An Experimental Study of Deviations from the Linear Transfer Function

1974 ◽  
Vol 32 ◽  
pp. 400-401
Author(s):  
William A. Voter ◽  
Harold P. Erickson
Keyword(s):  
Experimental Study ◽  
Image Formation ◽  
Order Theory ◽  
Second Order ◽  
Diffraction Spot ◽  
Order Effects ◽  
First Order ◽  
First Order Theory ◽  
Second Order Effects ◽  
The Fourier Transform

In a previous experimental study of image formation using a thin (20 nm) negatively stained catalase crystal, it was found that a linear or first order theory of image formation would explain almost entirely the changes in the Fourier transform of the image as a function of defocus. In this case it was concluded that the image is a valid picture of the object density. For thicker, higher contrast objects the first order theory may not be valid. Second order effects could generate false diffraction spots which would lead to spurious and artifactual image details. These second order effects would appear as deviations of the diffraction spot amplitudes from the first order theory. Small deviations were in fact noted in the study of the thin crystals, but there was insufficient data for a quantitative analysis.

scholarly journals Statistical analysis of second order effects variation with the stories height of reinforced concrete buildings

2017 ◽  
Vol 10 (2) ◽  
pp. 333-357
Author(s):  
D.M. OLIVEIRA ◽  
N.A. SILVA ◽  
C.C. RIBEIRO ◽  
S.E.C. RIBEIRO
Keyword(s):  
Reinforced Concrete ◽  
Statistical Analysis ◽  
Second Order ◽  
Order Effects ◽  
Reinforced Concrete Buildings ◽  
First Order ◽  
Concrete Buildings ◽  
Ideal Situation ◽  
Second Order Effects ◽  
The Ideal

Abstract In this paper the simplified method to evaluate final efforts using γ z coefficient is studied considering the variation of the second order effects with the height of the buildings. With this purpose, several reinforced concrete buildings of medium height are analyzed in first and second order using ANSYS software. Initially, it was checked that the (z coefficient should be used as magnifier of first order moments to evaluate final second order moments. Therefore, the study is developed considering the relation (final second order moments/ first order moments), calculated for each story of the structures. This moments relation is called magnifier of first order moments, "γ", and, in the ideal situation, it must coincide with the γ z value. However, it is observed that the reason γ /γ z varies with the height of the buildings. Furthermore, using an statistical analysis, it was checked that γ /γ z relation is generally lower than 1.05 and varies significantly in accordance with the considered building and with the presence or not of symmetry in the structure.

Global Buckling of Frames with Laced Compression Members

2016 ◽  
Vol 837 ◽  
pp. 103-108 ◽  
Author(s):  
Michal Kovac ◽  
Zsuzsanna Vanik
Keyword(s):  
Order Theory ◽  
Second Order ◽  
Order Effects ◽  
Engineering Practice ◽  
Buckling Mode ◽  
Column Method ◽  
Global Buckling ◽  
Second Order Effects ◽  
Buckling Length ◽  
Simplified Procedure

The planar frames whose members consist of a laced built-up members are often used in civil engineering practice. For chords of these structures the 1st order theory internal forces and the assessment by equivalent column method are mostly used. In the equivalent column method the buckling length according to the global buckling mode of the structures should be used. If the distance between neighboring nodes is used as the buckling length of the chord, which is the common case, the second order effects with only the bow imperfections between nodes are taken into account in the equivalent column method. For frames sensitive to buckling in a sway mode the second order effects on structures with initial sway imperfection should be taken into account. Therefore, also in frames with the laced compression columns, where the effects of additional sway deformation cause additional normal forces in the chords, the sway imperfection should be applied and the second order in frame analysis should be performed to check these additive forces. This paper deals with the simplified procedure how to evaluate additive forces due to second order effects on the structure with the global sway imperfection.

Numerical Calculation of Second-Order Wave Resistance

1977 ◽  
Vol 21 (02) ◽  
pp. 94-106
Author(s):  
Young S. Hong
Keyword(s):  
Numerical Calculation ◽  
Steady Motion ◽  
Order Theory ◽  
Iteration Scheme ◽  
Wave Resistance ◽  
Second Order ◽  
Lagrangian Coordinates ◽  
Restricted Range ◽  
First Order ◽  
First Order Theory

The wave resistance due to the steady motion of a ship was formulated in Lagrangian coordinates by Wehausen [1].2 By introduction of an iteration scheme the solutions for the first order and second order3 were obtained. The draft/length ratio was assumed small in order to simplify numerical computation. In this work Wehausen's formulas are used to compute the resistance numerically. A few models are selected and the wave resistance is calculated. These results are compared with other methods and experiments. Generally speaking, the second-order resistance shows better agreement with experiment than first-order theory in only a restricted range of Froude number, say 0.25 to 0.35, and even here not uniformly. For larger Froude numbers it underestimates seriously.

Polynomial rings and weak second-order logic

1985 ◽  
Vol 50 (4) ◽  
pp. 953-972 ◽  
Author(s):  
Anne Bauval
Keyword(s):  
Zero Divisor ◽  
Order Theory ◽  
Second Order ◽  
Order Logic ◽  
Polynomial Rings ◽  
Commutative Field ◽  
First Order ◽  
First Order Theory ◽  
Order Language ◽  
Second Order Logic

This article is a rewriting of my Ph.D. Thesis, supervised by Professor G. Sabbagh, and incorporates a suggestion from Professor B. Poizat. My main result can be crudely summarized (but see below for detailed statements) by the equality: first-order theory of F[Xi]i∈I = weak second-order theory of F.§I.1. Conventions. The letter F will always denote a commutative field, and I a nonempty set. A field or a ring (A; +, ·) will often be written A for short. We shall use symbols which are definable in all our models, and in the structure of natural numbers (N; +, ·):— the constant 0, defined by the formula Z(x): ∀y (x + y = y);— the constant 1, defined by the formula U(x): ∀y (x · y = y);— the operation ∹ x − y = z ↔ x = y + z;— the relation of division: x ∣ y ↔ ∃ z(x · z = y).A domain is a commutative ring with unity and without any zero divisor.By “… → …” we mean “… is definable in …, uniformly in any model M of L”.All our constructions will be uniform, unless otherwise mentioned.§I.2. Weak second-order models and languages. First of all, we have to define the models Pf(M), Sf(M), Sf′(M) and HF(M) associated to a model M = {A; ℐ) of a first-order language L [CK, pp. 18–20]. Let L1 be the extension of L obtained by adjunction of a second list of variables (denoted by capital letters), and of a membership symbol ∈. Pf(M) is the model (A, Pf(A); ℐ, ∈) of L1, (where Pf(A) is the set of finite subsets of A. Let L2 be the extension of L obtained by adjunction of a second list of variables, a membership symbol ∈, and a concatenation symbol ◠.

Complex language, complex thought?

2016 ◽  
Vol 33 ◽  
pp. 28-40
Author(s):  
Suzanne T.M. Bogaerds-Hazenberg ◽  
Petra Hendriks
Keyword(s):  
Theory Of Mind ◽  
Order Theory ◽  
Second Order ◽  
False Belief ◽  
Production Task ◽  
False Belief Task ◽  
First Order ◽  
First Order Theory ◽  
Complex Thought

Abstract It has been argued (e.g., by De Villiers and colleagues) that the acquisition of sentence embedding is necessary for the development of first-order Theory of Mind (ToM): the ability to attribute beliefs to others. This raises the question whether the acquisition of double embedded sentences is related to, and perhaps even necessary for, the development of second-order ToM: the ability to attribute beliefs about beliefs to others. This study tested 55 children (aged 7-10) on their ToM understanding in a false-belief task and on their elicited production of sentence embeddings. We found that second-order ToM passers produced mainly double embeddings, whereas first-order ToM passers produced mainly single embeddings. Furthermore, a better performance on second-order ToM predicted a higher rate of double embeddings and a lower rate of single embeddings in the production task. We conclude that children’s ability to produce double embeddings is related to their development of second-order ToM.

Application des miroirs électrostatiques à l'élimination de l'effet chromatique dans les spectromètres magnétiques. Première partie: théorie linéaire

1969 ◽  
Vol 47 (3) ◽  
pp. 331-340 ◽  
Author(s):  
Marcel Baril
Keyword(s):  
Matrix Algebra ◽  
Order Term ◽  
Order Theory ◽  
Second Order ◽  
Energy Dispersive ◽  
Powerful Method ◽  
First Order ◽  
First Order Theory ◽  
Electrostatic Mirror ◽  
Premiere Partie

Combining an energy-dispersive element with a magnetic prism results in an achromatic mass dispersive instrument, if parameters are chosen appropriately. A plane electrostatic mirror has been chosen as the energy-dispersive element. Trajectories are described in terms of lateral, angular, and energy variations about the principal trajectory. Achromatism and conjugate plane conditions have been calculated by the powerful method of matrix algebra. The first order theory is given in this article (part one), the second order term will be studied in part two which will be published later.

Decidability and undecidability of theories with a predicate for the primes

1993 ◽  
Vol 58 (2) ◽  
pp. 672-687 ◽  
Author(s):  
P. T. Bateman ◽  
C. G. Jockusch ◽  
A. R. Woods
Keyword(s):  
General Result ◽  
Order Theory ◽  
Second Order ◽  
The Other ◽  
Linear Case ◽  
Natural Numbers ◽  
Successor Function ◽  
First Order ◽  
First Order Theory

AbstractIt is shown, assuming the linear case of Schinzel's Hypothesis, that the first-order theory of the structure 〈ω; +, P〉, where P is the set of primes, is undecidable and, in fact, that multiplication of natural numbers is first-order definable in this structure. In the other direction, it is shown, from the same hypothesis, that the monadic second-order theory of 〈ω S, P〉 is decidable, where S is the successor function. The latter result is proved using a general result of A. L. Semënov on decidability of monadic theories, and a proof of Semënov's result is presented.

scholarly journals SECOND ORDER THEORY OF MANOMETER WAVE MEASUREMENT

1982 ◽  
Vol 1 (18) ◽  
pp. 8
Author(s):  
F. Biesel
Keyword(s):  
Gravity Wave ◽  
Wave Theory ◽  
Order Theory ◽  
Second Order ◽  
Order Effects ◽  
Mean Values ◽  
Surface Level ◽  
First Order ◽  
Wave Measurements ◽  
Wave Measurement

The paper refers to pressure gage wave measurements . First order transformation of the pressure spectrum into a surface level spectrum leads to hitherto unexplained discrepancies with prototype simultaneous pressure and level measurements . Use of second order gravity wave theory allows to draw the following conclusions » Second order effects appear to give a reasonable explanation of the observed discrepancies . A complete check would require specially made wave measurements and analyses . Second order corrections do not significantly affect mean values, such as significant height, if the manometer depth is not unduly large.

Phase Contrast Electron Microscopy and Compensation of Aberrations by Fourier image Processing

1970 ◽  
Vol 28 ◽  
pp. 248-249
Author(s):  
Harold P. Erickson ◽  
A. Klug
Keyword(s):  
Phase Contrast ◽  
Spherical Aberration ◽  
Mass Density ◽  
Order Theory ◽  
Two Dimensional ◽  
Fourier Image ◽  
First Order ◽  
First Order Theory ◽  
The Fourier Transform ◽  
Electron Microscope Image

The effects of spherical aberration and defocussing on the electron microscope image are much more simply and directly interpreted in the Fourier transform of the image than in the image itself. In terms of a linear or first order theory of image formation, the two dimensional transform of the image intensity is related to the transform of the projected (two dimensional) mass density of the specimen, by the expression:

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