20 research outputs found
Characterizing Triviality of the Exponent Lattice of A Polynomial through Galois and Galois-Like Groups
- Author
- Publication venue
- Publication date
- 05/05/2020
- Field of study
The problem of computing \emph{the exponent lattice} which consists of all
the multiplicative relations between the roots of a univariate polynomial has
drawn much attention in the field of computer algebra. As is known, almost all
irreducible polynomials with integer coefficients have only trivial exponent
lattices. However, the algorithms in the literature have difficulty in proving
such triviality for a generic polynomial. In this paper, the relations between
the Galois group (respectively, \emph{the Galois-like groups}) and the
triviality of the exponent lattice of a polynomial are investigated. The
\bbbq\emph{-trivial} pairs, which are at the heart of the relations between
the Galois group and the triviality of the exponent lattice of a polynomial,
are characterized. An effective algorithm is developed to recognize these
pairs. Based on this, a new algorithm is designed to prove the triviality of
the exponent lattice of a generic irreducible polynomial, which considerably
improves a state-of-the-art algorithm of the same type when the polynomial
degree becomes larger. In addition, the concept of the Galois-like groups of a
polynomial is introduced. Some properties of the Galois-like groups are proved
and, more importantly, a sufficient and necessary condition is given for a
polynomial (which is not necessarily irreducible) to have trivial exponent
lattice.Comment: 19 pages,2 figure
Lawson criterion for ignition exceeded in an inertial fusion experiment
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- Wickett ME
- Widmann K
- Widmayer C
- Wiedwald J
- Wilcox R
- Wilcox S
- Wild C
- Wilde BH
- Wilde CH
- Wilhelmsen K
- Wilke MD
- Wilkens H
- Wilkins P
- Wilks SC
- Williams EA
- Williams GJ
- Williams W
- Williams WH
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- Wilson DC
- Wilson E
- Wilson R
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- Wisoff J
- Wittman M
- Wolfe J
- Wong A
- Wong KW
- Wong L
- Wong N
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- Woodhouse D
- Woodruff J
- Woods DT
- Woods S
- Woodworth BN
- Wooten E
- Wootton A
- Work K
- Workman JB
- Wright J
- Wu M
- Wuest C
- Wysocki FJ
- Xu H
- Yamaguchi M
- Yang B
- Yang ST
- Yatabe J
- Yeamans CB
- Yee BC
- Yi SA
- Yin L
- Young B
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- Zika M
- Zimmerman GB
- Zobrist T
- Zuegel JD
- Zylstra AB
- Publication venue
- 'American Physical Society (APS)'
- Publication date
- 06/07/2022
- Field of study
For more than half a century, researchers around the world have been engaged in attempts to achieve fusion ignition as a proof of principle of various fusion concepts. Following the Lawson criterion, an ignited plasma is one where the fusion heating power is high enough to overcome all the physical processes that cool the fusion plasma, creating a positive thermodynamic feedback loop with rapidly increasing temperature. In inertially confined fusion, ignition is a state where the fusion plasma can begin "burn propagation" into surrounding cold fuel, enabling the possibility of high energy gain. While "scientific breakeven" (i.e., unity target gain) has not yet been achieved (here target gain is 0.72, 1.37Â MJ of fusion for 1.92Â MJ of laser energy), this Letter reports the first controlled fusion experiment, using laser indirect drive, on the National Ignition Facility to produce capsule gain (here 5.8) and reach ignition by nine different formulations of the Lawson criterion
Recent advances in amyotrophic lateral sclerosis
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- A Abraham
- A Al-Chalabi
- A Al-Chalabi
- A Blondet
- A Cannas
- A Cardenas-Blanco
- A Chio
- A Chio
- A Chio
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- A Czaplinski
- A Freischmidt
- A Grimm
- A Hensiek
- A Jawaid
- A Montuschi
- A Pestronk
- A Truini
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- AC Elden
- AC Lehn
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- Andersen PM Borasio GD, Dengler R, Hardiman O, Kollewe K, Leigh PN, Pradat PF, Silani V, Tomik B, Group EW
- Angelo Quattrini
- AV Strickland
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- C Armon
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- C Lomen-Hoerth
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- Filippi M Agosta F, Grosskreutz J, Benatar M, Kassubek J, Verstraete E, Turner MR, Neuroimaging Society in ALS
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- VS Kostic
- Y Chen
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- 'Springer Science and Business Media LLC'
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Evaluation of the Pharmacokinetics and Pharmacodynamics of Prasugrel in Japanese Elderly Subjects
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- 'Springer Science and Business Media LLC'
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Perioperative handling of antiplatelet therapy: watching the two sides of the coin
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- 'Springer Science and Business Media LLC'
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Investigation of parameters governing damage resistance of nematic liquid crystals for high-power or peak-intensity laser applications
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- Publication venue
- 'Springer Science and Business Media LLC'
- Publication date
- Field of study
Strange Attractors
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- AJ Lichtenberg
- AN Kolmogorov
- AN Kolmogorov
- D Ruelle
- EN Lorenz
- G Benettin
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- I Shimada
- J Guckenheimer
- J Milnor
- JA Yorke
- JMT Thompson
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- JS Turner
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- OE Lanford
- OE Lanford
- P Hartman
- R Shaw
- RF Williams
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- SD Feit
- VI Arnold
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- VS Afraimovich
- YG Sinai
- YG Sinai
- YuL Klimontovich
- Publication venue
- 'Springer Science and Business Media LLC'
- Publication date
- 01/01/1996
- Field of study
Revascularization for Advanced Coronary Artery Disease in Type 2 Diabetic Patients: Choosing Wisely Between PCI and Surgery
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- A Kapur
- A Patel
- AJ Tector
- DA American
- EA Magnuson
- F Feit
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- G Gargiulo
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- GB Mancini
- GD Dangas
- GM Lawrie
- GM Reaven
- HM Colhoun
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- JA Silva
- JE Shaw
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- KL Kozlov
- KM Detre
- L Mauri
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- Louai Razzouk
- M Emond
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- Michael E. Farkouh
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- RH Eckel
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- RR Holman
- S Bangalore
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- The Bypass Angioplasty Revascularization Investigation (BARI) Investigators
- VM Legrand
- WC Cushman
- WE Boden
- X Xie
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- 'Springer Science and Business Media LLC'
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Nonlinear interaction of elliptical q-Gaussian laser beams with plasmas with axial density ramp: effect of ponderomotive force
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- A El Sayed
- A Sharma
- A Singh
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- BT Spiers
- C Deutsch
- C Tsallis
- D Anderson
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- DN Gupta
- DN Gupta
- E Khalkhal
- F Cornolti
- G Purohit
- GA Askaryan
- H Hora
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- KH Kurniawan
- M Habibi
- M Leduc
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- M Yadav
- MD Feit
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- NA Roso
- P Hariharan
- PK Patel
- PL Kelley
- RY Chiao
- S Feng
- S Konar
- SA Akhmanov
- SD Patil
- T Singh
- T Tajima
- TH Maiman
- Y Wang
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- 'Springer Science and Business Media LLC'
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Chaos in Radiative Interactions
- Author
- A Bonifacio
- A Huberman
- A Szöke
- AN Sarkovskii
- BA Huberman
- CM Bender
- DA Russel
- E Abraham
- E Ott
- EN Lorenz
- FA Hopf
- FT Arecchi
- G Benettin
- G Benettin
- G Casati
- G Herzberg
- GC Stey
- H Haken
- H Nakatsuka
- HM Gibbs
- HM Gibbs
- J-P Eckmann
- JA Armstrong
- JH Eberly
- JH Shirley
- JJ Yeh
- JL Lam
- JN Elgin
- JR Ackerhalt
- K Ikeda
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- L Allen
- M Bixon
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- MJ Feigenbaum
- MJ Lighthill
- MW Hirsch
- N Minorsky
- NB Abraham
- P Stefan
- PW Miloni
- PW Milonni
- R Lefebre
- S Novak
- SD Feit
- SL McCall
- SL McCall
- T-Y Li
- VI Arnol’d
- Publication venue
- 'Springer Science and Business Media LLC'
- Publication date
- 01/01/1984
- Field of study