Quasi‐Relativistic Heat Equation via Lévy Stable Distributions: Exact Solutions

We introduce and study an extension of the heat equation relevant to relativistic energy formula involving square root of differential operators. We furnish exact solutions of corresponding Cauchy (initial) problem using the operator formalism invoking one‐sided Lévy stable distributions. We note a natural appearance of Bessel polynomials which allow one to obtain closed form solutions for a number of initial conditions. The resulting diffusion is slower than the non‐relativistic one, although it still can be termed a normal one. Its detailed statistical characterization is presented in terms of exact evaluation of arbitrary moments and kurtosis and is compared with the non‐relativistic case.     

Chemistry of the 2,3-oxaphosphabicyclo[2.2.2]octene ring system: Extrusion of metaphosphates

The 2,3-oxaphosphabicyclo[2.2.2]octene 3-oxide (or sulfide) ring system is of considerable value because it easily fragments on being heated or irradiated (254 nm) to provide three-coordinate phosphoryl species. The system is synthesized by O-insertion with peracids into a C P bond of 7-phosphanorbornene derivatives with a variety of P-substituents. With rare exception, the insertion has been found to proceed with retention of the configuration at phosphorus, as established by X-ray and NMR techniques. The thermal fragmentation that produces the metaphosphate derivatives EtO PO₂, EtO P(S)O, and Et₂N PO₂ follows first-order kinetics, and is independent of the concentration of a trapping agent for these species. Solvent effects and activation parameters join in defining a retrocycloaddition mechanism that ejects the free metaphosphate. The species Ph PO₂ can also be easily generated either thermally or photochemically. Metaphosphates have been found to attack ethereal oxygen in epoxides and oxetanes, and may undergo anchimeric participation with a properly placed methoxy group on the substituent used in the 2,3-oxaphosphabicyclo[2.2.2]octene precursor.     

ChemInform Abstract: Sulfur Compounds. Part 218. Does the Interconversion of Polysulfur Compounds Proceed via Hypervalent Intermediates? — An ab initio MO Study.

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Generalized Fictitious Sources Method for Heat Conduction

In the paper the influence of geometry of the body region for the rate of initial temperature evolution is shown. Free exchange of the boundary temperature was assumed. There was also investigated the influence of the Biot coefficient on the heat conduction process course. Generalisation of the fictitious sources method for the inhomogeneous initial condition was made.