Fourier Integral Methods of Pattern Analysis

Asymptotic theory is developed for local time density estimation for a general class of functionals of integrated and fractionally integrated time series. The main result provides a convenient basis for developing a limit theory for nonparametric cointegrating regression and nonstationary autoregression. The treatment directly involves local time estimation and the density function of the processes under consideration, providing an alternative approach to the Markov chain and Fourier integral methods that have been used in other recent work on these problems.

Download Full-text

Approximate Solutions for Symmetrically Loaded Thick-Walled Cylinders

Journal of Applied Mechanics ◽

10.1115/1.4009738 ◽

1947 ◽

Vol 14 (4) ◽

pp. A301-A311

Author(s):

C. W. MacGregor ◽

L. F. Coffin

Keyword(s):

Approximate Solution ◽

Exact Solutions ◽

Approximate Solutions ◽

Fourier Integral ◽

Integral Methods ◽

Pressure Distributions ◽

Internal Strains ◽

Walled Cylinder ◽

Simple Approximate Solution ◽

Good Agreement

Abstract Based upon an extension of the theory of a bar on an elastic foundation, a simple approximate solution is given in closed form for the analysis of the stresses and strains in a thick-walled cylinder loaded either internally or externally by an axially symmetrical system of forces. The analysis avoids the tedious computation of stresses inherent in exact solutions of this problem by the Fourier series or Fourier integral methods and is in a form which can easily be used by designers. The approximate solution for both semi-infinite pressure distributions and shorter bands of internal pressure are compared with the mathematically exact solutions and with experiment. Good agreement is found in all cases for external strains, while for internal strains the agreement is good except very close to the discontinuity in pressure. Since it is doubtful in practice that an abrupt discontinuity in pressure is often realized in such cases, the approximate solution may also be useful near this discontinuity. More important, however, is the fact that the effective stresses (based upon the distortion-energy theory of yielding), as determined both by the exact and approximate solutions, are in close agreement.

Download Full-text

Lifting-surface theory for cascade of blades in subsonic shear flow

Journal of Fluid Mechanics ◽

10.1017/s0022112069001960 ◽

1969 ◽

Vol 36 (4) ◽

pp. 735-757 ◽

Cited By ~ 2

Author(s):

Masanobu Namba

Keyword(s):

Mach Number ◽

Shear Flow ◽

Flow Theory ◽

Fourier Integral ◽

Uniform Flow ◽

Surface Theory ◽

Integral Methods ◽

Singularity Method ◽

Lifting Surface ◽

Significant Difference

A lifting-surface theory is presented for a cascade in subsonic shear flow by applying Fourier integral methods to the expressions of the perturbed flow field. The pressure distribution on the blade surface is determined by means of the socalled singularity method. Some numerical examples are presented and discussed in comparison with the results according to the lifting-line theory.A significant difference is found in the effect of compressibility between a shear flow and a uniform flow. In shear flows with the maximum Mach number close to one, no such great local lift force is found near the sonic station as would be predicted by the linearized subsonic uniform flow theory. The correlation between the local lift and the local effective angle of attack at high Mach number span-stations shows a great deviation from that according to the uniform flow theory.

Download Full-text

Eigenfunctions of plane elastostatics I. The strip

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1964.0029 ◽

1964 ◽

Vol 277 (1370) ◽

pp. 385-400 ◽

Cited By ~ 22

Keyword(s):

Fourier Transforms ◽

Fourier Integral ◽

Infinite Strip ◽

Eigenfunction Expansions ◽

Closed Solution ◽

Integral Methods ◽

Beam Bending ◽

Differential Difference Equation ◽

Plane Elastostatics ◽

Continuation Technique

By the use of an analytic continuation technique, the problem of the strip in plane elastostatics is reduced to the solution of a differential-difference equation by Fourier transforms. The resulting integrals are evaluated by residue theory to give eigenfunction expansions. Previous workers have used either Fourier integral methods, or eigenfunction expansions, and it is shown how these two distinct approaches can be unified in a single theory. The completeness of the eigenfunction expansions is established and it is shown how the singularities at the origin of the integrands of the Fourier integrals give rise to polynomial solutions, corresponding to the eigenvalues zero. These polynomials represent the classical beam bending and stretching theories, while the other terms in the eigenfunction expansions illustrate St Venant’s principle for the strip. Particular examples of isolated loads on the boundaries are used to illustrate the theory. In the latter part of the paper, the problem of the semi-infinite strip is discussed. A closed solution is obtained for the particular case of plate flexture in which the short edge is simply supported and the two long edges are clamped. A closed solution in the general case having not yet been found, a technique for obtaining a good approximate solution is suggested.

Download Full-text

Automated Image Analysis Of Nuclear And Cytoplasmic Changes In Exfoliated Cells From Tracheas Treated With Carcinogen

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100078638 ◽

1977 ◽

Vol 35 ◽

pp. 220-221

Author(s):

S.F. Stinson ◽

J.C. Lilga ◽

M.B. Sporn

Keyword(s):

Image Analysis ◽

Pattern Analysis ◽

Relative Proportion ◽

Automated Image Analysis ◽

Image Analyzer ◽

Cross Sectional ◽

Exfoliated Cells ◽

Neoplastic Lesions ◽

Analysis System ◽

Morphologic Criterion

Increased nuclear size, resulting in an increase in the relative proportion of nuclear to cytoplasmic sizes, is an important morphologic criterion for the evaluation of neoplastic and pre-neoplastic cells. This paper describes investigations into the suitability of automated image analysis for quantitating changes in nuclear and cytoplasmic cross-sectional areas in exfoliated cells from tracheas treated with carcinogen.Neoplastic and pre-neoplastic lesions were induced in the tracheas of Syrian hamsters with the carcinogen N-methyl-N-nitrosourea. Cytology samples were collected intra-tracheally with a specially designed catheter (1) and stained by a modified Papanicolaou technique. Three cytology specimens were selected from animals with normal tracheas, 3 from animals with dysplastic changes, and 3 from animals with epidermoid carcinoma. One hundred randomly selected cells on each slide were analyzed with a Bausch and Lomb Pattern Analysis System automated image analyzer.

Download Full-text

An Interactive Minicomputer Program for the Indexing and Simulation of Electron Diffraction Patterns

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100092670 ◽

1976 ◽

Vol 34 ◽

pp. 542-543

Author(s):

R.P. Goehner ◽

W.T. Hatfield ◽

Prakash Rao

Keyword(s):

Electron Diffraction ◽

Real Time ◽

Pattern Analysis ◽

Flow Diagram ◽

Hard Copy ◽

Time Analysis ◽

Real Time Analysis ◽

Transmission Electron ◽

One Step ◽

Diffraction Patterns

Computer programs are now available in various laboratories for the indexing and simulation of transmission electron diffraction patterns. Although these programs address themselves to the solution of various aspects of the indexing and simulation process, the ultimate goal is to perform real time diffraction pattern analysis directly off of the imaging screen of the transmission electron microscope. The program to be described in this paper represents one step prior to real time analysis. It involves the combination of two programs, described in an earlier paper(l), into a single program for use on an interactive basis with a minicomputer. In our case, the minicomputer is an INTERDATA 70 equipped with a Tektronix 4010-1 graphical display terminal and hard copy unit.A simplified flow diagram of the combined program, written in Fortran IV, is shown in Figure 1. It consists of two programs INDEX and TEDP which index and simulate electron diffraction patterns respectively. The user has the option of choosing either the indexing or simulating aspects of the combined program.

Download Full-text