn des constantes qu'il n'est pas necessaire de connaître.De nombreuses déterminations de NaCl ont été effectuées en présence de diverses substances concomitantes gênantes. Ce n'est que dans des cas exceptionnels que l'erreur relative s'est élevée au-dessus de 10%, indépendamment de l'importance des perturbations apportées par les substances concomitantes.On propose de rechercher l'influence de certaines conditions d'excitation sur la relation logC-logI et d'établir une méthode de contrôle de la fonctionC-I, qui seraient d'une grande valeur pratique. Dans quelques cas particuliers la méthode du double coefficient ne nécessite qu'une technique très simplifiée.

     

Inclusion polymerization of Isoprene in the channels of sepiolite

We have tried an inclusion polymerization in the channels of sepiolite, and studied the structure of polymer formed inside and outside the channels. Isoprene was polymerized not only on the outer surface but also in the channels of the sepiolite at 25 °C. Strong Brønsted acid sites in the outer and inner surfaces of the sepiolite intitiate a polymerization of isoprene and styrene. Double bonds of polyisoprene formed in the channels were protonated by the strong Brønsted acid sites of the sepiolite. The interaction between the protonated double bonds and the acid sites changed the color to violet. The outer surface of the folded sepiolite whose channels were collapsed formed a usual polyisoprene which caused no color change.     

Diffusion Imaging with HyperpolarizedHe Gas

We used MRI of hyperpolarized³He to demonstrate some novel aspects of gas diffusion. Two different techniques were used. First, a slice was burned into a one-dimensional image by inverting the spins in the slice and diffusion was studied by measuring the magnetization as it filled the depleted slice. A diffusion coefficient was determined by the fit of these data. Second, one-dimensional diffusion images were made using a Stejskal–Tanner PGSE method. This was done with and without a temperature gradient present, showing that the effect of temperature can be dynamically monitored by such diffusion images.     

Einfluß von Äthanol auf die asymmetrische Synthese,die durch Poly(5-benzyl-L-glutamat) und Poly(4-benzyl-Laspartat) katalysiert wird

Ohne Zusammenfassung     

Observation of spectral line profiles emitted by an inductively coupled plasma—I.: On the wavelength shift of spectral lines

Profiles of 16 spectral lines stemming from 8 elements (Ar, Na, Cu, Sr, Cd, Ba, Mg and Li) emitted by an inductively coupled plasma (ICP) have been observed and measured with a pressure-scanning Fabry-Perot interferometer. In the process of profile observations, we have found wavelength shifts of spectral lines in an ICP and for the first time studied this phenomenon quantitatively and systematically in a spectrochemical source. The profiles of spectral lines emitted by the ICP have been compared with those emitted by hollow cathode lamps. The magnitude of the wavelength shift to the red or the blue varied more or less with the plasma conditions, observation position and the concentration of a concomitant, cesium. In the present work the observed line profiles were not deconvoluted for the apparatus profiles. Typically the order of magnitude of the wavelength shift measured for spectral lines that show large shifts at an observation height of about 4 mm in an “analytical” ICP is n × 10^?3 nm, where n is about 4 for Ar I 427.2 nm and about 1 for Cu I 521.8 nm and Sr II 430.5 nm. With regard to the wavelength shift, several trends and/or regularities were found. The Stark effect is considered as the main cause of the phenomena.     

Coordination number of Ge atoms in Na2OGeO2 glasses studied by chemical shift measurements

The coordination number of Ge atoms in Na₂OGeO₂ glasses was estimated from chemical shift of GeK α₁. As the concentration of Na₂O increases, the chemical shift tends to increase, reaching a maximum at a concentration between 15–20 mol.% Na₂O, and then to decrease. The concentration of six-coordinated Ge atoms was found to be about 25% at its maximum and zero at 35 mol.% Na₂O.     

Penalty function theory for general convex programming problems

A class of penalty functions for solving convex programming problems with general constraint sets is considered. Convergence theorems for penalty methods are established by utilizing the concept of infimal convergence of a sequence of functions. It is shown that most existing penalty functions are included in our class of penalty functions.     

Mechanische und thermische Eigenschaften von mit Borax vernetztem Polyvinylalkohol

Ohne Zusammenfassung