Pseudo-cross-conjugated mesomeric betaines. 1. Synthesis of pseudo-cross-conjugated mesomeric betaines from quinoxaline derivatives

A new method for the synthesis of pseudo-cross-conjugated mesomeric betainic heterocyclic compounds with an angular nitrogen atom has been developed consisting in the reaction of 1,4-dielectrophile — -carbethoxy-2-(3-chloro)quinoxalylacetonitrile with azoles. Experimental regularities have been studied and a reaction mechanism has been proposed including the stage of formation of an ylide from a quaternary azolium salt. A pseudo-crossconjugated mesomeric betainic heterocyclic compound containing a thiazole ring compound has been synthesized for the first time.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 11, pp. 1528–1533, November, 1992.     

Synthesis and investigation of the mesomorphic properties of pyran derivatives

4-[(5,6-Dihydro-2H-pyran-4-yl)methoxy]benzylidene-4-alkoxyanilines, which have the properties of smectic liquid crystals, were synthesized. The effect of the pyran ring in the benzylidene component and the length of the aliphatic radical in the aniline component on the type and thermal stability of the meso phase was ascertained.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 3, pp. 327–328, March, 1992.     

Humulenoids from plants of the family Apiaceae spatial structure of α-apienes

A conformational analysis has been made by the method of molecular mechanics of the -apienes — natural sesquiterpenes isolated from plants of the Apiaceae family. The results of the mathematical method with the inclusion of those x-ray structural studies have shown that in the molecules under consideration it is possible to expect the predominant realization of four conformations of the 11-membered ring:₁₄A ₈ ⁷ ,¹⁴A ₇ ⁸ ,₁₄A ₇ ⁸ , and¹⁴A ₈ ⁷ . These four conformations of unsubstituted -apiene and its natural derivatives have been characterized energetically, and the barriers to their interconversions have been evaluated.Institute of Chemistry of Plant Substances, Uzbekistan Academy of Sciences, Tashkent. Translated from Khimiya Prirodnykh Soedinenii, No. 2, pp. 197–202, March–April, 1992.     

Harary-Read numbers for catafusenes: Complete classification according to symmetry

The classical Harary-Read numbers for catafusenes (catacondensed simply connected polyhexes) are reproduced without using generating functions. A complete (mathematical) solution is given for the distribution of these numbers over the different symmetry groups to which the catafusenes belong.     

Synthesis of 2-R-fluorantheno[2,3-d]- and 2-R-fluorantheno[3,2-d]oxazoles

2-R-Fluorantheno[2,3-d]- and 2-R-fluorantheno[3,2-d]oxazoles were synthesized, and their UV and IR spectra were studied. Ten new compounds are described.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 7, pp. 905–907, July, 1974.     

Relativistic correction to the triton binding energy in the framework of relativistic Hamiltonian dynamics

The relativistic correction to the triton binding energy approximated to the order (v/c)² is calculated in the framework of relativistic Hamiltonian dynamics. We discuss the generator representation of the Poincaré group for three relativistic particles and its connection with the Feynman diagrams in the infinite-momentum frame (the light-front dynamics). The relativistic correction enhances the attraction in the three-nucleon system. The five-channel calculation with the Reid soft-core potential yeilds the result =–0.54 MeV, which is governed mainly by theD-wave contribution. TheS-wave contributions to are only –0.10 MeV.     

Problems of pion-nucleus interaction

The review of new theoretical and experimental results in the field of the pion-nucleus interaction which are presented in the contributed papers at the IV International symposium Mesons and Light Nuclei (Bechyn, 1988) is given. The discussion covers a wide area of problems from the -nucleon interaction to the pion interaction with light nuclei at low and intermediate energies.Rapporteur talk at the symposium Mesons and Light Nuclei, IV, Bechyn, Czechoslovakia, September 5–10, 1988.     

Physics with and without the equivalence principle

A differential manifold (d-manifold, for short) can be defined as a pair (M, C), where M is any set and C is a family of real functions on M which is (i) closed with respect to localization and (ii) closed with respect to superposition with smooth Euclidean functions; one also assumes that (iii) M is locally diffeomorphic to Rⁿ. These axioms have a straightforward physical interpretation. Axioms (i) and (ii) formalize certain compatibility conditions which usually are supposed to be assumed tacitly by physicists. Axiom (iii) may be though of as a (nonmetric) version of Einstein's equivalence principle. By dropping axiom (iii), one obtains a more general structure called a differential space (d-space). Every subset of Rⁿ turns out to be a d-space. Nevertheless it is mathematically a workable structure. It might be expected that somewhere in the neighborhood of the Big Bang there is a domain in which space-time is not a d-manifold but still continues to be a d-space. In such a domain we would have a physics without the (usual form of the) equivalence principle. Simple examples of d-spaces which are not d-manifolds elucidate the principal characteristics the resulting physics would manifest.on leave of absence from the Institute of Nuclear Physics, Department of Theoretical Physics, ul. Radzikowskiego 152, 31–342 Cracow, Poland.     

Stimulated emission of relativistic particles by external sources in spacetime

Explicit solutions are derived for transition amplitudes associated with stimulated emission of relativistic particles by external sources inspacetime. More precisely, exact expressions are obtained for transition amplitudes for any process where there are initially, at a given time, an arbitrary number of particles localized in various regions of space, prior to the switching on of an intervening source, and then, finally, at a later time when the intervening source ceases to operate, a given number of particles are found to be localized in various regions of space. The analysis is given for massive particles ofarbitrary integer and half-integer spins. The solutions are obtained by carrying out a unitarity expansion inconfiguration space, where particles travel between emitters and detectors in the presence of an intervening source. Considered as an application is the process: particlearbitrary number of particles, where the latter particles emerge spatially with a cone.     

Density and uniqueness in percolation

Two results on site percolation on thed-dimensional lattice,d1 arbitrary, are presented. In the first theorem, we show that for stationary underlying probability measures, each infinite cluster has a well-defined density with probability one. The second theorem states that if in addition, the probability measure satisfies the finite energy condition of Newman and Schulman, then there can be at most one infinite cluster with probability one. The simple arguments extend to a broad class of finite-dimensional models, including bond percolation and regular lattices.