Technical report by Stanford University

(
serial
)
in
English and Undetermined
and held by
18
libraries
worldwide

Technical report
(
serial
)
in
English
and held by
9
libraries
worldwide

Convexity of functionals by transplantation by George Pólya

(
Book
)
1
edition published
in
1953
in
English
and held by
6
libraries
worldwide

The dependence of various functionals on their domain of definition is discussed. The functionals are defined by certain extremum problems. The methods of transplanting extremum functions and of variation are applied to the problem of utilizing the knowledge of the functional for a few special domains to obtain knowledge about the same functional in the general case. Functionals such as torsional rigidity, virtual mass, outer conformal radius, and electrostatic capacity are treated. A discussion is given of a theorem of Poincare which permits an easy simultaneous estimation of the N first eigenvalues of a general type of eigenvalue problem. The convexity of various combinations of eigenvalues is studied for the case in which the domain of definition is deformed by stretching or by conformal transformation. The usefulness of the fact that the initial domain D(1) has symmetry properties is indicated. The invariance of the class of harmonic functions in D under conformal mapping can be used to derive convexity statements for some functionals connected with the Green's function for Laplace's equation. A numerical application is given for the torsional rigidity of isosceles triangles and rectangles

Convexity of domain functionals by Paul Garabedian

(
Book
)
1
edition published
in
1953
in
English
and held by
5
libraries
worldwide

A rigorous theory is developed for variation of domain functions in a space of 3 dimensions as well as in the plane. The classical Hadamard variational formulas in space are discussed, and the so-called interior variational method is generalized to 3 dimensions. Interior variations of a 3- dimensional domain D are defined by means of differential mappings of D which depend on a small parameter Epsilon. The first-order shifts in terms of Epsilon of the Green's function, Neumann's function, and eigen-values, which result from this variation of D, are calculated rigorously by referring all varied quantities back to the original D through the infinitesimal mappings. Since proof is possible that the varied domain functions can be expanded in powers of Epsilon, the perturbation method is employed to calculate the second variations of these functions. Second variation expressions are obtained for the capacity, virtual mass, and eigenvalues corresponding to various particular ways in which D can be shifted. The variational theory is specialized to the case of 2 independent variables to show the existence of vortex sheets in axially symmetric, irrotational flow of an incompressible fluid. An external characterization of vortex sheets in 3-dimensional space without symmetry of any kind is sketched heuristically. In a study of the eigen functions and eigenvalues of the vibrating membrane, the second variation is used to show that under certain conformal mappings of a domain, which depend on a suitable parameter, the inverse square of the principal frequency of the domain becomes a convex function of the parameter

Sampling plans for inspection by variables by Gerald J Lieberman

(
Book
)
2
editions published
in
1954
in
English
and held by
3
libraries
worldwide

Notes on Fourier analysis and spectral windows by Emanuel Parzen

(
Book
)
3
editions published
in
1963
in
English
and held by
3
libraries
worldwide

A systematic development of some basic ideas about Fourier analysis and spectral windows is presented in order to have a convenient reference for results to be used in other work on statistical spectral analysis

Connections and conformal mapping by M Schiffer

(
Book
)
1
edition published
in
1961
in
English
and held by
3
libraries
worldwide

Contents: The integral equation for circular mapping Variational theory for moduli Connections on plane domains Variational theory for connections Connections on closed Riemann surfaces Variation of connections on Riemann surfaces

On the economic welfare function by Kenʼichi Inada

(
Book
)
1
edition published
in
1961
in
English
and held by
3
libraries
worldwide

Statistical inference on time series by Hilbert space methods, I by Emanuel Parzen

(
Book
)
2
editions published
in
1959
in
English
and held by
3
libraries
worldwide

Tables for estimating a proportion or a Poisson mean with prescribed precision by Allan Birnbaum

(
Book
)
2
editions published
in
1956
in
English
and held by
3
libraries
worldwide

Technical report
(
serial
)
in
English
and held by
3
libraries
worldwide

Continuous sampling procedures without control by Cyrus Derman

(
Book
)
3
editions published
in
1958
in
English
and held by
2
libraries
worldwide

Cycling by Stanford University

(
Book
)
2
editions published
in
1956
in
English
and held by
2
libraries
worldwide

Optimal inventory depletion by Peter W Zehna

(
Book
)
2
editions published
in
1959
in
English
and held by
2
libraries
worldwide

An improved criterion for tightened inspection under the double sampling plans of Mil-Std-105B by Barnard Elliot Smith

(
Book
)
2
editions published
in
1960
in
English
and held by
2
libraries
worldwide

On models for the probability of fatique failure of a structure by Emanuel Parzen

(
Book
)
2
editions published
in
1959
in
English
and held by
2
libraries
worldwide

The paper represents an attempt by a person trained in probability theory to survey some of the problems involved in evaluating structural safety. A review is presented of the probabilistic considerations involved in evaluating the strength of materials, and the construction of so called S-N curves. A probabilistic model for the life before fatigue failure of a structure is developed. (Author)

A new two-sided acceptance region for sampling by variables by Stanford University

(
Book
)
3
editions published
in
1952
in
English
and held by
1
library
worldwide

Sequential design of experiments by Stanford University

(
Book
)
3
editions published
in
1958
in
English
and held by
1
library
worldwide