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Good bases for tame polynomials

Mathias Schulze
2005 Journal of symbolic computation  
An algorithm to compute a good basis of the Brieskorn lattice of a cohomologically tame polynomial is described. This algorithm is based on the results of C.  ...  Douai for convenient Newton non-degenerate polynomials.  ...  Acknowledgements The author is grateful to Claude Sabbah for drawing his attention to the subject and to Gert-Martin Greuel for valuable hints and discussions.  ... 
doi:10.1016/j.jsc.2004.10.001 fatcat:euiltgtkergtflucu5ghmtcha4

Efficient Resource Allocation in Hybrid Wireless Networks Increase the Capacity

B. Senbagappriya, S. S. Dhenakaran
2021 International Journal of Scientific Research in Computer Science Engineering and Information Technology  
In this project we implemented a new technique with an algorithm named GNDA Good Node Detection Algorithm Based Approach technique with Wireless Sensor Networks.  ...  This project describes a polynomial pool based approach hybrid three-tier general framework that permits the use of any pairwise key predistribution scheme as its basic component.  ...  Tame-based key pre-distribution approach, where we exploit tame auto orphisms to get symmetric and two-one bivariate maps for the pairwise key establishment.  ... 
doi:10.32628/cseit21715 fatcat:kza4wlwm3zerzmxszjqo4hujge

Tame Pool-Based Pairwise Key Predistribution for Large-Scale Sensor Networks

Yen-Hua Liao, Chin-Laung Lei, Ai-Nung Wang, Wen-Chi Tsai
2009 GLOBECOM 2009 - 2009 IEEE Global Telecommunications Conference  
It turns out that this tame map can substitute the conventional polynomial in any existing polynomial-based scheme to offer deterministic authentication service.  ...  This tame-based approach can provide deterministic authentication between two parties. We then present a general framework for the key predistribution, on the basis of the tame-based approach.  ...  Due to the use of conventional polynomials for key predistribution, the polynomial pool-based schemes (The basic scheme [7] is a special case of the polynomial pool-based approach.) have collision problem  ... 
doi:10.1109/glocom.2009.5425302 dblp:conf/globecom/LiaoLWT09 fatcat:m4y2uxaawrezdilorfvey5zfca

Page 4836 of Mathematical Reviews Vol. , Issue 93i [page]

1993 Mathematical Reviews  
If a polynomial is not good then the map g is generally not a fibration. The paper under review introduces a large class of polynomials, semi-tame polynomials, for which the mapping @ is a fibration.  ...  Like many of the other types of polynomials the definition is based on a gradient condition: f is semi-tame if for every sequence {z,} such that ||z;,|| - oo and grad f(z;,) = A,z, we have gradf(z,) —  ... 

Taming Reasoning in Temporal Probabilistic Relational Models [article]

Marcel Gehrke, Ralf Möller, Tanya Braun
2019 arXiv   pre-print
To counteract groundings over time and to keep reasoning polynomial by restoring a lifted representation, we present temporal approximate merging (TAMe), which incorporates (i) clustering for grouping  ...  In exchange for faster runtimes, TAMe introduces a bounded error that becomes negligible over time.  ...  do converge, allowing TAMe to keep reasoning polynomial.  ... 
arXiv:1911.07040v1 fatcat:6vsxusczqfbnvmxiyylddxvte4

Automorphisms of Weyl Algebra and a Conjecture of Kontsevich [article]

Alexei Kanel-Belov, Andrey Elishev, Jie-Tai Yu
2018 arXiv   pre-print
Our proof uses lifting of polynomial symplectomorphisms to Weyl algebra automorphisms by means of approximation by tame symplectomorphisms and gauging of the lifted morphism.  ...  Approximation by tame symplectomorphisms is the symplectic version of the well-known theorem of D. Anick and is a result of our prior work.  ...  This statement provides the base case for the processing of the higher-order terms. The gauging acts upon the term at 2 .  ... 
arXiv:1802.01225v1 fatcat:r5b5knyytnbedgk3yya7jv4kwa

Locally tame plane polynomial automorphisms

Joost Berson, Adrien Dubouloz, Jean-Philippe Furter, Stefan Maubach
2012 Journal of Pure and Applied Algebra  
For automorphisms of a polynomial ring in two variables over a domain R, we show that local tameness implies global tameness provided that every 2-generated locally free R-module of rank 1 is free.  ...  The last author is funded by Veni-grant of council for the physical sciences, Netherlands Organisation for Scientific Research (NWO).  ...  Acknowledgements The first author is funded by a free competition grant of the Netherlands Organisation for Scientific Research (NWO).  ... 
doi:10.1016/j.jpaa.2011.05.013 fatcat:5vvpphfn2zhgliormi7qw5pvua

Page 7806 of Mathematical Reviews Vol. , Issue 2001K [page]

2001 Mathematical Reviews  
, calculate inverses, or determine tameness over certain base rings.  ...  Emphasis is given to two topics: (1) Questions of tameness and stable tameness of particular automor- phisms; (2) Algorithms (which use Grdbner bases), e.g., decide whether an endomorphism is an automorphism  ... 

Tame torsion, the tame inverse Galois problem, and endomorphisms

Matthew Bisatt
2020 Manuscripta mathematica  
As an application, we consider the tame inverse Galois problem and are able to realise general symplectic groups as Galois groups of tame extensions of Q.  ...  We prove the existence of a genus g curve C/Q such that the mod p representation of its Jacobian is tame by imposing conditions on the endomorphism ring.  ...  Acknowledgements I would like to thank Vladimir Dokchitser for suggesting this approach and helpful conversations. I am also indebted to the referee for suggesting the proof of Theorem 5.2.  ... 
doi:10.1007/s00229-020-01213-2 fatcat:vjb6fx655vhtbdcr2w5bwdhzmi

Locally tame plane polynomial automorphisms [article]

Joost Berson, Adrien Dubouloz , Stefan Maubach
2010 arXiv   pre-print
For automorphisms of a polynomial ring in two variables over a domain R, we show that local tameness implies global tameness provided that every 2-generated invertible R-module is free.  ...  This could suggest that, at least for plane polynomial automorphisms, tameness is a property that can be checked locally on the base ring.  ...  A good starting point would be to have in general an effective algorithmic way to recognize tame automorphisms.  ... 
arXiv:1011.0976v1 fatcat:3ecr4rrq6fdprflr2bgrqoyvue

Tame torsion and endomorphisms [article]

Matthew Bisatt
2019 arXiv   pre-print
We prove the existence of a genus g curve C/Q such that the mod p representation of its Jacobian is tame by imposing conditions on the endomorphism algebra.  ...  For primes ℓ 2g+1, ℓ = p choose a polynomial f ℓ (x) of degree 2g+2 such that C f ℓ has good reduction at ℓ (in the case of ℓ = 2, explicit conditions are given in [AD19, Lemma 7.7]).  ...  Observe that for p = 2, the hyperelliptic curve C n has good reduction at p for p ∤ n.  ... 
arXiv:1912.08033v1 fatcat:rx46ysi4tnallkjxqagtb76eve

Page 4991 of Mathematical Reviews Vol. , Issue 92i [page]

1992 Mathematical Reviews  
A good measure of knot complexity is defined to be a function F from the equivalence classes of (tame) knots to [0, 00) such that F(unknot) = 0 and for which there exists a class k, with F (nk,#k) > nF  ...  In this paper, the author presents new state models for a special- ization of the Kauffman polynomial.  ... 

An Algebraic Proof of Thurston's Rigidity for a Polynomial [article]

Alon Levy
2012 arXiv   pre-print
We provide an algebraic proof of this fact for tamely ramified maps for which at least one of the critical points is periodic. We also produce wildly ramified counterexamples.  ...  The situation for polynomials is much simpler. Not only do we not need S in the proof of Theorem 2.4, but also we obtain: Theorem 3.7. Let f (z) be an absolutely tamely ramified PCF polynomial.  ...  The case of polynomials is already known: Theorem 1.9. [2] Rigidity holds for polynomials whenever their reduction after any coordinate change is still tamely ramified, which is the case if they are of  ... 
arXiv:1201.1969v2 fatcat:z3bikc4hrncuvnfla76jdfdlha

Page 979 of Mathematical Reviews Vol. , Issue 2000b [page]

2000 Mathematical Reviews  
Ultimately, the authors formulate Conjecture 2.7, which makes an assertion about the face polynomials of a 3-dimensional tame automorphism.  ...  In the modular case, it can be computed by a Molien-type formula, and it gives fairly good con- straints on the possible degrees of the elements of a homogeneous set of parameters for k[V]°, i.e., of a  ... 

Tame Galois Realizations of over

S. Arias-de-Reyna, N. Vila
2010 International mathematics research notices  
In this paper we obtain realizations of the 4-dimensional general symplectic group over a prime field of characteristic ℓ > 3 as the Galois group of a tamely ramified Galois extension of Q.  ...  We obtain an explicit family of curves of genus 2 such that the Galois representation attached to the ℓ-torsion points of their Jacobian varieties provide tame Galois realizations of the desired symplectic  ...  representation yielding a finite Galois extension K/Q, tamely ramified, with Galois group GSp 4 (F ℓ ), thus providing an affirmative answer to the Tame Inverse Galois Problem for this group.  ... 
doi:10.1093/imrn/rnq144 fatcat:d3g3heb6k5fbzoqy5lxa6bduqu
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