scholarly journals Upper bounds for the coefficients of irreducible integer polynomials in several variables

2001 ◽  
Vol 99 (1) ◽  
pp. 1-12 ◽  
Author(s):  
Francesco Amoroso ◽  
Maurice Mignotte
Keyword(s):  
Upper Bounds ◽  
Integer Polynomials ◽  
Several Variables

scholarly journals Estimating Mahler's measure

1995 ◽  
Vol 51 (1) ◽  
pp. 145-151
Author(s):  
G.R. Everest
Keyword(s):  
Linear Forms In Logarithms ◽  
Algebraic Numbers ◽  
Linear Forms ◽  
Riemann Sums ◽  
Integer Polynomials ◽  
Several Variables ◽  
Logarithmic Integral ◽  
Baker's Theorem

In 1962, Mahler defined a measure for integer polynomials in several variables as the logarithmic integral over the torus. Many results exist about the values taken by the measure but many unsolved problems remain. In one variable, it is possible to express the measure as an effective limit of Riemann sums. We show that the same is true in several variables, using a non-obvious parametrisation of the torus together with Baker's Theorem on linear forms in logarithms of algebraic numbers.

scholarly journals Weighted multiple ergodic averages and correlation sequences

2016 ◽  
Vol 38 (1) ◽  
pp. 81-142 ◽  
Author(s):  
NIKOS FRANTZIKINAKIS ◽  
BERNARD HOST
Keyword(s):  
Bounded Sequence ◽  
Regularity Conditions ◽  
Uniform Density ◽  
Ergodic Averages ◽  
Multiple Correlation ◽  
Mean Convergence ◽  
Integer Polynomials ◽  
Several Variables ◽  
Convergence Results ◽  
Correlation Sequences

We study mean convergence results for weighted multiple ergodic averages defined by commuting transformations with iterates given by integer polynomials in several variables. Roughly speaking, we prove that a bounded sequence is a good universal weight for mean convergence of such averages if and only if the average of this sequence times any nilsequence converges. Two decomposition results of independent interest play key roles in the proof. The first states that every bounded sequence in several variables satisfying some regularity conditions is a sum of a nilsequence and a sequence that has small uniformity norm (this generalizes a result of the second author and Kra); and the second states that every multiple correlation sequence in several variables is a sum of a nilsequence and a sequence that is small in uniform density (this generalizes a result of the first author). Furthermore, we use these results in order to establish mean convergence and recurrence results for a variety of sequences of dynamical and arithmetic origin and give some combinatorial implications.

A note on trigonometric sums in several variables

1986 ◽  
Vol 99 (2) ◽  
pp. 189-193 ◽  
Author(s):  
R. W. K. Odoni
Keyword(s):  
Random Walk ◽  
Broad Class ◽  
Upper Bounds ◽  
Total Degree ◽  
Trigonometric Sums ◽  
Absolute Value ◽  
Independent Variables ◽  
Several Variables ◽  
The Absolute ◽  
Image Position

In [3, 4] we showed how the use of a random-walk analogue can be made to yield non-trivial information about the behaviour of certain trigonometric sums in one variable. Our aim here is to show how our method can be adapted to yield similar results for a broad class of trigonometric sums in several variables. Letbe a polynomial in v independent variables with integral coefficients. We choose integers n ≥ 0, d ≥ 1 and p ≥ 2 with p prime, and assume that f(x) has total degree ≤ d + 1. We shall consider the problem of obtaining non-trivial upper bounds for the absolute value of sums of the typewhere P = {1, 2, …, p} and f is non-constant.

The Exact Estimates of Fourier-Haar Coefficients of Functions of Bounded Variation

2016 ◽  
Vol 4 ◽  
pp. 14-22 ◽  
Author(s):  
Alexander N. Shchitov
Keyword(s):  
Bounded Variation ◽  
Upper Bounds ◽  
Functions Of Bounded Variation ◽  
Exact Results ◽  
Several Variables

The exact values of the upper bounds of the modulus of Fourier-Haar coefficients of functions of one variable has been obtained on the classes of functions of boundary variations KVp(1≤p<∞). The behavior of Fourier-Haar coefficients of functions of several variables has been investigated for functions of boundary variations from the classes Vp,d(IId), KVp,d(1≤p<∞) and KV*1,d. On these classes of functions of several variables the exact results has been obtained.

Topographische Orientierung bei Patienten mit erworbener Hirnschädigung

1999 ◽  
Vol 10 (2) ◽  
pp. 77-86
Author(s):  
Martina Kindsmüller ◽  
Andrea Kaindl ◽  
Uwe Schuri ◽  
Alf Zimmer
Keyword(s):  
Brain Damage ◽  
Cognitive Deficits ◽  
Hospital Setting ◽  
Hospital Staff ◽  
Reading Test ◽  
Map Reading ◽  
Several Variables ◽  
Topographical Orientation ◽  
The One ◽  
Behavioral Memory

Topographical Orientation in Patients with Acquired Brain Damage Abstract: A study was conducted to investigate the abilities of topographical orientation in patients with acquired brain damage. The first study investigates the correlation between wayfinding in a hospital setting and various sensory and cognitive deficits as well as the predictability of navigating performance by specific tests, self-rating of orientation ability and rating by staff. The investigation included 35 neuropsychological patients as well as 9 control subjects. Several variables predicted the wayfinding performance reasonably well: memory tests like the one introduced by Muramoto and a subtest of the Rivermead Behavioral Memory Test, the Map Reading Test and the rating by hospital staff. Patients with hemianopia experienced significant difficulty in the task.

Pengaruh Lintas Budaya Pada Pemasaran Internasional Dengan Pendekatan Perilaku Konsumen

2017 ◽  
Vol 1 (2) ◽  
pp. 168-176
Author(s):  
Endy Gunanto ◽  
Yenni Kurnia Gusti
Keyword(s):  
Consumer Behavior ◽  
Marketing Strategy ◽  
Consumer Culture ◽  
International Organization ◽  
Future Research ◽  
Special Issue ◽  
Cross Culture ◽  
Several Variables ◽  
Cultural Orientations ◽  
The Impact

In this article we present a conceptual of the effect of cross culture on consumer behavior incorporating the impact of globalization. This conceptual idea shows that culture inûuences various domains of consumer behavior directly as well as through international organization to implement marketing strategy. The conceptual identify several factors such as norm and value in the community, several variables and also depicts the impact of other environmental factors and marketing strategy elements on consumer behavior. We also identify categories of consumer culture orientation resulting from globalization. Highlights of each of the several other articles included in this special issue in Asia region. We conclude with the contributions of the articles in terms of the consumer cultural orientations and identify directions for future research.

Courting the Youth Vote in 2008: The Obama Effect

2009 ◽  
Vol 5 ◽  
Author(s):  
Lindsey C Bohl
Keyword(s):  
Presidential Elections ◽  
Voter Registration ◽  
The Internet ◽  
The Past ◽  
Several Variables ◽  
High Turnout ◽  
Short And Long Term ◽  
Use Of The Internet ◽  
Youth Vote

This paper examines a few of the numerous factors that may have led to increased youth turnout in 2008 Election. First, theories of voter behavior and turnout are related to courting the youth vote. Several variables that are perceived to affect youth turnout such as party polarization, perceived candidate difference, voter registration, effective campaigning and mobilization, and use of the Internet, are examined. Over the past 40 years, presidential elections have failed to engage the majority of young citizens (ages 18-29) to the point that they became inclined to participate. This trend began to reverse starting in 2000 Election and the youth turnout reached its peak in 2008. While both short and long-term factors played a significant role in recent elections, high turnout among youth voters in 2008 can be largely attributed to the Obama candidacy and campaign, which mobilized young citizens in unprecedented ways.

Frontiers in Complex Dynamics

2014 ◽  
Author(s):  
Araceli Bonifant ◽  
Misha Lyubich ◽  
Scott Sutherland
Keyword(s):  
Historical Perspective ◽  
Complex Dynamics ◽  
Short Paper ◽  
Combinatorial Group Theory ◽  
Entropy Theory ◽  
Holomorphic Dynamics ◽  
Eightieth Birthday ◽  
Several Variables ◽  
Fields Medal ◽  
Combinatorial Group

John Milnor, best known for his work in differential topology, K-theory, and dynamical systems, is one of only three mathematicians to have won the Fields medal, the Abel prize, and the Wolf prize, and is the only one to have received all three of the Leroy P. Steele prizes. In honor of his eightieth birthday, this book gathers together surveys and papers inspired by Milnor's work, from distinguished experts examining not only holomorphic dynamics in one and several variables, but also differential geometry, entropy theory, and combinatorial group theory. The book contains the last paper written by William Thurston, as well as a short paper by John Milnor himself. Introductory sections put the papers in mathematical and historical perspective, color figures are included, and an index facilitates browsing.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

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