Stanford University Applied Mathematics and Statistics Laboratory
Overview
Works:  423 works in 575 publications in 1 language and 631 library holdings 

Roles:  Publisher 
Classifications:  HG4028.C4, 332.670182 
Publication Timeline
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Most widely held works about
Stanford University
 Sampling tables for inspection by variables by William Grant Ireson( Book )
 Academic computing collection by Charles Babbage Institute( )
 Academic computing collection by Charles Babbage Institute( )
Most widely held works by
Stanford University
Convexity of domain functionals by
Paul Garabedian(
Book
)
1 edition published in 1953 in English and held by 5 WorldCat member 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 socalled 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 firstorder shifts in terms of Epsilon of the Green's function, Neumann's function, and eigenvalues, 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 3dimensional 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
1 edition published in 1953 in English and held by 5 WorldCat member 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 socalled 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 firstorder shifts in terms of Epsilon of the Green's function, Neumann's function, and eigenvalues, 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 3dimensional 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
Convexity of functionals by transplantation by
George Pólya(
Book
)
1 edition published in 1953 in English and held by 5 WorldCat member 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
1 edition published in 1953 in English and held by 5 WorldCat member 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
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 WorldCat member libraries worldwide
2 editions published in 1959 in English and held by 3 WorldCat member libraries worldwide
Optimal policy for dynamic inventory process with stochastic demands subject to seasonal vartiations by
Stanford University(
Book
)
4 editions published in 1960 in English and held by 3 WorldCat member libraries worldwide
4 editions published in 1960 in English and held by 3 WorldCat member 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 WorldCat member libraries worldwide
2 editions published in 1956 in English and held by 3 WorldCat member libraries worldwide
Connections and conformal mapping by
Menahem Schiffer(
Book
)
1 edition published in 1961 in English and held by 3 WorldCat member 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
1 edition published in 1961 in English and held by 3 WorldCat member 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
Notes on Fourier analysis and spectral windows by
Emanuel Parzen(
Book
)
3 editions published in 1963 in English and held by 3 WorldCat member 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
3 editions published in 1963 in English and held by 3 WorldCat member 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
On the economic welfare function by
Kenʼichi Inada(
Book
)
1 edition published in 1961 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1961 in English and held by 3 WorldCat member libraries worldwide
Sampling plans for inspection by variables by
Gerald J Lieberman(
Book
)
2 editions published in 1954 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1954 in English and held by 3 WorldCat member libraries worldwide
Optimal inventory depletion by
Peter W Zehna(
Book
)
2 editions published in 1959 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1959 in English and held by 2 WorldCat member libraries worldwide
The evaluation of risky interrelated investments by
Frederick S Hillier(
Book
)
3 editions published in 1969 in English and held by 2 WorldCat member libraries worldwide
A study was made of the problem of evaluating a set of risky interrelated investments. Choosing present value and expected utility of present value as criteria, exact and approximate procedures were developed for selecting the optimal combination of investments under various sets of assumptions. Necessary conditions for optimality were derived and a model for describing a proposed set of investments was developed. This model would be used for determining the mean, variance, and possibly the functional form of the probability distribution of present value. The question of when this distribution would be normal or approximately normal was extensively explored. Several models were developed for finding expected utility. Given these results, the problem can be solved by selecting the combination of investments which maximizes expected utility from among the feasible combinations for which the necessary conditions for optimality hold. The problem was also studied in a broader dynamic context. This study led to the formulation of a changeconstrained mathematical programming model. (Author)
3 editions published in 1969 in English and held by 2 WorldCat member libraries worldwide
A study was made of the problem of evaluating a set of risky interrelated investments. Choosing present value and expected utility of present value as criteria, exact and approximate procedures were developed for selecting the optimal combination of investments under various sets of assumptions. Necessary conditions for optimality were derived and a model for describing a proposed set of investments was developed. This model would be used for determining the mean, variance, and possibly the functional form of the probability distribution of present value. The question of when this distribution would be normal or approximately normal was extensively explored. Several models were developed for finding expected utility. Given these results, the problem can be solved by selecting the combination of investments which maximizes expected utility from among the feasible combinations for which the necessary conditions for optimality hold. The problem was also studied in a broader dynamic context. This study led to the formulation of a changeconstrained mathematical programming model. (Author)
Sampling tables for inspection by variables by
William Grant Ireson(
Book
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member 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 WorldCat member 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 SN curves. A probabilistic model for the life before fatigue failure of a structure is developed. (Author)
2 editions published in 1959 in English and held by 2 WorldCat member 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 SN curves. A probabilistic model for the life before fatigue failure of a structure is developed. (Author)
On a pseudosolution to a scheduling problem by
Stanford University(
Book
)
2 editions published in 1962 in English and held by 2 WorldCat member libraries worldwide
The scheduling problem considered is relatively simple. All the operations were considered as equally important, and it was assumed that each of the operations could be performed at any time uninterruptedly. In reality, most of the scheduling problems are more complicated. Some operations often require priority over other operations in the sense that they are more profitABLE OR A HIGHER UTILITY WEIGHT IS ATTACHED TO THEM. In these cases, the scheduling problem might be more complicated, since there are more restrictions in the case of priorities, and more freedom of choice in the case of discontinuous operations. Yet, no way of finding a general optimal solution, which is short of complete enumeration, was established. Pseudosolutions, based on an extra assumption concerning the dependence structure among the earliest starting points of operations, were derived by the method of dynamic programming. (Author)
2 editions published in 1962 in English and held by 2 WorldCat member libraries worldwide
The scheduling problem considered is relatively simple. All the operations were considered as equally important, and it was assumed that each of the operations could be performed at any time uninterruptedly. In reality, most of the scheduling problems are more complicated. Some operations often require priority over other operations in the sense that they are more profitABLE OR A HIGHER UTILITY WEIGHT IS ATTACHED TO THEM. In these cases, the scheduling problem might be more complicated, since there are more restrictions in the case of priorities, and more freedom of choice in the case of discontinuous operations. Yet, no way of finding a general optimal solution, which is short of complete enumeration, was established. Pseudosolutions, based on an extra assumption concerning the dependence structure among the earliest starting points of operations, were derived by the method of dynamic programming. (Author)
An improved criterion for tightened inspection under the double sampling plans of MilStd105B by Barnard Elliot Smith(
Book
)
2 editions published in 1960 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1960 in English and held by 2 WorldCat member libraries worldwide
Cycling by
Stanford University(
Book
)
2 editions published in 1956 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1956 in English and held by 2 WorldCat member libraries worldwide
The sequential design of experiments for infinitely many states of nature by
Stanford University(
Book
)
3 editions published in 1959 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1959 in English and held by 2 WorldCat member libraries worldwide
Foundations of statistical learning theory. II: The stimulus sampling model by
William K Estes(
Book
)
in English and held by 2 WorldCat member libraries worldwide
in English and held by 2 WorldCat member libraries worldwide
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Related Identities
 United States Office of Naval Research
 National Science Foundation (U.S.)
 Stanford University Department of Statistics
 Parzen, Emanuel 19292016 Author
 Stanford University Department of Operations Research
 Karlin, S. Author
 United States Office of Ordnance Research
 Suppes, P. Author
 Olkin, Ingram Author
 Hillier, Frederick S. Author
Associated Subjects
Acceptance sampling Capital investmentsMathematical models CarnegieMellon University Case Institute of Technology Case Institute of Technology.Systems Research Center Computation laboratories Conformal mapping Connections (Mathematics) Cornell Aeronautical Laboratory Cornell University Differential equations, Partial Experimental design Fourier analysis Functional analysis Functions Harvard University.Computation Laboratory InventoriesMathematical models InvestmentsMathematics Learning, Psychology ofMathematical models MaterialsFatigueMathematical models Mathematical models New York University Ohio State University Pennsylvania State University Poisson distribution Probabilities Project MAC (Massachusetts Institute of Technology) Quality controlStatistical methods Risk Sampling (Statistics) Spectral theory (Mathematics) Stanford University Stanford University.Applied Mathematics and Statistics Laboratory Stanford University.Computer Science Department State University of New York Structural engineering Structural failures Timeseries analysis University of California, Berkeley University of California, Los Angeles University of California, Los Angeles.Department of Engineering University of California, Los Angeles.Health Sciences Computing Facility University of Hawaii (Honolulu) University of Illinois (UrbanaChampaign campus).Digital Computer Laboratory University of Minnesota University of Pennsylvania Variables (Mathematics) Wayne State University Welfare economicsMathematical models Whirlwind computer
Alternative Names
Applied Mathematics & Statistics Laboratory.
Applied Mathematics and Statistics Laboratories
Applied Mathematics and Statistics Laboratory
Behavioral Sciences Division. Applied Mathematics and Statistics Laboratory.
Stanford University Applied Mathematics and Statistics Laboratories
Stanford University. Behavioral Sciences Division. Applied Mathematics and Statistics Laboratory.
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