Zinn und Antimon in Legierungen

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L-Curve and Curvature Bounds for Tikhonov Regularization

The L-curve is a popular aid for determining a suitable value of the regularization parameter when solving linear discrete ill-posed problems by Tikhonov regularization. However, the computational effort required to determine the L-curve and its curvature can be prohibitive for large-scale problems. Recently, inexpensively computable approximations of the L-curve and its curvature, referred to as the L-ribbon and the curvature-ribbon, respectively, were proposed for the case when the regularization operator is the identity matrix. This note discusses the computation and performance of the L- and curvature-ribbons when the regularization operator is an invertible matrix.     

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Equational partiality

A special kind of partiality of heterogeneous algebraic structures is introduced. Every operator of a heterogeneous operator domain is associated with a set of term equations as necessary and sufficient domain condition.It is shown that some kind of hierarchy condition for the system of domain equations is equivalent to the condition that every injective weak homomorphism is a strong homomorphism which is equivalent to the statement that every bijective weak homomorphism is an isomorphism.On the base of this result the notions of a quasi-variety and of a variety of equationally partial heterogeneous algebras are suggested. The class of all small categories becomes a standard example of a variety of equational partial heterogeneous algebras.Presented by V. Trnková.     

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Book reviews

     

Fluorine in Small Molecules: Fluoromethyl Azide and Chalcogenocyanates

Fluoromethylating agents are a highly studied and controversely discussed class of compounds. New fluoromethyl pseudohalides FCH₂N₃, FCH₂SCN, and FCH₂SeCN were prepared for the first time and their physical and spectroscopic properties investigated. Their synthesis is performed conveniently by fluoromethylation of the respective silver or potassium pseudohalogenides with fluoroiodomethane.     

Reagents for Selective Fluoromethylation: A Challenge in Organofluorine Chemistry

The introduction of a monofluoromethyl moiety has undoubtedly become a very important area of research in recent years. Owing to the beneficial properties of organofluorine compounds, such as their metabolic stability, the incorporation of the CH₂F group as a bioisosteric substitute for various functional groups is an attractive strategy for the discovery of new pharmaceuticals. Furthermore, the monofluoromethyl unit is also widely used in agrochemistry, in pharmaceutical chemistry, and in fine chemicals. The problems associated with climate change and the growing need for environmentally friendly industrial processes mean that alternatives to the frequently used CFC and HFBC fluoromethylating agents (CH₂FCl and CH₂FBr) are urgently needed and also required by the Montreal Protocol. This has recently prompted many researchers to develop alternative fluoromethylation agents. This Minireview summarizes both the classical and new generation of fluoromethylating agents. Reagents that act via electrophilic, nucleophilic, and radical pathways are discussed, in addition to their precursors.     

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