scholarly journals Pointwise characteristic factors for Wiener–Wintner double recurrence theorem

2015 ◽  
Vol 36 (4) ◽  
pp. 1037-1066 ◽  
Author(s):  
IDRIS ASSANI ◽  
DAVID DUNCAN ◽  
RYO MOORE
Keyword(s):  
Full Measure ◽  
Orthogonal Complement ◽  
Ergodic System ◽  
Absolute Value ◽  
Recurrence Theorem ◽  
The Absolute ◽  
Image Position ◽  
Null Set

In this paper we extend Bourgain’s double recurrence result to the Wiener–Wintner averages. Let $(X,{\mathcal{F}},{\it\mu},T)$ be a standard ergodic system. We will show that for any $f_{1},f_{2}\in L^{\infty }(X)$, the double recurrence Wiener–Wintner average $$\begin{eqnarray}\frac{1}{N}\mathop{\sum }_{n=1}^{N}f_{1}(T^{an}x)f_{2}(T^{bn}x)e^{2{\it\pi}int}\end{eqnarray}$$ converges off a single null set of $X$ independent of $t$ as $N\rightarrow \infty$. Furthermore, we will show a uniform Wiener–Wintner double recurrence result: if either $f_{1}$ or $f_{2}$ belongs to the orthogonal complement of the Conze–Lesigne factor, then there exists a set of full measure such that the supremum on $t$ of the absolute value of the averages above converges to $0$.

scholarly journals ON SOME PEXIDER-TYPE FUNCTIONAL EQUATIONS CONNECTED WITH THE ABSOLUTE VALUE OF ADDITIVE FUNCTIONS. PART II

2012 ◽  
Vol 85 (2) ◽  
pp. 202-216 ◽  
Author(s):  
BARBARA PRZEBIERACZ
Keyword(s):  
Functional Equation ◽  
Abelian Group ◽  
Functional Equations ◽  
Additive Functions ◽  
Absolute Value ◽  
Real Functions ◽  
The Absolute ◽  
Image Position

AbstractWe investigate the Pexider-type functional equation where f, g, h are real functions defined on an abelian group G. We solve this equation under the assumptions G=ℝ and f is continuous.

A rational invariant for certain infinite discrete groups

1993 ◽  
Vol 113 (3) ◽  
pp. 473-478
Author(s):  
F. E. A. Johnson
Keyword(s):  
Euler Characteristic ◽  
Discrete Groups ◽  
Fundamental Groups ◽  
Intersection Form ◽  
Absolute Value ◽  
Rational Invariant ◽  
The Absolute ◽  
Image Position ◽  
Aspherical Manifolds

We introduce a rational-valued invariant which is capable of distinguishing between the commensurability classes of certain discrete groups, namely, the fundamental groups of smooth closed orientable aspherical manifolds of dimensional 4k(k ≥ 1) whose Euler characteristic χ(Λ) is non-zero. The invariant in question is the quotientwhere Sign (Λ) is the absolute value of the signature of the intersection formand [Λ] is a generator of H4k(Λ; ℝ).

scholarly journals ON SOME PEXIDER-TYPE FUNCTIONAL EQUATIONS CONNECTED WITH THE ABSOLUTE VALUE OF ADDITIVE FUNCTIONS. PART I

2012 ◽  
Vol 85 (2) ◽  
pp. 191-201 ◽  
Author(s):  
BARBARA PRZEBIERACZ
Keyword(s):  
Functional Equation ◽  
Abelian Group ◽  
Functional Equations ◽  
Additive Functions ◽  
Absolute Value ◽  
Real Functions ◽  
The Absolute ◽  
Image Position

AbstractWe investigate the Pexider-type functional equation where f,g,h are real functions defined on an abelian group G.

scholarly journals Quantitative Equidistribution for Certain Quadruples in Quasi-Random Groups: Erratum

2015 ◽  
Vol 25 (3) ◽  
pp. 484-485 ◽  
Author(s):  
TIM AUSTIN
Keyword(s):  
First Line ◽  
Absolute Value ◽  
Formula Group ◽  
The Absolute ◽  
Image Position ◽  
The Right ◽  
Random Groups ◽  
Complex Valued

In my recent paper [1] there is a mistake in the proof of Corollary 3. The first line of the displayed equation in that proof asserts that \[\int_G|\langle u,\pi^g v\rangle_V|^2\,\rm{d} g = \int_G\langle u\otimes u,(\pi^g\otimes \pi^g)(v\otimes v)\rangle_{V\otimes V}\, \rm{d} g.\] However, since the paper uses complex-valued representations, the integrand on the right here may not retain the absolute value of that on the left. Without this equality, the proof of Corollary 3 can no longer be reduced to an application of Lemma 2. However, it can be proved directly from Schur Orthogonality along very similar lines to the proof of Lemma 2.

scholarly journals On the growth of the cyclotomic polynomial in the interval (0, 1)

1957 ◽  
Vol 3 (2) ◽  
pp. 102-104 ◽  
Author(s):  
P. Erdös
Keyword(s):  
Positive Constant ◽  
Cyclotomic Polynomial ◽  
Absolute Value ◽  
The Absolute ◽  
Image Position

Letbe the rath cyclotomic polynomial, and denote by An the absolute value of the largest coefficient of Fn(x).Schur proved thatand Emma Lehmer [5] showed that An>cn1/3 for infinitely many n; in fact she proved that n can be chosen as the product of three distinct primes. I proved [3] that there exists a positive constant q such that, for infinitely many nand Bateman [1] proved very simply that, for every ∈>0 and all n>no(∈),

Quantitative χn analysis of HREM images with applications to planar defects

1996 ◽  
Vol 54 ◽  
pp. 98-99
Author(s):  
H. Zhang ◽  
L. D. Marks
Keyword(s):  
Experimental Data ◽  
Cross Correlation ◽  
Planar Defects ◽  
Absolute Value ◽  
Background Levels ◽  
Correlation Analyses ◽  
The Absolute ◽  
Image Position ◽  
R Factors ◽  
Calculated Image

A number of different methods have been suggested in the literature for using HREM in a quantitative fashion, including R factors and cross-correlation analyses. The problem with many of these is that it is difficult to realistically gauge the errors involved when they are applied to real systems. For instance, R-factors defined by:(1)(where n=1 or 2 and Ic is the calculated image, Ie the experimental data) assume a signal independent error. Furthermore, the absolute value of R is strongly dependent upon background levels which is misleading.

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.

scholarly journals A good universal weight for nonconventional ergodic averages in norm

2015 ◽  
Vol 37 (4) ◽  
pp. 1009-1025 ◽  
Author(s):  
IDRIS ASSANI ◽  
RYO MOORE
Keyword(s):  
Positive Integer ◽  
Measurable Function ◽  
Full Measure ◽  
Ergodic Averages ◽  
Bounded Functions ◽  
Recurrence Theorem ◽  
Image Position

We will show that the sequence appearing in the double recurrence theorem is a good universal weight for the Furstenberg averages. That is, given a system$(X,{\mathcal{F}},\unicode[STIX]{x1D707},T)$and bounded functions$f_{1},f_{2}\in L^{\infty }(\unicode[STIX]{x1D707})$, there exists a set of full-measure$X_{f_{1},f_{2}}$in$X$that is independent of integers$a$and$b$and a positive integer$k$such that, for all$x\in X_{f_{1},f_{2}}$, for every other measure-preserving system$(Y,{\mathcal{G}},\unicode[STIX]{x1D708},S)$and for each bounded and measurable function$g_{1},\ldots ,g_{k}\in L^{\infty }(\unicode[STIX]{x1D708})$, the averages$$\begin{eqnarray}\frac{1}{N}\mathop{\sum }_{n=1}^{N}f_{1}(T^{an}x)f_{2}(T^{bn}x)g_{1}\circ S^{n}g_{2}\circ S^{2n}\cdots g_{k}\circ S^{kn}\end{eqnarray}$$converge in$L^{2}(\unicode[STIX]{x1D708})$.

scholarly journals Incentive Function of Audit Opinion for the Increase of Regional Operational Expenditure and Own-Source Revenues Through Sensitivity Analysis in Indonesia

2020 ◽  
Vol 11 (1) ◽  
pp. 20
Author(s):  
Muhammad Ikbal Abdullah ◽  
Andi Chairil Furqan ◽  
Nina Yusnita Yamin ◽  
Fahri Eka Oktora
Keyword(s):  
Sensitivity Analysis ◽  
Significant Influence ◽  
Provincial Government ◽  
Sensitivity Testing ◽  
Audit Opinion ◽  
Absolute Value ◽  
Operating Expenditure ◽  
The Absolute ◽  
Operational Expenditure

This study aims to analyze the sensitivity testing using measurements of realization of regional own-source revenues and operating expenditure and to analyze the extent of the effect of sample differences between Java and non-Java provinces by using samples outside of Java. By using sensitivity analysis, the results found the influence of audit opinion on the performance of the provincial government mediated by the realization of regional operating expenditure. More specifically, when using the measurement of the absolute value of the realization of regional operating expenditure it was found that there was a direct positive and significant influence of audit opinion on the performance of the Provincial Government. However, no significant effect of audit opinion was found on the realization value of regional operating expenditure and the effect of the realization value of regional operating expenditure on the performance of the Provincial Government. This result implies that an increase in audit opinion will be more likely to be used as an incentive for the Provincial Government to increase the realization of regional operating expenditure.

Die Bedeutung der Homogenisationsart und -intensität für die Größe und Konstanz der Sauerstoffaufnahme von Meerschweinchen-Leberhomogenat / The Influence of Mode and Intensity of Homogenization on the Absolute Value and Stability of Oxygen Consumption of Guinea Pig Liver Homogenates

1977 ◽  
Vol 32 (11-12) ◽  
pp. 908-912 ◽  
Author(s):  
H. J. Schmidt ◽  
U. Schaum ◽  
J. P. Pichotka
Keyword(s):  
Oxygen Uptake ◽  
Guinea Pig ◽  
Measuring Time ◽  
Pig Liver ◽  
Absolute Value ◽  
Modified Method ◽  
Simultaneous Measurements ◽  
Liver Homogenates ◽  
The Absolute ◽  
Guinea Pig Liver

Abstract The influence of five different methods of homogenisation (1. The method according to Potter and Elvehjem, 2. A modification of this method called Potter S, 3. The method of Dounce, 4. Homogenisation by hypersonic waves and 5. Coarce-grained homogenisation with the “Mikro-fleischwolf”) on the absolute value and stability of oxygen uptake of guinea pig liver homogenates has been investigated in simultaneous measurements. All homogenates showed a characteristic fall of oxygen uptake during measuring time (3 hours). The modified method according to Potter and Elvehjem called Potter S showed reproducible results without any influence by homogenisation intensity.

Sign in / Sign up

Export Citation Format

Share Document