scholarly journals Multiple correlation sequences not approximable by nilsequences

2021 ◽  
pp. 1-12
Author(s):  
JOP BRIËT ◽  
BEN GREEN
Keyword(s):  
Multiple Correlation ◽  
Approximate Integral ◽  
Correlation Sequences

Abstract We show that there is a measure-preserving system $(X,\mathscr {B}, \mu , T)$ together with functions $F_0, F_1, F_2 \in L^{\infty }(\mu )$ such that the correlation sequence $C_{F_0, F_1, F_2}(n) = \int _X F_0 \cdot T^n F_1 \cdot T^{2n} F_2 \, d\mu $ is not an approximate integral combination of $2$ -step nilsequences.

scholarly journals Integer part polynomial correlation sequences

2016 ◽  
Vol 38 (4) ◽  
pp. 1525-1542 ◽  
Author(s):  
ANDREAS KOUTSOGIANNIS
Keyword(s):  
Error Term ◽  
Uniform Density ◽  
Integer Part ◽  
Ergodic Averages ◽  
Multiple Correlation ◽  
Transference Principle ◽  
The Mean ◽  
Correlation Sequences ◽  
Measure Preserving Actions ◽  
Invent Math

Following an approach presented by Frantzikinakis [Multiple correlation sequences and nilsequences. Invent. Math. 202(2) (2015), 875–892], we prove that any multiple correlation sequence defined by invertible measure preserving actions of commuting transformations with integer part polynomial iterates is the sum of a nilsequence and an error term, which is small in uniform density. As an intermediate result, we show that multiple ergodic averages with iterates given by the integer part of real-valued polynomials converge in the mean. Also, we show that under certain assumptions the limit is zero. A transference principle, communicated to us by M. Wierdl, plays an important role in our arguments by allowing us to deduce results for $\mathbb{Z}$-actions from results for flows.

scholarly journals High-entropy dual functions over finite fields and locally decodable codes

2021 ◽  
Vol 9 ◽  
Author(s):  
Jop Briët ◽  
Farrokh Labib
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Multiple Correlation ◽  
High Entropy ◽  
Polynomial Phase ◽  
Locally Decodable Codes ◽  
Phase Functions ◽  
Correlation Sequences ◽  
Locally Decodable ◽  
Dual Functions

Abstract We show that for infinitely many primes p there exist dual functions of order k over ${\mathbb{F}}_p^n$ that cannot be approximated in $L_\infty $ -distance by polynomial phase functions of degree $k-1$ . This answers in the negative a natural finite-field analogue of a problem of Frantzikinakis on $L_\infty $ -approximations of dual functions over ${\mathbb{N}}$ (a.k.a. multiple correlation sequences) by nilsequences.

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.

scholarly journals Nilsequences, null-sequences, and multiple correlation sequences

2013 ◽  
Vol 35 (1) ◽  
pp. 176-191 ◽  
Author(s):  
A. LEIBMAN
Keyword(s):  
Finite Measure ◽  
Null Sequence ◽  
Uniform Density ◽  
Multiple Correlation ◽  
Uniform Limit ◽  
Polynomial Sequence ◽  
Correlation Sequences

AbstractA ($d$-parameter) basic nilsequence is a sequence of the form $\psi (n)= f({a}^{n} x)$,$n\in { \mathbb{Z} }^{d} $, where $x$ is a point of a compact nilmanifold $X$, $a$ is a translation on $X$, and$f\in C(X)$; a nilsequence is a uniform limit of basic nilsequences. If $X= G/ \Gamma $ is a compact nilmanifold, $Y$ is a subnilmanifold of $X$, $\mathop{(g(n))}\nolimits_{n\in { \mathbb{Z} }^{d} } $ is a polynomial sequence in $G$, and $f\in C(X)$, we show that the sequence $\phi (n)= \int \nolimits \nolimits_{g(n)Y} f$ is the sum of a basic nilsequence and a sequence that converges to zero in uniform density (a null-sequence). We also show that an integral of a family of nilsequences is a nilsequence plus a null-sequence. We deduce that for any invertible finite measure preserving system $(W, \mathcal{B} , \mu , T)$, polynomials ${p}_{1} , \ldots , {p}_{k} : { \mathbb{Z} }^{d} \longrightarrow \mathbb{Z} $, and sets ${A}_{1} , \ldots , {A}_{k} \in \mathcal{B} $, the sequence $\phi (n)= \mu ({T}^{{p}_{1} (n)} {A}_{1} \cap \cdots \cap {T}^{{p}_{k} (n)} {A}_{k} )$, $n\in { \mathbb{Z} }^{d} $, is the sum of a nilsequence and a null-sequence.

Visual Evoked-Response Correlates of Speechreading Performance in Normal-Hearing Adults

1983 ◽  
Vol 26 (1) ◽  
pp. 2-9 ◽  
Author(s):  
Vincent J. Samar ◽  
Donald G. Sims
Keyword(s):  
Multiple Correlation Coefficient ◽  
Evoked Response ◽  
Multiple Correlation ◽  
Potential Significance ◽  
Visual Evoked Response ◽  
Latency Measure ◽  
Two Measures ◽  
Components Analysis ◽  
The Relationship ◽  
Visual Evoked

The relationship between the latency of the negative peak occurring at approximately 130 msec in the visual evoked-response (VER) and speechreading scores was investigated. A significant product-moment correlation of -.58 was obtained between the two measures, which confirmed the fundamental effect but was significantly weaker than that previously reported in the literature (-.90). Principal components analysis of the visual evoked-response waveforms revealed a previously undiscovered early VER component, statistically independent of the latency measure, which in combination with two other components predicted speechreading with a multiple correlation coefficient of S4. The potential significance of this new component for the study of individual differences in speechreading ability is discussed.

IMBALAN DAN GAYA KEPEMIMPINAN PENGARUHNYA TERHADAP KEPUASAN KERJA KARYAWAN DI BALAI BESAR INDUSTRI HASIL PERTANIAN BOGOR

2018 ◽  
Vol 1 (01) ◽  
pp. 17
Author(s):  
Ramlan Ruvendi
Keyword(s):  
Job Satisfaction ◽  
Multiple Regression ◽  
Correlation Coefficient ◽  
Analysis Of Variance ◽  
Partial Correlation ◽  
Multiple Correlation Coefficient ◽  
Multiple Correlation ◽  
Average Value ◽  
Partial Correlation Coefficient

The study was carried out to find out whether there were influence and correlation bet-ween : a) Reward received by the IRDABI’s employees on their job satisfaction. b) style of the leader-ship on the job satisfaction. c) Reward together with style of leadership on the job satisfaction of IR-DABI’s employees.The result of the study showed that there was significant correlation and influence between the reward on the job satisfaction with was shown by the value of partial correlation coefficient of 0.6185 and coefficient of multiple regression for reward variable (β1) of 0.412. The influence of variable for style of leadership on the job satisfaction was also significant with the partial correlation coefficient of 0.5495 and coefficient of multiple regression (β2) of 0.355.In the test of Analysis of Variance (ANOVA) on the equation of multiple regression show that F-value was bigger that F-table (F = 58.97 > F-table = 3.098) or the Probability Value smaller than 0.05. At showed that there was significant correlation and influence between reward variables all together with style of leadership on the job satisfaction of employees. The value of multiple correlation coefficient (R) was 0.751 and R Square (R2) was 0.564. Value of R Square (0.564) meant that 56.5% of variation pro-portion total of job satisfaction can be eliminated of equation of multiple regression was used as the es-timator rather than using average value of job satisfaction as the estimator.

PENGARUH AKTIVA TETAP DAN AKTIVA LANCAR TERHADAP PENDAPATAN PADA SIMPAN PINJAM PEREMPUAN UPK GERBANG SARI KECAMATAN RENGAT BARAT

2019 ◽  
Vol 7 (2) ◽  
pp. 101-108
Author(s):  
Angga Hapsila
Keyword(s):  
Hypothesis Testing ◽  
Significant Influence ◽  
Quantitative Methods ◽  
Correlation Coefficients ◽  
Multiple Correlation ◽  
Savings And Loans ◽  
Savings And Loan ◽  
Fixed Assets ◽  
Multiple Determination ◽  
Regression Correlation

This research is about savings and loans for women UPK Gerbang Sari, Rengat Barat District. The research lasted for 5 (five) months. This research try to determine the effect of whether there was a significant influence between fixed assets and current assets on income on women's savings and loans UPK Gerbang Sari, Rengat Barat District. The formulation of the problem to be investigated is whether there is a simultaneous and partial effect between fixed assets and current assets on women's savings and loan income UPK Gerbang Sari, Rengat Barat District. This research used quantitative methods, that illustrates whether there is a significant influence between fixed assets and current assets on income on savings and loans for women UPK Gerbang Sari, Rengat Barat District. To analyzed the data, this research used multiple regression, correlation coefficients, and Hypothesis testing which will be assisted using SPSS version 21. From the results of the study with the regression equation Y = 1,379,231-1,075 X1 + 0,214X2. This means: a = if the fixed assets and current assets are equal to Zero (0), then the value of income is equal to 1,379,231. The coefficient of multiple correlation R is 0.686. and furthermore tested with multiple determination Keofisie (R2 is 0.471. This indicates that (X1) fixed assets and (X2) current assets have together an influence of 47.10% and the remaining 52.90% is influenced by variables other than ( X1) and (X2). Hypothesis testing in which F arithmetic (0.891) <Ftable (3.00), then there is no significant effect simultaneously between fixed assets and current assets to income on savings and loans for women in UPK Gerbang Sari, Rengat Barat District.

Sign in / Sign up

Export Citation Format

Share Document