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Author:François Lucas , Daniel Schaub , Mark Spivakovsky
Data Source:[J].Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas(IF 0.733), 2019, Vol.113 (4), pp.4227-4262Springer
Abstract:Abstract(#br)This paper contains a partial result on the Pierce–Birkhoff conjecture on piecewise polynomial functions defined by a finite collection $$\left\{ f_1,\ldots ,f_r\right\} $$ f 1 , … , f r of polynomials. In the 1980s, generalizing the problem from the polynomial ...
Author:Charef Beddani , Mark Spivakovsky
Data Source:[J].Journal of Pure and Applied Algebra(IF 0.534), 2015, Vol.219 (5), pp.1711-1719Elsevier
Abstract:Abstract(#br)An important result of Ito and Izumi about a Diophantine inequality and the linearity of the Artin approximation function has been generalized recently by Hickel, Ito and Izumi for any excellent Henselian local domain. Our objective is to show that their results are ...
Author:Charef Beddani , Mark Spivakovsky
Data Source:[J].Journal of Algebra(IF 0.583), 2015, Vol.438, pp.48-59Elsevier
Abstract:Abstract(#br)This paper shows that if ( R , m ) is a Nœtherian unibranch local domain with field of fractions K , then the integral closure S of R in K is analytically irreducible and finite over R if and only if R is analytically irreducible. We also prove the equality betw...
Author:Mark Spivakovsky , Massoud Amini ...
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2012, Vol.50 (9), pp.2606-2622Springer
Abstract:Abstract(#br)The present article is part III of a series devoted to extending the Repeat Space Theory (RST) to apply to carbon nanotubes and related molecular networks. In this part III, four problems concerning the above-mentioned extension of the RST have been formulated. ...
Author:Mark Spivakovsky , Keith F. Taylor
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2010, Vol.48 (3), pp.776-790Springer
Abstract:Abstract(#br)The present article is a direct continuation of the previous part III of this series of articles, which have been devoted to cultivating a new interdisciplinary region between chemistry and mathematics. In the present part IV, we develop two sets of fundamental ...
Author:Mark Spivakovsky , Eiji Yoshida ...
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2011, Vol.49 (8), pp.1700-1712Springer
Abstract:Abstract(#br)The present article is a direct continuation of part IV of this series. The Local Analyticity Proposition (LAP1), which admits a proof via resolution of singularities is a major key to proving the Fukui conjecture via resolution of singularities and related meth...
Author:Mark Spivakovsky , Keith F. Taylor
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 2005, Vol.37 (1), pp.75-91Springer
Abstract:Abstract(#br)The present article is the preliminary part of a series devoted to extending the foundation of the Asymptotic Linearity Theorems (ALTs), which prove the Fukui conjecture concerning the additivity problem of the zero-point vibrational energies of hydrocarbons. In this...
Author:Shigeru Arimoto , Mark Spivakovsky
Data Source:[J].Journal of Mathematical Chemistry(IF 1.226), 1993, Vol.13 (1), pp.217-247Springer
Abstract:Abstract(#br)By using the approach via the aspect of form and general topology, as well as basic notions of abstract algebra, a theoretical framework has been developed which elucidates the mechanism of the additivity relationships between structure and properties in molecul...

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