In our previous paper we have shown that the NSR tring sigma-model with the massless 5-form vertex operator in D = 10 NSR string theory: V5∼eψ0ψ1ψ2ψ3ψt∂̄Xe x (t = 4, ..9) reproduces the correlators of the N = 4 D = 4 super Yang-Mills theory. In particular, this implies that the sigma-model with the V5 operator in flat space-time should be the NSR analogue of the GS string theory on AdS5 × S. Thi...

Descent via an isogeny on an elliptic curve is used to construct two subrings of the field of rational numbers, which are complementary in a strong sense, and for which Hilbert's Tenth Problem is undecidable. This method further develops that of Poonen, who used elliptic divisibility sequences to obtain undecid-ability results for some large subrings of the rational numbers. In 1970, Matijasevi...

In previous paper [1] an approach to nonlinear dynamical modeling of interaction between automatic (A) and conscious (C) processes in the brain was presented. The idea is to use complex field with real and imaginary components representing Aand C-processes. The interaction is due to the nonlinearity of the system. This approach was illustrated on the nonlinear equation for the current density i...

Among other things we show that for each n-tuple of positive rational numbers (a 1 ,. .. , a n) there are sets of primes S of arbitrarily large cardinality s such that the solutions of the equation a 1 x 1 +· · ·+a n x n = 1 with x 1 ,. .. , x n S-units are not contained in fewer than exp((4 + o(1))s 1/2 (log s) −1/2) proper linear subspaces of C n. This generalizes a result of Erd˝ os, Stewart...