Imaging of tilted, extended, thin phase-objects

1978 ◽  
Vol 36 (1) ◽  
pp. 216-217
Author(s):  
P. Schiske
Keyword(s):  
Wave Field ◽  
The Other ◽  
Single Exposure ◽  
Coordinate Axis ◽  
Other Hand ◽  
Spatial Frequencies ◽  
Geometrical Data ◽  
Image Position ◽  
Transfer Properties ◽  
Different Parts

In images of extended strongly tilted specimens, different parts of the object are subject to different defocus. This makes it possible to obtain, by a single exposure, an overall view of the transfer properties of the objective [1,2]; on the other hand, in reconstruction work it requires the use of correcting procedures [3]. The importance of both points seems to justify formal investigation--restricted here to thin phase objects. The geometrical data are shown in Fig. 1; the axis of tilt is normal to the plane of the drawing and is used as coordinate axis X2. Representing the scattered amplitude by u(k1,k2) where spatial frequencies k by δ = λk represent the inclination δ of the different components of the wave field a(x1,x2,z), one hasPutting z = x1 one finds for the amplitude immediately beyond the object(1)

On functional Nörlund methods

1970 ◽  
Vol 67 (1) ◽  
pp. 47-60 ◽  
Author(s):  
B. Choudhary
Keyword(s):  
The Other ◽  
Integral Transformations ◽  
Other Hand ◽  
Nörlund Means ◽  
The One ◽  
Image Position

Integral transformations analogous to the Nörlund means have been introduced and investigated by Kuttner, Knopp and Vanderburg(6), (5), (4). It is known that with any regular Nörlund mean (N, p) there is associated a functionregular for |z| < 1, and if we have two Nörlund means (N, p) and (N, r), where (N, pr is regular, while the function is regular for |z| ≤ 1 and different) from zero at z = 1, then q(z) = r(z)p(z) belongs to a regular Nörlund mean (N, q). Concerning Nörlund means Peyerimhoff(7) and Miesner (3) have recently obtained the relation between the convergence fields of the Nörlund means (N, p) and (N, r) on the one hand and the convergence field of the Nörlund mean (N, q) on the other hand.

scholarly journals Distribution of rational points on the real line

1973 ◽  
Vol 15 (2) ◽  
pp. 243-256 ◽  
Author(s):  
T. K. Sheng
Keyword(s):  
Algebraic Number ◽  
Rational Number ◽  
Real Line ◽  
Rational Points ◽  
The Other ◽  
Liouville Numbers ◽  
The Real ◽  
Other Hand ◽  
Image Position

It is well known that no rational number is approximable to order higher than 1. Roth [3] showed that an algebraic number is not approximable to order greater than 2. On the other hand it is easy to construct numbers, the Liouville numbers, which are approximable to any order (see [2], p. 162). We are led to the question, “Let Nn(α, β) denote the number of distinct rational points with denominators ≦ n contained in an interval (α, β). What is the behaviour of Nn(α, + 1/n) as α varies on the real line?” We shall prove that and that there are “compressions” and “rarefactions” of rational points on the real line.

The institutional basis of anglophone western centrality

2020 ◽  
Vol 43 (1) ◽  
pp. 180-188
Author(s):  
Afonso de Albuquerque
Keyword(s):  
The Other ◽  
Educational Institutions ◽  
Cultural Backgrounds ◽  
Global Impact ◽  
European Universities ◽  
Other Hand ◽  
The World ◽  
Personal Contribution ◽  
The One ◽  
Different Parts

Non-western scholars usually face a dilemma if they want to pursue an international scholarly career: On the one hand, mastering western media theories is mandatory for taking part in international forums and exchanging experiences with people from different parts of the world; on the other hand, these theories are, in many aspects, foreign to their cultural backgrounds and, in many cases, seem inadequate for describing their own societies. My personal contribution to the debate arises from the fact that, although having some experience in participating in Anglophonic communication meetings and publishing in international academic vehicles, I never had first-hand experience, either as a student or as a professor, in American or European universities. In consequence, I was exposed to Western Anglophonic theories without being socialized in a scholarly environment in which they are taken as ‘natural’. Based on this experience, I contend that the global impact of western theories cannot be explained only by their intrinsic merits, but as the result of the socialization of scholars from all parts on the world in western educational institutions, and the networks built around them.

Configuration of Quadrivalent Atoms

1929 ◽  
Vol 25 (2) ◽  
pp. 219-221
Author(s):  
T. M. Lowry
Keyword(s):  
The Other ◽  
Tetrahedral Configuration ◽  
X Ray ◽  
Metallic Atom ◽  
Other Hand ◽  
Function Change ◽  
The One ◽  
Image Position ◽  
Octahedral Configuration ◽  
As If

Two alternative views have been expressed in regard to the configuration of quadrivalent atoms. On the one hand le Bel and van't Hoff assigned to quadrivalent carbon a tetrahedral configuration, which has since been confirmed by the X-ray analysis of the diamond. On the other hand, Werner in 1893 adopted an octahedral configuration for radicals of the type MA6, e.g. inand then suggested that “the molecules [MA4]X2 are incomplete molecules [MA6]X2. The radicals [MA4] result from the octahedrally-conceived radicals [MA6] by loss of two groups A, but with no function-change of the acid residue…. They behave as if the bivalent metallic atom in the centre of the octahedron could no longer bind all six of the groups A and lost two of them leaving behind the fragment [MA4]” (p. 303).

A System of Linear Equations with an Infinity of Unknowns

1924 ◽  
Vol 22 (3) ◽  
pp. 282-286
Author(s):  
E. C. Titchmarsh
Keyword(s):  
Present Note ◽  
Linear Equations ◽  
The Other ◽  
System Of Linear Equations ◽  
Other Hand ◽  
Image Position ◽  
Monotonic Character

I have collected in the present note some theorems regarding the solution of a certain system of linear equations with an infinity of unknowns. The general form of the equations isthe numbers a1, a2, … c1, c2, … being given. Equations of this type are of course well known; but in studying them it is generally assumed that the series depend for convergence on the convergence-exponent of the sequences involved, e.g. that and are convergent. No assumptions of this kind are made here, and in fact the series need not be absolutely convergent. On the other hand rather special assumptions are made with regard to the monotonic character of the sequences an and cn.

The Saxon Invasion and its Influence on our Character as a Race

1885 ◽  
Vol 2 (2) ◽  
pp. 173-196 ◽  
Author(s):  
J. Foster Palmer
Keyword(s):  
The Other ◽  
Tall Stature ◽  
East Anglia ◽  
Ammianus Marcellinus ◽  
Brown Hair ◽  
Other Hand ◽  
Social Scale ◽  
The People ◽  
The Social ◽  
Different Parts

In the following paper the term ‘Ancient Briton’ is applied to the whole of the mixed races which inhabited this island prior to the Teutonic irruption. They consisted of the two Celtic families (the Gaels and the Brythons, or Cymri), and the pre-Celtic races. On the divisions of the latter anthropology has not yet decidedly pronounced, though it seems probable that they were not homogeneous. In any case the principal pre-Celtic type at present discovered, which may generically be termed Iberian, and which appears to correspond with that of the original neolithic inhabitants, was dark, small, and short, the average stature being only sixty-three inches. The pure Celt, on the other hand, was extremely tall, the average stature being sixty-nine inches, and that of the Saxon sixty-seven. This agrees with the statements of Polybius, Strabo, and Ammianus Marcellinus as to the height of the Celt, and at the same time accounts for the Britons being spoken of as short and thick-set. For in this country the Celt was found mixed to a large extent with the short pre-Celtic race or races. The people, therefore, that the Saxons had to contend with were, on an average, of shorter stature than themselves. They varied, no doubt, in different parts of the country, but probably the purest Iberian blood, and consequently the shortest stature, would be at the bottom of the social scale. If any pure Celtic blood remained in the country it would be chiefly in the east; and it is to the permanence of this, rather than to the superior stature of the Angles over the rest of the invaders, that I attribute the height of the present inhabitants of the Anglian districts. The prevailing physiognomy of East Anglia also supports this view; the tall stature, brown hair, grey eye, and arched nose of the pure Celt is not uncommon there.

The extreme points of some classes of polynomials

1985 ◽  
Vol 101 (1-2) ◽  
pp. 99-110 ◽  
Author(s):  
D. A. Brannan ◽  
J. G. Clunie
Keyword(s):  
Extreme Points ◽  
The Other ◽  
Other Hand ◽  
Image Position

SynopsisWe study the extreme points of two classes of polynomials of degree at most n:It turns out that f ∈ Ext if and only if Re f(eiθ) has exactly 2n zeros in [0, 2π). On the other hand, if f∈Hn and 1−|f(eiθ)|2 has 2n zeros in [0, 2π), then either f ∈ Ext Hn or else f(z) = α + βzn where |α|+|β| = l and αβ≠0; if 1−|f(eiθ)|2 has 2m zeros, 2n, then f may or may not belong to Ext Hn.

The No-Three-In-Line Problem

1968 ◽  
Vol 11 (4) ◽  
pp. 527-531 ◽  
Author(s):  
Richard K. Guy ◽  
Patrick A. Kelly
Keyword(s):  
Finite Number ◽  
The Other ◽  
Probabilistic Argument ◽  
Number Of Solutions ◽  
Other Hand ◽  
Image Position

Let Sn be the set of n2 points with integer coordinates n (x, y), 1 ≤ x, y <n. Let fn be the maximum cardinal of a subset T of Sn such that no three points of T are collinear. Clearly fn < 2n.For 2 ≤ n ≤ 10 it is known ([2], [3] for n = 8, [ 1] for n = 10, also [4], [6]) that fn = 2n, and that this bound is attained in 1, 1, 4, 5, 11, 22, 57, 51 and 156 distinct configurations for these nine values of n. On the other hand, P. Erdös [7] has pointed out that if n is prime, fn ≥ n, since the n points (x, x2) reduced modulo n have no three collinear. We give a probabilistic argument to support the conjecture that there is only a finite number of solutions to the no-three-in-line problem. More specifically, we conjecture that

scholarly journals Pronominale demonstrativer: nye perspektiver fra norsk og svensk

2021 ◽  
Vol 11 (2) ◽  
pp. 201-224
Author(s):  
Kari Kinn ◽  
Ida Larsson
Keyword(s):  
19Th Century ◽  
Noun Phrase ◽  
Spoken Language ◽  
The Other ◽  
Other Hand ◽  
The 19Th Century ◽  
Different Parts ◽  
The Way

This paper is concerned with pronominal demonstatives (referred to as psychologically distal demonstratives by Johannessen 2008a, b) in older Norwegian spoken language, and written Swedish from the 19th century and the present-day. We show that pronominal demonstratives can be attested in speakers born in different parts of Norway in the 19th century, and in Swedish texts from the same period. However, the pronominal forms do not seem to be used in precisely the same way in the two languages. In Swedish, han/hon ‘he/she’ do not seem to behave formally like demonstratives. Instead, we propose that they are syntactically reduced pronouns at the edge of the DP, above the position for demonstratives, and that they double features lower down in the noun phrase. In Norwegian, on the other hand, han/hun are used as demonstratives already in the 19th century, in the way described for present-day Norwegian by Johannessen (2008a, b).

On Bernstein's Inequality

1979 ◽  
Vol 31 (2) ◽  
pp. 347-353 ◽  
Author(s):  
A. Giroux ◽  
Q. I. Rahman ◽  
G. Schmeisser
Keyword(s):  
The Other ◽  
Bernstein’S Inequality ◽  
Other Hand ◽  
Famous Result ◽  
Bernstein's Inequality ◽  
Image Position

1. Introduction and statement of results. If pn(z) is a polynomial of degree at most n, then according to a famous result known as Bernstein's inequality (for references see [4])(1)Here equality holds if and only if pn(z) has all its zeros at the origin and so it is natural to seek for improvements under appropriate assumptions on the zeros of pn(z). Thus, for example, it was conjectured by P. Erdös and later proved by Lax [2] that if pn(z) does not vanish in │z│ < 1, then (1) can be replaced by(2)On the other hand, Turán [5] showed that if pn(z) is a polynomial of degree n having all its zeros in │z│ ≦ 1, then(3)

Sign in / Sign up

Export Citation Format

Share Document