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.     

On the behavior of solutions of the equation for components of a normal system of differential equations

We obtain necessary and sufficient conditions for the existence of a sliding mode and also for the knotting of solutions of the equation for components of a normal system of first-order differential equations.     

Dynamical approach to complex regional economic growth based on Keynesian model for China

The paper addresses the problem of complex regional economic growth by using nonlinear Keynesian model with focusing on direct foreign investments effects. We investigate the dynamics of the model for the broad range of parameters which, in particular, contains the parameter values obtained recently by econometric analysis of the data for economic growth in China. For the single-region model we give conditions for which the dynamics of the model will be chaotic or regular. The parameters which prevent the economic stagnation are indicated. Further, we consider the model for two regions with a common trade as a coupling factor. The conditions are given for the two trading systems to exhibit chaotic synchronization, in-phase and out-of-phase behavior.     

Synchronizing distant nodes: a universal classification of networks

Stability of synchronization in delay-coupled networks of identical units generally depends in a complicated way on the coupling topology. We show that for large coupling delays synchronizability relates in a simple way to the spectral properties of the network topology. The master stability function used to determine the stability of synchronous solutions has a universal structure in the limit of large delay: It is rotationally symmetric around the origin and increases monotonically with the radius in the complex plane. This allows a universal classification of networks with respect to their synchronization properties and solves the problem of complete synchronization in networks with strongly delayed coupling.     

Excitons in monoclinic zinc diphosphide: Orthoexciton and polariton effects at n=1 resonance

Quantitative investigations of the hydrogen-like exciton B series in the absorption spectra of the β-ZnP₂ crystal for various wave vector directions and polarization states of radiation are conducted. It is shown that the B spectrum constitutes a single orthoexciton series with S-type envelope functions, and low-energy components in doublet lines belong to the S-type for lines in the series with n≥3. Polariton effects are clearly manifested at the B _n=1 exciton resonance, and Bouguer’s law is violated. The oscillator strength tensor components are determined for transitions to the exciton states of the B series, and the polariton parameters at the B _n=1 exciton resonance are calculated.