Alexey Ovchinnikov

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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)
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)
The automatic real-time detection of spike-wave discharges (SWDs), the electroencephalographic hallmark of absence seizures, would provide a complementary tool for rapid interference with electrical deep brain stimulation in both patients and animal models. This paper describes a real-time detection algorithm for SWDs based on continuous wavelet analyses in(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)
  • Linda Keen, Arthur W Apter, Sergei Artemov, Alberto Baider, Ara Basmajian, Jason Behrstock +89 others
  • 2014
THE PROGRAM The Ph.D. Program in Mathematics provides students of high ability and strong preparation with an opportunity to begin study for the doctoral degree either immediately upon graduation from college or after completing some graduate work in the colleges of the City University or at other accredited institutions. Doctoral work in mathematics is(More)
a r t i c l e i n f o a b s t r a c t Kronecker's Theorem and Rabin's Theorem are fundamental results about computable fields F and the decidability of the set of irreducible polynomials over F. We adapt these theorems to the setting of differential fields K, with constrained pairs of differential polynomials over K assuming the role of the irreducible(More)
We compute an upper bound for the orders of derivatives in the Rosenfeld-Grobner algorithm. This algorithm computes a regular decomposition of a radical differential ideal in the ring of differential polynomials over a differential field of characteristic zero with an arbitrary number of commuting derivations. This decomposition can then be used to test for(More)
We study integrability conditions for systems of parameterized linear difference equations and related properties of linear differential algebraic groups. We show that isomonodromicity of such a system is equivalent to isomonodromicity with respect to each parameter separately under a linearly differentially closed assumption on the field of differential(More)