Further irreducibility criteria for polynomials with non-negative coefficients

2016 ◽  
Author(s):  
Morgan Cole ◽  
Scott Dunn ◽  
Michael Filaseta
Keyword(s):  
Irreducibility Criteria

scholarly journals Subordinate semigroups and order properties

1981 ◽  
Vol 31 (1) ◽  
pp. 59-76 ◽  
Author(s):  
Akitaka Kishimoto ◽  
Derek W. Robinson
Keyword(s):  
Banach Space ◽  
Holomorphic Semigroups ◽  
Irreducibility Criteria

AbstractLet St = exp{−tH}, Tt = exp{−tK}, be C0-semigroups on a Banach space . For appropriate f one can define subordinate semigroups Sft = exp{−tf(H)}, Ttf = exp{−tf(K)}, on and examine order properties of the pairs S, T, and Sf, Tf. If , = Lp(X;dv) we define St≽ Tt ≽ 0 if St − Tt and Tt map non-negative functions into non-negative functions. Then for p fixed in the range 1 > p > ∞ we characterize the functions for which St ≽ Tt ≽ 0 implies Sft ≽ Tft ≽ 0 for each Lp(X;dv) and the converse is true for all Lp(X;dv). Further we give irreducibility criteria for the strict ordering of holomorphic semigroups. This extends earlier results for L2-spaces.

scholarly journals Numerical irreducibility criteria for handlebody links

2020 ◽  
Vol 284 ◽  
pp. 107361
Author(s):  
Giovanni Bellettini ◽  
Maurizio Paolini ◽  
Yi-Sheng Wang
Keyword(s):  
Irreducibility Criteria

Irreducibility criteria for sums of two relatively prime multivariate polynomials

2015 ◽  
Vol 87 (3-4) ◽  
pp. 255-267 ◽  
Author(s):  
NICOLAE CIPRIAN BONCIOCAT ◽  
YANN BUGEAUD ◽  
MIHAI CIPU ◽  
MAURICE MIGNOTTE
Keyword(s):  
Multivariate Polynomials ◽  
Irreducibility Criteria

Irreducibility Criteria

1972 ◽  
Vol s2-5 (1) ◽  
pp. 133-138
Author(s):  
H. Kleiman
Keyword(s):  
Irreducibility Criteria

Irreducibility Criteria for Polynomials with non-negative Coefficients

1988 ◽  
Vol 40 (2) ◽  
pp. 339-351 ◽  
Author(s):  
Michael Filaseta
Keyword(s):  
The Third ◽  
Special Cases ◽  
Image Position ◽  
Irreducibility Criteria

In [7, b.2, VIII, 128] Pólya and Szegö state the following theorem of A. Cohn:THEOREM 1. Let dndn−x … d0 be the decimal representation of a prime. Thenis irreducible.Thus, for example, since 1289 is prime, x3 + 2x2 + 8x + 9 is irreducible. Brillhart, Odlyzko, and the author generalized Cohn's Theorem in three different directions. As examples of these types of generalizations, we note the following results, the first two of which are special cases of a result in [1] and the third of a result in [3].THEOREM 2. Let dndn−x … d0 be the base b representation of a prime where b is an integer ≧2. Thenis irreducible.THEOREM 3. Letbe such that f(10) is prime and 0 ≦ dj ≦ 167 for j = 0, 1, …, n. Then f(x) is irreducible.

scholarly journals Irreducibility criteria for skew polynomials

2009 ◽  
Vol 322 (11) ◽  
pp. 3797-3822 ◽  
Author(s):  
Richard C. Churchill ◽  
Yang Zhang
Keyword(s):  
Skew Polynomials ◽  
Irreducibility Criteria

scholarly journals Irreducibility criteria of Schur-type and Pólya-type

2010 ◽  
Vol 163 (4) ◽  
pp. 415-443 ◽  
Author(s):  
K. Győry ◽  
L. Hajdu ◽  
R. Tijdeman
Keyword(s):  
Irreducibility Criteria
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