Arbitrary polynomial transformations

2000 ◽  
Vol 3 (2) ◽  
pp. 38-40 ◽  
Author(s):  
S.A. Dyer ◽  
J.S. Dyer
2002 ◽  
Vol 12 (2) ◽  
Author(s):  
M.V. Larin

AbstractWe give a complete description of the polynomials f(x) with integer coefficients such that the period of the recurring sequence u


2013 ◽  
Vol 14 (8) ◽  
pp. 623-633
Author(s):  
Jorge A. Ruiz-Vanoye ◽  
Joaquín Pérez-Ortega ◽  
Rodolfo A. Pazos Rangel ◽  
Ocotlán Díaz-Parra ◽  
Héctor J. Fraire-Huacuja ◽  
...  

2021 ◽  
Author(s):  
Nick Pepper ◽  
Francesco Montomoli ◽  
Sanjiv Sharma ◽  
Francesco Giacomel ◽  
Michele Pinelli ◽  
...  

2003 ◽  
Vol 55 (2) ◽  
pp. 225-246 ◽  
Author(s):  
William D. Banks ◽  
Asma Harcharras ◽  
Igor E. Shparlinski

AbstractWe extend to the setting of polynomials over a finite field certain estimates for short Kloosterman sums originally due to Karatsuba. Our estimates are then used to establish some uniformity of distribution results in the ring [x]/M(x) for collections of polynomials either of the form f−1g−1 or of the form f−1g−1 + afg, where f and g are polynomials coprime to M and of very small degree relative to M, and a is an arbitrary polynomial. We also give estimates for short Kloosterman sums where the summation runs over products of two irreducible polynomials of small degree. It is likely that this result can be used to give an improvement of the Brun-Titchmarsh theorem for polynomials over finite fields.


Author(s):  
Ning Chen ◽  
Jiaojiao Chen ◽  
Shengwen Yin

An interval and random moment-based arbitrary polynomial chaos method (IRMAPCM) is proposed in this paper for the analysis of periodical composite structural-acoustic systems with multi-scale uncertain-but-bounded parameters. In IRMAPCM, the response of structural-acoustic system is approximated as moment-based arbitrary polynomial chaos (maPC) expansion. IRMAPCM can construct the polynomial basis according to the moment of the random variable without knowing the Probability Density Function (PDF), which can avoid the errors introduced by estimating the PDF. Numerical examples of a hexahedral box and an automobile passenger compartment are given to investigate the effectiveness of IRMAPCM for the prediction of the sound pressure response of structural-acoustic systems.


2011 ◽  
Vol 235 (16) ◽  
pp. 4851-4865 ◽  
Author(s):  
Jorge A. Ruiz-Vanoye ◽  
Joaquín Pérez-Ortega ◽  
Rodolfo A. Pazos R. ◽  
Ocotlán Díaz-Parra ◽  
Juan Frausto-Solís ◽  
...  

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