First‐Order Theory of Electrical Focusing in Cyclotron‐Type Two‐Dimensional Lenses with Static and Time‐Varying Potentials

1971 ◽  
Vol 42 (11) ◽  
pp. 4128-4138 ◽  
Author(s):  
Martin Reiser
Keyword(s):  
Order Theory ◽  
Time Varying ◽  
Two Dimensional ◽  
First Order ◽  
First Order Theory

A first order theory for Newtonian flow over two-dimensional airfoils

1987 ◽  
Vol 91 (910) ◽  
pp. 471-478 ◽  
Author(s):  
Hamdi T. Hemdan
Keyword(s):  
Order Theory ◽  
Two Dimensional ◽  
Small Disturbance ◽  
Newtonian Flow ◽  
Approximate Methods ◽  
First Order ◽  
Specific Heats ◽  
First Order Theory ◽  
Free Stream Mach Number ◽  
Recent Formulation

Summary A simple closed-form formula for the coefficient of surface pressure, Cp is given in this paper. The formula is based on first and second approximations of the full problem and can be used for the Newtonian flow past two-dimensional thin airfoils at small angles of attack and with attached shock waves. It thus extends Cole's zero order theory to the effects of non-zero (γ – 1) and finite values of Mx where γ is the ratio of the specific heats of the gas and Mx is the free stream Mach number. The analysis presented relies on a previous recent formulation of the hypersonic small disturbance theory which has proved to be more advantageous than the hypersonic small disturbance theory. The results are compared with other approximate methods and the agreement is found to be generally good.

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:

Compressible Subsonic Flow in Two-dimensional Channels

1955 ◽  
Vol 6 (4) ◽  
pp. 254-276 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Circular Cylinder ◽  
Subsonic Flow ◽  
Constant Pressure ◽  
Order Theory ◽  
Standard Theory ◽  
Two Dimensional ◽  
First Order ◽  
First Order Theory

SummaryThe theory developed in Part I is applied to a number of problems of aeronautical interest, the most important of which is to the setting of “ streamline “ walls about a symmetrical aerofoil placed in the centre of a channel. It is shown how the position of the streamline wall can be deduced from the (experimentally determined) position of a constant pressure wall. This theory is applicable to symmetrical aerofoils of any given shape, and makes allowance for the presence of the aerofoil's wake. To illustrate the theory, and to test it by an extreme example, the flow is calculated about a circular cylinder, with a diameter about half the tunnel height, for both straight and constant pressure walls. The solid blockage is calculated in each case and compared with the standard first order theory. For this extreme example the standard theory fails badly for straight walls, but is reasonably accurate for constant pressure walls.

scholarly journals A first-order theory of Ulm type

Computability ◽  
2019 ◽  
Vol 8 (3-4) ◽  
pp. 347-358
Author(s):  
Matthew Harrison-Trainor
Keyword(s):  
Order Theory ◽  
First Order ◽  
First Order Theory

scholarly journals Quasi-decidability of a Fragment of the First-Order Theory of Real Numbers

2015 ◽  
Vol 57 (2) ◽  
pp. 157-185 ◽  
Author(s):  
Peter Franek ◽  
Stefan Ratschan ◽  
Piotr Zgliczynski
Keyword(s):  
Order Theory ◽  
Real Numbers ◽  
First Order ◽  
First Order Theory
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