Geodesic plasma compressibility effects on the magnetic islands in a tokamak

It is shown that the stability of rotating magnetic islands in a tokamak plasma is affected by plasma compressibility related to the geodesic curvature in an inhomogeneous magnetic field. A robust contribution has been found to the Rutherford evolution equation. It is shown that the sign of the geodesic curvature contribution is opposite to the sign of the polarization term. It is suggested that this mechanism plays a crucial role in the stability of small scale magnetic islands.     

Protonation,deuteration, and formylation of aceperidazylenes

1H-1,2-Diazaphenalene derivatives in which the pyridazine ring is ortho- and peri-fused to acenaphthene and acenaphthylene (1H-indeno[6,7,1-def]cinnolines) have been synthesized. It has been found that electrophilic attack on these compounds is directed at C⁶.     

The construction of graph models for calculations of the properties of substitution isomers of basis structures on the basis of additivity of energy contributions

A method for the construction of additive models for calculations of the properties of substitution isomers of basis structures is described for the example of a series of X-substituted methylsilanes CH_{3 − k} X _k -SiH_{3 − l} X _l (where X = CH₃, F, Cl, …, k, l = 0, 1, 2, 3). The method is based on similarity of subgraphs in graphs of several molecules and the arrangement of polygonal numbers (triangular, tetrahedral) of the Pascal triangle. Parameters taking into account multiple nonvalence interactions (-C-Si<, >C-Si<, …) through two atoms along the molecular chain of an X-substituted methylsilane (X = CH₃) were for the first time explicitly included in the calculation scheme. Taking these interactions into account allows us to completely differentiate all the structural isomers of certain molecules and obtain numerical parameter values for predicting properties P under consideration in various approximations. Numerical calculations of Δ_f H _{g,298 K}^o were performed for 16 alkylsilanes (as X-substituted methylsilanes), including 7 compounds not studied experimentally.     

Submanifolds in five-dimensional pseudo-Euclidean spaces and four-dimensional FRW universes

Equations for submanifolds, which correspond to embeddings of the four-dimensional FRW universes in five-dimensional pseudo-Euclidean spaces, are presented in convenient form in general case. Several specific examples are considered.