One-step synthesis of substituted 3,5-dinitropiperidines and 1,5-dinitro-3,7-diazabicyclo[3.3.1]nonanes from 1,3-dinitropropanes

1,5-Dinitro-3,7-diazabicyclo[3.3.1]nonane derivatives were synthesized in up to 83%yields by the Mannich reaction of 1,3-dinitropropanes with excess formaldehyde and primary amines. In some cases, for instance, when 2,2-dimethyl-1,3-dinitropropane and benzylamine or monoethanolamine are used, the reaction occurs with low yields or stops at the step of formation of 3,5-dinitropiperidines. The influence of the structure of the starting compounds and reaction conditions on the yields of 1,5-dinitro-3,7-diazabicyclo[3.3.1]nonanes and 3,5-dinitropiperidines was studied.__________Published in Russian in Izvestiya Akademii Nauk. Seriya Khimicheskaya, No. 2, pp. 405–411, February, 2005.     

Generalization of the Martinelli-Bochner integral representation

The well known Martinelli-Bochner integral formula from the theory of holomorphic functions of many variables is extended to arbitrary unbounded domains.     

On Harmonic Continuation of Differentiable Functions Defined on Part of the Boundary

We establish an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., we give an explicit solution to the Cauchy problem for the Laplace equation.     

Influence of vertex coulomb effects on peripheral partial amplitudes for the consecutive transfer of two protons in A(X,Y)B peripheral nuclear reactions induced by light loosely bound (exotic) nuclei at low energies

The amplitude for the consecutive transfer of two protons in A(X, Y)B peripheral nuclear reactions induced by loosely bound light (exotic) nuclei and described by a nonrelativistic square Feynman diagram in which the first transferred proton is loosely bound while the second one in tightly bound is considered. It is shown that the inclusion of three-ray Coulomb vertex effects in the square diagram leads to the appearance of an additional “Coulomb” singularity in the variable cos θ (here, θ is the c.m. scattering angle), this singularity being closer to the physical domain, −1 ≤ cos θ ≤ 1, than the well-known “triangle” singularities corresponding to the amplitude of the square diagram in which the internal line is contracted. The asymptotic behavior of the partial-wave amplitudes for l ≫ 1 that are generated by the aforementioned singularities is found explicitly. A comparative analysis of the resulting partial-wave amplitudes for l ≫ 1 is performed for specific peripheral nuclear reactions induced by ⁸B and ¹²N ions at various energies.     

A Carleman Function and the Cauchy Problem for the Laplace Equation

We suggest an explicit formula for reconstruction of a harmonic function in a domain from its values and the values of its normal derivative on part of the boundary; i.e., we give an explicit continuation formula and a regularization procedure for a solution to the Cauchy problem for the Laplace equation.     

Representation of harmonic functions as potentials and the Cauchy problem

In this paper, we propose an explicit formula for the reconstruction of a harmonic function in the domain from its known values and from the values of its normal derivative on part of the boundary, i.e., we give an explicit continuation and a regularization formula of the solution of the Cauchy problem for the Laplace equation.     

Three-body coulomb effects in one-particle transfer reactions

The behaviour of the DWBA amplitudes in the vicinity of the nearest singularity in the cosθ-plane for the neutron and charged particle transfer reactions is investigated. It is shown that Coulomb interactions transform the pole singularity into a branch point. The main singular terms of the complete and the post-approximation DWBA cross sections are compared with the exact three-body results. They differ only by the Coulomb renormalization factors (CRF), which define the renormalization of the singularity strength generated by the Coulomb interactions. In the case of neutron transfer it is shown that the complete DWBA and exact CRFs practically coincide and slightly differ from CRF obtained in post-approximation DWBA. For charged particle transfer reactions the exact CRF may differ considerably from the one obtained in DWBA and especially in the post-approximation DWBA. Our conclusion therefore is that in order to obtain a reliable value of the vertex constant by extrapolating the differential cross-section to the nearest singularity, the exact three-body approach should be used.     

On a Cauchy problem for Laplace's equation

We obtain a formula which expresses the values of a harmonic function at points of a threedimensional domain in terms of its values and the values of its normal derivative on a portion of the domain boundary.     

Cauchy problem for a system of equations of three-dimensional elasticity theory

Samarkand. Translated from Sibirskii Matematicheskii Zhurnal, Vol. 33, No. 1, pp. 186–190, January–February 1992.