George Nakos

Quantifier Elimination and the Ellipticity of Systems of Partial Differential Equations

On Ideals Annihilating the Toral Class of BP*((BZ/PK)N)

Canadian mathematical bulletin, Sep 1, 1993

A sequence of ideals I kn Ç BP* is introduced, with the property: h,n ^ Ann(7jk, n), where l kn i... more A sequence of ideals I kn Ç BP* is introduced, with the property: h,n ^ Ann(7jk, n), where l kn is the toral class of the Brown-Peterson homology of the «-fold product BZ/p k x • • • x BZ/p k. These ideals seem to play an interesting and yet unclear role in understanding Ann(7^n). They are defined by using the formal group law of the Brown-Peterson spectrum BP, and some of their elementary properties are established. By using classical theorems of Landweber and of Ravenel-Wilson, the author computes the radicals of I k^n and Kvm(l kn), and discusses a few examples.

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Álgebra Lineal Con Aplicaciones

... Impreso en México Page 5. Este libro está dedicado a Constantine, Helen, Debra, Constantine, ... more

On the [pk]-series in Brown-Peterson homology

Journal of Pure and Applied Algebra, Oct 1, 1990

The coefficients of the [pk]-series for the Brown-Peterson homology lie in products of prime inva... more

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Quantifier Elimination and the Ellipticity of Systems of Partial Differential Equations

Algebraic Criteria for Qualitative Analysis of Nonlinear Dynamics in Biochemistry

ASME 2008 Dynamic Systems and Control Conference, Parts A and B, 2008

Aggregate modeling can approximate the convex hull of local matrices to nonlinear dynamics for an... more Aggregate modeling can approximate the convex hull of local matrices to nonlinear dynamics for any given accuracy. The authors use aggregate models to extend sufficient conditions for asymptotic stability of linear differential inclusions to nonlinear dynamics. An example illustrates the applicability of the proposed criteria to the analysis of nonlinear biochemical reaction chains.

On the [pk]-series in Brown-Peterson homology

Journal of Pure and Applied Algebra, 1990

The coefficients of the [pk]-series for the Brown-Peterson homology lie in products of prime inva... more

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The Brown-Peterson [2k]-series revisited

Journal of Pure and Applied Algebra, Oct 1, 1996

Each coefficient ak, s of the [2k]-series for Brown-Peterson homology has a distinguished shortes... more

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Fraction-free algorithms for linear and polynomial equations

ACM SIGSAM Bulletin, 1997

This paper extends the ideas behind Bareiss's fraction-free Gauss elimination algorithm in a ... more This paper extends the ideas behind Bareiss's fraction-free Gauss elimination algorithm in a number of directions. First, in the realm of linear algebra, algorithms are presented for fraction-free LU "factorization" of a matrix and for fraction-free algorithms for both forward and back substitution. These algorithms are valid not just for integer computation but also for any matrix system where the entries are taken from a unique factorization domain such as a polynomial ring. The second part of the paper introduces the application of the fraction-free formulation to resultant algorithms for solving systems of polynomial equations. In particular, the use of fraction-free polynomial arithmetic and triangularization algorithms in computing the Dixon resultant of a polynomial system is discussed.

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$Research paper thumbnail of On the BP homology and cohomology of $P^{2n}\wedge P^{2m}$$