Die Anwendung von Kaliummanganat in der quantitativen Analyse

Zusammenfassung Es wird gezeigt, daß die photometrische Titration von Manganat mit As^III sehr gut durchzuführen ist. Da diese Methode schneller und genauer ist als die potentiometrische, schlagen wir vor, bei der Arbeitsweise A³ und bei der direkten Titration den Endpunkt photometrisch zu bestimmen. Auf diese Weise ist es möglich, Mengen von 0,1-1 mÄq mit dem E.E.L.-Titrator zu bestimmen, was mit Thiosulfat, Chrom(III) und Ameisens äure demonstriert wird.Es ist auch möglich, kleinere Mengen zu bestimmen (1-0,2 mg Thiosulfat), wenn die Titration mit kleineren Volumina Manganatlösung im Elko-Photometer durchgeführt wird.Die Fehler betragen im Falle von etwa 1 mÄq Substanz maximal 0,3% und bei 1-0,2 mg Thiosulfat maximal 1,5%.

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Summary The photometric titration of manganate with As^III solution can be easily performed. As this method is more rapid and precise than the potentiometric one it is proposed to determine the end point in procedure A³ and in the direct titration in that way. It is possible to determine quantities of 0.1-1 milli-equiv. by help of the E.E.L. titrator as demonstrated with thiosulphate, chromium(IIl) and formic acid. Also smaller quantities (1-0.2 mg of thiosulphate) can be determined if smaller volumes of manganate solution are used and the Elko II photometer (Zeiss) is employed for the titration. Maximum erros are 0.3% for quantities of about 1 milli-equiv. and 1.5% for 1-0.2 mg of thiosulphate.

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An dieser Stelle möchten wir Herrn R. Obbes für die genaue Durchführung vieler Bestimmungen danken.

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VIII. Mitteilung: Polak, H. L., H. F. Pronk u. G. Den Boef: diese Z. 190, 377 (1962).     

Algorithms for optimization problems with exclusion constraints

This paper proposes algorithms for minimizing a continuously differentiable functionf(x): ⁿ subject to the constraint thatx does not lie in specified bounded subsets of ⁿ . Such problems arise in a variety of applications, such as tolerance design of electronic circuits and obstacle avoidance in the selection of trajectories for robot arms. Such constraints have the form . The function is not continuously differentiable. Algorithms based on the use of generalized gradients have considerable disadvantages because of the local concavity of at points where the set {j|g ^j (x)=(x)} has more than one element. Algorithms which avoid these disadvantrages are presented, and their convergence is established.This research was sponsored in part by the National Science Foundation under Grant ECS-81-21149, the Air Force Office of Scientific Research (AFSC), United States Air Force under Contract F49620-79-C-0178, the Office of Naval Research under Grant N00014-83-K-0602, the Air Force Office of Scientific Research under Grant AFOSR-83-0361, and the Semiconductor Research Consortium under Grant SRC-82-11-008.     

Coprecipitation as a means of separation in substoichiometric isotope dilution analysis

Chromium has been determined by isotope dilution in artificial standards and in standard alloys using the substoichiometric principle. As a substoichiometric reaction the reduction of Cr(VI) to Cr(III) was used, followed by separation of these species by coprecipitation of the trivalent chromium on a Ti(OH)₄ precipitate. For amounts smaller than 1 μg the standard method had to be modified owing to spontaneous reduction of hexavalent chromium in the solution. Interferences from other metals, if they occur, can be easily overcome. The method is simple and inexpensive.     

A recursive quadratic programming algorithm for semi-infinite optimization problems

The well known, local recursive quadratic programming method introduced by E. R. Wilson is extended to apply to optimization problems with constraints of the type , where ranges over a compact interval of the real line. A scheme is proposed, which results in a globally convergent conceptual algorithm. Finally, two implementable versions are presented both of which converge quadratically.Research sponsored by the National Science Foundation Grant ECS-79-13148 and the Air Force Office of Scientific Research (AFOSR) United States Air Force Contract No. F49620-79-C-0178     

Computer-aided optimization of stepwise gradient profiles in thin-layer chromatography

Summary Two mixtures, one containing model coloured solutes and the other glycosides from the Digitalis species were separated by stepwise gradient thin-layer chromatography, the first in the system silica-toluene + ethyl acetate, the second in the system silica-ethyl acetate + methanol. The optimal gradient programs (i.e., for which maximal spread of spots along the plate is observed) were determined using a computer program reported in an earlier paper. Good separation and satisfactory agreement of predicted and experimental R_F values were obtained; the non-aqueous system for the separation of lanatosides permits considerable shortening of elution time owing to the lower viscosity of ethyl acetate-methanol mixtures.Dedicated to Professor Leslie S. Ettre on the occasion of his 70th birthday.     

A new radiometric titration method based on separation by means of ion exchange

The determination of zinc with EDTA is chosen as an example for the earlier suggested new radio-complexometric titration procedure, in which phase separation is achieved by means of a strongly basic anion exchanger in the solution. Concentrations of zinc solutions down to 10⁻⁶ M have been determined. The reverse titration,viz. of EDTA with zinc solution, which can be used as back-titration in complexometry, is also possible. However, theoretical relations for this latter type of titration are not simple.     

Asymptotic Growth of Solutions of Neutral Type Systems

We consider a differential system of neutral type with distributed delay. We obtain a precise norm estimation of semigroup generated by the operator corresponding to the system in question. Our result is based on a spectral analysis of the operator and some uniform estimation of norms of the exponentials of matrices. We also discuss the stability properties of corresponding solutions and the existence of the fastest growing solution.     

Separation of Some Aromatic Amino Acid Enantiomers with Pressurized Planar Electrochromatography and TLC

Influence of buffer pH, buffer concentration and ratio of methanol to acetonitrile in ternary mobile phase on migration distance of enantiomers of phenylalanine, tyrosine and DOPA in pressurized planar electrochromatography (PPEC) and thin-layer chromatography (TLC) systems is presented and compared. The applied operating variables in PPEC system more strongly influence on separation selectivity of investigated solutes than those in TLC one. Higher separation efficiency of PPEC system relative to TLC one is also demonstrated.     

A conformal decomposition finite element method for modeling stationary fluid interface problems

A method is developed for modeling fluid transport in domains that do not conform to the finite element mesh. One or more level set functions are used to describe the fluid domain. A background, non‐conformal mesh is decomposed into elements that conform to the level set interfaces. Enrichment takes place by adding nodes that lie on the interfaces. Unlike other enriched finite element methods, the proposed technique requires no changes to the underlying element assembly, element interpolation, or element quadrature. The complexity is entirely contained within the element decomposition routines. It is argued that the accuracy of the method is no less than that for eXtended Finite Element Methods (XFEM) with Heaviside enrichment. The accuracy is demonstrated using multiple numerical tests. In all cases, optimal rates of convergence are obtained for both volume and surface quantities. Jacobi preconditioning is shown to remove the ill‐conditioning that may result from the nearly degenerate conformal elements. Copyright © 2009 John Wiley & Sons, Ltd.     

First-Order Algorithms for Generalized Semi-Infinite Min-Max Problems

We present a first-order algorithm for solving semi-infinite generalized min-max problems which consist of minimizing a function f⁰(x) = F(¹(x), .... , ^m (x)), where F is a smooth function and each ⁱ is the maximum of an infinite number of smooth functions.In Section 3.3 of [17] Polak finds a methodology for solving infinite dimensional problems by expanding them into an infinite sequence of consistent finite dimensional approximating problems, and then using a master algorithm that selects an appropriate subsequence of these problems and applies a number of iterations of a finite dimensional optimization algorithm to each of these problems, sequentially. Our algorithm was constructed within this framework; it calls an algorithm by Kiwiel as a subroutine. The number of iterations of the Kiwiel algorithm to be applied to the approximating problems is determined by a test that ensures that the overall scheme retains the rate of convergence of the Kiwiel algorithm.Under reasonable assumptions we show that all the accumulation points of sequences constructed by our algorithm are stationary, and, under an additional strong convexity assumption, that the Kiwiel algorithm converges at least linearly, and that our algorithm also converges at least linearly, with the same rate constant bounds as Kiwiel's.