General Base Catalysis by Organic Bases of the Reaction of Diphenylphosphinic Hydrazide with Phenyl Isocyanate in Benzene

The kinetics of the reaction of diphenylphosphinic hydrazide with phenyl isocyanate in the presence of organic bases in benzene at 25°C were studied. The catalytic activity of the bases correlates with spectroscopic and thermodynamic Taft (pK _{H B}), Koppel-Palm (B), and Gutmann (DN) parameters. A common general base mechanism of the catalysis of semicarbazide formation by bases belonging to different classes of organic compounds is offered and discussed.     

Organic solvents as catalysts of formation of phosphorus-containing thiosemicarbazides

The kinetics of the reaction of O,O-diphenyl phosphorohydrazidothioate with phenyl isothiocyanate at 25°C in benzene in the presence of organic bases is studied. The dependences of the catalytic activity on the nature and structure of organic bases and on various parameters characterizing their basicity are analyzed. The catalytic activity exhibited in the formation of phosphorus-containing thiosemicarbazides by donor solvents added to benzene correlates well with both spectroscopic and thermodynamic parameters of basicity: Taft (pK _HB), Koppel-Palm (B), and Gutmann (DN) parameters. A common mechanism of the base catalysis of the thiosemicarbazide formation by organic bases of different classes is suggested and discussed.     

Effect of reaction medium on the kinetic rules of formation of phosphorus-containing picrylhydrazides

Rate constants of the reaction of diphenylphosphinic acid hydrazide with picryl chloride in the solvents of different nature may be quantitatively connected with their physicochemical characteristics by means of the linear tetraparametric Coppel-Palm equation. The rule obtained permits to carry out quantitative analysis of the solvatational effects of solvents under study. Reaction rate depends mainly on the solvent basicity and polarity. Reaction mechanism is discussed and possible scheme of solvatation is offered.     

Quantitative estimation of the α-effect in the reactions yielding phosphorus-containing thiosemicarbazides

The α-effect in the reactions of O,O-diaryl phosphorohydrazidothioates with phenyl isothiocyanate in benzene at 25°C was quantitatively evaluated from the kinetic data. The probable reaction mechanism was suggested, and the causes of the α-effect in these reactions are discussed. An approximate linear correlation is observed between the α-effect in the reactions of O,O-diaryl phosphorohydrazidothioates with phenyl isothiocyanate, basicity constants of the hydrazides, and σ^p constants of the substituents at the P atom. The value of the α-effect is largely determined by the structure of the transition state.     

Structures and magnetic properties of tetranuclear nickel(II) complexes with unusual mu3-1,1,3 azido bridges

Pyrazolate-based dinucleating ligands with thioether-containing chelate arms have been used for the synthesis of a family of novel tetranuclear nickel(II) complexes [L2Ni4(N3)3(O2CR)](ClO4)2 that incorporate three azido bridges and one carboxylate (R = Me, Ph). Molecular structures have been elucidated by X-ray crystallography in four cases, revealing Ni4 cores with a unique topology in which two of the azido ligands adopt an unusual mu3-1,1,3 bridging mode. The compounds were further characterized by mass spectrometry, IR spectroscopy, and variable-temperature magnetic susceptibility measurements. Magnetic data analyses indicate a combination of significant intramolecular ferromagnetic and antiferromagnetic exchange interactions that give rise to an overall S(T) = 0 ground state. The sign and the magnitude of the individual couplings have been rationalized in the framework of the common magnetostructural correlations for end-to-end and end-on azido linkages, suggesting that these correlations also remain valid for the respective fragments of multiply bridging mu3-1,1,3 azido ligands.     

The raised-cosine wavelets in computerized tomography

In Computerized Tomography (CT), an image must be recovered from its sampled projections in the form of values of the Radon transform. In this work a method of recovering the image is based on the properties of the raised-cosine wavelet. This wavelet has a closed form which allows for certain precomputations and avoids convolution. The rate of convergence of the resulting algorithm to the image density function is found under suitable hypotheses. This algorithm is then tested on the standard Shepp–Logan     

Polynomials: a theme which should not be forgotten

There is a definite movement to remove many of the topics concerning polynomials from the school curriculum. The purpose of this paper is to point out why this movement is misguided and should be reversed.     

Mathematical attitudes and semantic differentials

The semantic differential—one approach to attitude measurement— basically records a combination of a person's associations with a particular concept with a scaling procedure. This paper considers the implications of such a device for teachers of mathematics.