We propose an algorithm for transforming a characteristic decomposition of a radical differential ideal from one ranking into another. The algorithm is based on a new bound: we show that, in the ordinary case, for any ranking, the order of each element of the canonical characteristic set of a characterizable differential ideal is bounded by the order of the… (More)
We propose a new method to describe the interacting bose gas at zero temperature. For three-dimensional system the correction to the ground-state energy in density is reproduced. For two-dimensional dilute bose gas the ground-state energy in the leading order in the parameter | ln α 2 ρ| −1 where α is a scattering length is obtained.
We consider low-dimensional dynamical systems exposed to a heat bath and to additional ac fields. The presence of these ac fields may lead to a breaking of certain spatial or temporal symmetries, which in turn cause nonzero averages of relevant observables. Nonlinear (non)adiabatic response is employed to explain the effect. We consider a case of a particle… (More)
Consider the Rosenfeld-Groebner algorithm for computing a regular decomposition of a radical differential ideal. We propose a bound on the orders of derivatives occurring in all intermediate and final systems computed by this algorithm. We also reduce the problem of conversion of a regular decomposition of a radical differential ideal from one ranking to… (More)
Harrington extended the first half of Rabin's Theorem to differential fields, proving that every computable differential field can be viewed as a computably enumerable subfield of a computable presentation of its differential closure. For fields F , the second half of Rabin's Theorem says that this subfield is Turing-equivalent to the set of irre-ducible… (More)
On the exactly-solvable pairing models for bosons. Abstract We discuss the construction of the exactly solvable pairing models for bosons in the framework of the Quantum Inverse Scattering method. It is stressed that this class of models is naturally appears in the quasiclassical limit of the algebraic Bethe ansatz transfer matrix. It is pointed out that… (More)
Exactly solvable discrete BCS-type Hamiltonians and the Six-Vertex model. Abstract We propose the new family of the exactly solvable discrete state BCS-type Hamilto-nians based on its relationship to the six-vertex model in the quasiclassical limit both in the rational and the trigonometric cases. We establish the relation of the BCS Hamilto-nian and its… (More)
We show new upper and lower bounds for the effective differential Nullstellensatz for differential fields of characteristic zero with several commuting derivations. Seidenberg was the first to address this problem in 1956, without giving a complete solution. The first explicit bounds appeared in 2009 in a paper by Golubitsky, Kondratieva, Szanto, and… (More)