Carleman problem for two pairs of functions in a ring

We consider a particular case of the matrix Carleman problem for two pairs of functions in a ring and find a constructive solution of this problem. In addition, we propose an algorithm for the construction of solutions for two infinite systems of smooth transition and for a system of two singular equations of special type. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 662–671, May, 1997     

Count(q) versus the pigeon-hole principle

For each there exists a model of which satisfies the Count() principle. Furthermore, if contains all prime factors of there exist and a bijective map mapping onto . A corollary is a complete classification of the Count() versus Count() problem. Another corollary shows that the pigeon-hole principle for injective maps does not follow from any of the Count() principles. This solves an open question [Ajtai 94]. Received August 16, 1994 / Revised version received April 29, 1996     

On instability of conservative systems with gyroscopic forces

Theorems on equilibrium instability of conservative systems with gyroscopic forces are proved. The theorems obtained are nonlinear analogs of the Kelvin theorem. The equilibrium instability of the Chaplygin nonholonomic systems is considered. Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 10, pp. 1422–1428, October, 1997.     

On 2-ciass field towers of some imaginary quadratic number fields

We construct an infinite family of imaginary quadratic number fields with 2-class groups of type (2, 2, 2) whose Hilbert 2-class fields are finite.     

Algebraic fermion bosonization

By exploiting the construction of charged field algebras as canonical extensions of CCR current algebras in 1+1 dimensions and nonregular representations of extended algebras, we provide an algebraic construction of local Fermi fields as ultrastrong limits of bosonic variables in all representations which are locally Fock with respect to the ground-state representation of the massless scalar field.     

Unexpected heterocyclization of 1,4-naphthoquinone thioglucosides

Translated from Izvestiya Akademii Nauk SSSR, Seriya Khimicheskaya, No. 12, p. 2899, December, 1991.