A curvilinear method based on minimal-memory BFGS updates

We present a new matrix-free method for the computation of negative curvature directions based on the eigenstructure of minimal-memory BFGS matrices. We determine via simple formulas the eigenvalues of these matrices and we compute the desirable eigenvectors by explicit forms. Consequently, a negative curvature direction is computed in such a way that avoids the storage and the factorization of any matrix. We propose a modification of the L-BFGS method in which no information is kept from old iterations, so that memory requirements are minimal. The proposed algorithm incorporates a curvilinear path and a linesearch procedure, which combines two search directions; a memoryless quasi-Newton direction and a direction of negative curvature. Results of numerical experiments for large scale problems are also presented.     

Photochemical Activation of Aromatic Aldehydes: Synthesis of Amides,Hydroxamic Acids and Esters

A cheap, facile and metal-free photochemical protocol for the activation of aromatic aldehydes has been developed. Utilizing thioxanthen-9-one as the photocatalyst and cheap household lamps as the light source, a variety of aromatic aldehydes have been activated and subsequently converted in a one-pot reaction into amides, hydroxamic acids and esters in good to high yields. The applicability of this method was highlighted in the synthesis of Moclobemide, a drug against depression and social anxiety. Extended and detailed mechanistic studies have been conducted, in order to determine a plausible mechanism for the reaction.     

An improved selective determination of mercury(II) by complexometric titration

A simple and accurate method has been developed for selective determination of mercury in alkaline solution. It involves the addition of an excess of EDTA to the mercury solution, titration of unreacted EDTA with a standard zinc solution, and then addition of N-allylthiourea solution at pH ? 9. By heating, the mercury-EDTA chelate is decomposed selectively, mercury sulfide is precipitated, and the EDTA freed is again titrated with standard zinc solution. Eriochrome Black T is used as indicator. Interference of some cations is discussed.     

Fire‐Retardant and Thermally Insulating Phenolic‐Silica Aerogels

Energy efficient buildings require materials with a low thermal conductivity and a high fire resistance. Traditional organic insulation materials are limited by their poor fire resistance and inorganic insulation materials are either brittle or display a high thermal conductivity. Herein we report a mechanically resilient organic/inorganic composite aerogel with a thermal conductivity significantly lower than expanded polystyrene and excellent fire resistance. Co‐polymerization and nanoscale phase separation of the phenol‐formaldehyde‐resin (PFR) and silica generate a binary network with domain sizes below 20 nm. The PFR/SiO₂ aerogel can resist a high‐temperature flame without disintegration and prevents the temperature on the non‐exposed side from increasing above the temperature critical for the collapse of reinforced concrete structures.     

A practical method for solving large-scale TRS

We present a nearly-exact method for the large scale trust region subproblem (TRS) based on the properties of the minimal-memory BFGS method. Our study is concentrated in the case where the initial BFGS matrix can be any scaled identity matrix. The proposed method is a variant of the Moré–Sorensen method that exploits the eigenstructure of the approximate Hessian B, and incorporates both the standard and the hard case. The eigenvalues of B are expressed analytically, and consequently a direction of negative curvature can be computed immediately by performing a sequence of inner products and vector summations. Thus, the hard case is handled easily while the Cholesky factorization is completely avoided. An extensive numerical study is presented, for covering all the possible cases arising in the TRS with respect to the eigenstructure of B. Our numerical experiments confirm that the method is suitable for very large scale problems.     

Model for successive determination of aluminium and fluoride by combination of fluorimetric and potentiometric methods

Summary The paper represents a non-conventional approach to the successive determination of aluminium and fluoride in the same sample. It is based on the mathematical correction of a complex analytical signal for aluminium in the presence of fluoride (obtained by the fluorescence method). Additionally, a potentiometric determination of the fluoride content is necessary to complete the analysis. A mathematical model to describe the dependence between the complex analytical signal and the concentrations of aluminium and fluoride for a wide range of concentrations of both species is obtained. The approach seems to be useful for continuous monitoring of samples containing both aluminium and fluoride such as tooth paste, cryolite, industrial waste waters etc.

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Ein Modell für die aufeinanderfolgende Bestimmung von Aluminium und Fluorid durch Kombination von Fluorimetrie und Potentiometrie

Zusammenfassung Die Arbeit beschreibt eine nichtkonventionelle Methode für die Bestimmung von Aluminium und Fluorid in einer Probe. Sie beruht auf der mathematischen Korrektur eines komplexen analytischen Signal für Aluminium in Anwesenheit von Fluorid (durch Fluorescenzverfahren) und nachfolgende Bestimmung von Fluorid durch Potentiometrie. Ein mathematisches Modell, das den Zusammenhang zwischen dem komplexen Signal und den Konzentrationen von Aluminium und Fluorid für einen breiten Konzentrationsbereich beider Ionen beschreibt, wird dargestellt. Die Methode kann für die kontinuierliche Analyse von Proben, die Aluminium und Fluorid gleichzeitig enthalten (z. B. Zahnpasta, Kryolith, Abwasser usw.) eingesetzt werden.

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On leave from Fac. of Chemistry, Chair of Analyt. Chemistry, Univ. of Sofia, 1126 Sofia, A. Ivanov 1, Bulgaria