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.

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).

Studies on the Thermochemistry of Rubber. I. Heat of Vulcanization of Rubber

1931 ◽  
Vol 4 (4) ◽  
pp. 507-513 ◽  
Author(s):  
Kyoichi Hada ◽  
Koichi Fukaya ◽  
Takeji Nakajima
Keyword(s):  
Experimental Data ◽  
Experimental Results ◽  
Absolute Value ◽  
The Absolute ◽  
The Difference

Abstract 1. The heat of vulcanization of the system: pure rubber-sulfur is determinated. 2. The absolute value of the experimental data is in doubt, however, since the results were widely different from those of Blake. 3. The experimental results are discussed. 4. The results of Blake are discussed. 5. The difference from the results of Blake is attributed to the difference in the content of resinous substances in the sample.

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(∈),

The Radio Emission of the Moon on 4 mm

1962 ◽  
Vol 14 ◽  
pp. 511-518 ◽  
Author(s):  
A. G. Kislyakov
Keyword(s):  
Experimental Data ◽  
Radio Emission ◽  
Experimental Research ◽  
Homogeneous Model ◽  
The Moon ◽  
Radio Brightness ◽  
Phase Dependence ◽  
Absolute Value ◽  
The Absolute ◽  
Good Agreement

The aim of this communication is to present the results of an experimental research on the intensity of the radio emission of the Moon at 4 mm and to describe the method followed in observations and reductions. It was established that the radio brightness of the Moon,Tl, varies during the lunation according to the law:Tl= 230° + 73° cos (Ω0t-24°)K. The accuracy in measuring the absolute value of Moon's radio temperature is about ± 10%. The comparison between the phase dependence of the radio emission of the Moon at 4 mm and the data from observations of the radio temperature of the lunar disk on other wave lengths demonstrated that the homogeneous model of Moon's surface is in good agreement with the experimental data.

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 Measurements of the absorption of wireless waves in the ionosphere

1935 ◽  
Vol 151 (873) ◽  
pp. 370-383 ◽  
Author(s):  
F. T. Farmer ◽  
John Ashworth Ratcliffe ◽  
Edward Victor Appleton
Keyword(s):  
Experimental Data ◽  
Total Absorption ◽  
Absolute Value ◽  
Ionization Density ◽  
The Absolute ◽  
Theoretical Results ◽  
Different Levels

In most of the investigation which have been made on wireless waves reflected from the ionosphere the experiments have been so designed as to provide information concerning the ionization density at different levels. The experimental data sought in such cases are usually critical penetration frequencies and equivalent heights of reflection. If, however, the amplitude of the downcoming waves is also observed, and the total absorption measured, it is possible to obtain information about the frequency of collision between electrons and molecules at different heights in the ionosphere. The measurements described in the present paper have been made so as to provide the latter type of information, and in particular to give evidence concerning the location of that part of the ionosphere which is of importance in producing absorption. For this purpose it is necessary to measure the absolute value of the absorption suffered by the wave, so that results on different wave-lengths may be compared. The methods which we have employed in making these measurements are described in § 2 and the results are discussed in § 4. The theoretical results which are used in § 4 are reviewed shortly in § 3. Most of the measurements discussed in this paper have been made on wave-lengths less than 200 m; a few measurements made with longer waves are discussed in § 6.

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