Wing, G. Milton (George Milton) 1923
Overview
Works:  42 works in 128 publications in 1 language and 1,835 library holdings 

Genres:  Conference papers and proceedings Festschriften Academic theses 
Roles:  Author, Contributor, Honoree 
Classifications:  QA431, 515 
Publication Timeline
.
Most widely held works about
G. Milton Wing
 The General and his boys by G. Milton Wing( Book )
 Wing, George Milton : applied mathematics( )
Most widely held works by
G. Milton Wing
An introduction to invariant imbedding by
Richard Bellman(
Book
)
30 editions published between 1970 and 1992 in English and held by 614 WorldCat member libraries worldwide
Here is a book that provides the classical foundations of invariant imbedding, a concept that provided the first indication of the connection between transport theory and the Riccati Equation. The reprinting of this classic volume was prompted by a revival of interest in the subject area because of its uses for inverse problems. The major part of the book consists of applications of the invariant imbedding method to specific areas that are of interest to engineers, physicists, applied mathematicians, and numerical analysts. A large set of problems can be found at the end of each chapter. Numerous problems on apparently disparate matters such as Riccati equations, continued fractions, functional equations, and Laplace transforms are included. The exercises present the reader with "reallife" situations. The material is accessible to a general audience, however, the authors do not hesitate to state, and even to prove, a rigorous theorem when one is available. To keep the original flavor of the book, very few changes were made to the manuscript; typographical errors were corrected and slight changes in word order were made to reduce ambiguities
30 editions published between 1970 and 1992 in English and held by 614 WorldCat member libraries worldwide
Here is a book that provides the classical foundations of invariant imbedding, a concept that provided the first indication of the connection between transport theory and the Riccati Equation. The reprinting of this classic volume was prompted by a revival of interest in the subject area because of its uses for inverse problems. The major part of the book consists of applications of the invariant imbedding method to specific areas that are of interest to engineers, physicists, applied mathematicians, and numerical analysts. A large set of problems can be found at the end of each chapter. Numerous problems on apparently disparate matters such as Riccati equations, continued fractions, functional equations, and Laplace transforms are included. The exercises present the reader with "reallife" situations. The material is accessible to a general audience, however, the authors do not hesitate to state, and even to prove, a rigorous theorem when one is available. To keep the original flavor of the book, very few changes were made to the manuscript; typographical errors were corrected and slight changes in word order were made to reduce ambiguities
An introduction to transport theory by
G. Milton Wing(
Book
)
16 editions published in 1962 in English and Undetermined and held by 437 WorldCat member libraries worldwide
16 editions published in 1962 in English and Undetermined and held by 437 WorldCat member libraries worldwide
A primer on integral equations of the first kind : the problem of deconvolution and unfolding by
G. Milton Wing(
Book
)
18 editions published in 1991 in English and held by 280 WorldCat member libraries worldwide
Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, and other scientists an elementary level explanation of integral equations of the first kind. It maintains a casual, conversational approach. The book emphasizes understanding, while deliberately avoiding special methods of highly limited application. Special features: all problems illustrate important topics covered in the text; the subject is explained using a fairly nonrigorous approach to introduce any mathematics not commonly understood by the intended audience; designed for selfstudy, but can also be used as a text
18 editions published in 1991 in English and held by 280 WorldCat member libraries worldwide
Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, and other scientists an elementary level explanation of integral equations of the first kind. It maintains a casual, conversational approach. The book emphasizes understanding, while deliberately avoiding special methods of highly limited application. Special features: all problems illustrate important topics covered in the text; the subject is explained using a fairly nonrigorous approach to introduce any mathematics not commonly understood by the intended audience; designed for selfstudy, but can also be used as a text
Transport theory, invariant imbedding, and integral equations : proceedings in honor of G.M. Wing's 65th birthday by
P Nelson(
Book
)
8 editions published in 1989 in English and held by 188 WorldCat member libraries worldwide
8 editions published in 1989 in English and held by 188 WorldCat member libraries worldwide
Problems for a computeroriented calculus course, with an appendix on elementary FORTRAN programming by
Richard C Allen(
Book
)
9 editions published in 1973 in English and held by 168 WorldCat member libraries worldwide
9 editions published in 1973 in English and held by 168 WorldCat member libraries worldwide
The method of invariant imbedding with applications to transport theory and other areas of mathematical physics by
G. Milton Wing(
Book
)
3 editions published in 1965 in English and held by 32 WorldCat member libraries worldwide
3 editions published in 1965 in English and held by 32 WorldCat member libraries worldwide
Transport theory and spectral problems by
G. Milton Wing(
)
2 editions published in 1959 in English and held by 26 WorldCat member libraries worldwide
A simple model of timeindependent neutron transport on a line as a stochastic process, using the method of invariant imbedding, is considered. Non linear equations for the expected values (flux) are also obtained and solved, the results are compared with the ordinary linear theory, and possible advantages of the new formulation are cited. Generalizations to a large class of transport problems are discussed. The nonlinear timedependent operator for transport in one dimension is considered in detail. It has a pure point spectrum, and expansion theorems can be proved. These results contrast with those for isotropic onevelocity neutron transport in the infinite slab. Here there are only a finite number of points in the point spectrum, with a halfplane in the continuous spectrum. Approximations to the eigenvalues and eigenfunctions for the slab case, as well as extensions to the multivelocity problem, are mentioned. There is a brief discussion of recent spectral and expansion theorems for very general geometries. (auth)
2 editions published in 1959 in English and held by 26 WorldCat member libraries worldwide
A simple model of timeindependent neutron transport on a line as a stochastic process, using the method of invariant imbedding, is considered. Non linear equations for the expected values (flux) are also obtained and solved, the results are compared with the ordinary linear theory, and possible advantages of the new formulation are cited. Generalizations to a large class of transport problems are discussed. The nonlinear timedependent operator for transport in one dimension is considered in detail. It has a pure point spectrum, and expansion theorems can be proved. These results contrast with those for isotropic onevelocity neutron transport in the infinite slab. Here there are only a finite number of points in the point spectrum, with a halfplane in the continuous spectrum. Approximations to the eigenvalues and eigenfunctions for the slab case, as well as extensions to the multivelocity problem, are mentioned. There is a brief discussion of recent spectral and expansion theorems for very general geometries. (auth)
On Riccati and Riccatilike equations arising in onedimensional diffusion problems by I. I Kolodner(
)
2 editions published in 1962 in English and held by 20 WorldCat member libraries worldwide
2 editions published in 1962 in English and held by 20 WorldCat member libraries worldwide
On a method for obtaining bounds on the eigenvalues of certain integral equations by
G. Milton Wing(
)
2 editions published in 1965 in English and held by 14 WorldCat member libraries worldwide
2 editions published in 1965 in English and held by 14 WorldCat member libraries worldwide
A note on the numerical integration of a class of nonlinear hyperbolic differential equations by
Richard Bellman(
Book
)
2 editions published in 1957 in English and held by 6 WorldCat member libraries worldwide
The purpose of this paper was to introduce a new method for the numerical integration of a class of nonlinear hyperbolic partial differential equations which admit shocks. The equation u sub t = uu sub x is discussed, and numerical results are given. (Author)
2 editions published in 1957 in English and held by 6 WorldCat member libraries worldwide
The purpose of this paper was to introduce a new method for the numerical integration of a class of nonlinear hyperbolic partial differential equations which admit shocks. The equation u sub t = uu sub x is discussed, and numerical results are given. (Author)
A primer on integral equations of the first kind by
G. Milton Wing(
Book
)
2 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1991 in English and held by 5 WorldCat member libraries worldwide
Transport theory, invariant imbedding, and integral equations : Conference : Revised papers(
Book
)
1 edition published in 1989 in English and held by 3 WorldCat member libraries worldwide
1 edition published in 1989 in English and held by 3 WorldCat member libraries worldwide
The mean convergence of orthogonal series by
G. Milton Wing(
)
2 editions published in 1949 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1949 in English and held by 3 WorldCat member libraries worldwide
Syllabus for a course on the theory of particle transport by
G. Milton Wing(
Book
)
1 edition published in 1961 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1961 in English and held by 2 WorldCat member libraries worldwide
An introduction to invariant imbedding [by] R. Bellman [and] G.M. Wing by
Richard Bellman(
Book
)
1 edition published in 1975 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1975 in English and held by 2 WorldCat member libraries worldwide
Invariant imbedding and the calculation of eigenvalues for SturmLiouville systems by M. R Scott(
)
1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1969 in English and held by 2 WorldCat member libraries worldwide
Invariant imbedding and neutron transport theory  a generalized approach by
Richard Bellman(
Book
)
2 editions published in 1958 in English and held by 2 WorldCat member libraries worldwide
In previous papers the theory of invariant imbedding has been applied to a variety of transport problems. Each problem has been treated individually and any change in the geometry of the medium or energy distribution of the neutrons has called for a new investigation. A general method is presented for dealing with many such cases. A single formula is developed which covers most of the problems considered in past work and leads to new results. A few specializations are indicated. (Author)
2 editions published in 1958 in English and held by 2 WorldCat member libraries worldwide
In previous papers the theory of invariant imbedding has been applied to a variety of transport problems. Each problem has been treated individually and any change in the geometry of the medium or energy distribution of the neutrons has called for a new investigation. A general method is presented for dealing with many such cases. A single formula is developed which covers most of the problems considered in past work and leads to new results. A few specializations are indicated. (Author)
Transport problems in media with periodic structure by Richard C Allen(
Book
)
2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
The problem of transport of particles in a slab geometry is considered, the unique feature being that the slab is assumed to have a periodic structure. It is shown that the particle density at any point in the slab can be obtained numerically by integrating a set of differential equations of initial value type over one period, followed by the use of certain relatively easy difference and functional equations. There are strong indications that considerable advantage is gained in time, accuracy, stability, etc. over the standard method of handling such problems. Several rather simple numerical examples are given. Agreement with results obtained in other ways is excellent. It is noted that the algorithm produced is really applicable to a wide class of twopoint boundary value problems having little or nothing to do with transport theory per se. (Author)
2 editions published in 1971 in English and held by 2 WorldCat member libraries worldwide
The problem of transport of particles in a slab geometry is considered, the unique feature being that the slab is assumed to have a periodic structure. It is shown that the particle density at any point in the slab can be obtained numerically by integrating a set of differential equations of initial value type over one period, followed by the use of certain relatively easy difference and functional equations. There are strong indications that considerable advantage is gained in time, accuracy, stability, etc. over the standard method of handling such problems. Several rather simple numerical examples are given. Agreement with results obtained in other ways is excellent. It is noted that the algorithm produced is really applicable to a wide class of twopoint boundary value problems having little or nothing to do with transport theory per se. (Author)
Invariant imbedding and mathematical physics(
Book
)
1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
Dissipation functions and invariant imbedding, i(
Book
)
1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
In a series of papers dating from 1956, the authors have used the theory of invariant imbedding to derive a variety of nonlinear functional equations for the description of radiative transfer, neutron transport, diffusion and heat conduction, scattering and random walk, and wave propagation. In this paper a new method is presented for establishing the existence of solutions of these equations in the cases where no creation of matter is involved. This method is based upon the introduction of a new class of physically important functions, the dissipation functions. Combining these new functiwions with the functions utilized in the past, the reflection and transmission functions, we easily obtain a basic conservation relation upon which all else hinges. The uniqueness proofs follow conventional lines. (Author)
1 edition published in 1960 in English and held by 1 WorldCat member library worldwide
In a series of papers dating from 1956, the authors have used the theory of invariant imbedding to derive a variety of nonlinear functional equations for the description of radiative transfer, neutron transport, diffusion and heat conduction, scattering and random walk, and wave propagation. In this paper a new method is presented for establishing the existence of solutions of these equations in the cases where no creation of matter is involved. This method is based upon the introduction of a new class of physically important functions, the dissipation functions. Combining these new functiwions with the functions utilized in the past, the reflection and transmission functions, we easily obtain a basic conservation relation upon which all else hinges. The uniqueness proofs follow conventional lines. (Author)
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Algorithms CalculusData processing Canada Differential equations Differential equations, HyperbolicNumerical solutions Differential equations, NonlinearNumerical solutions Eigenvalues FORTRAN (Computer program language) Integral equations Invariant imbedding Mathematical physics Periodic law Prospecting Riccati equationNumerical solutions Scientists Series, Orthogonal Transport theory United States Wing, G. Milton(George Milton),
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Alternative Names
George Milton Wing born:1923 ied:2008 Wing, G. Milton (George Milton), 1923; Wing, George Milton; Wing, George, 19262008;
Wing, G. Milton
Wing, G. M.
Wing, G. M. 1923
Wing, G. M. (George Milton), 1923
Wing, G. Milton.
Wing, George
Wing, George Milton 1923
Wing, Milt 1923
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