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On the Factorization of the Poincaré Polynomial: A Survey

Akyıldız, Ersan (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 13P05, 14M15, 14M17, 14L30.Factorization is an important and very difficult problem in mathematics. Finding prime factors of a given positive integer n, or finding the roots of the polynomials in the complex plane are some of the important problems not only in algorithmic mathematics but also in cryptography.

On the method of Esclangon

Ján Andres, Tomáš Turský (1996)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

On the oscillation of a class of linear homogeneous third order differential equations

N. Parhi, P. Das (1998)

Archivum Mathematicum

In this paper we have considered completely the equation y ' ' ' + a ( t ) y ' ' + b ( t ) y ' + c ( t ) y = 0 , ( * ) where a C 2 ( [ σ , ) , R ) , b C 1 ( [ σ , ) , R ) , c C ( [ σ , ) , R ) and σ R such that a ( t ) 0 , b ( t ) 0 and c ( t ) 0 . It has been shown that the set of all oscillatory solutions of (*) forms a two-dimensional subspace of the solution space of (*) provided that (*) has an oscillatory solution. This answers a question raised by S. Ahmad and A.  C. Lazer earlier.

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