Garabedian, Paul
Overview
Works:  42 works in 136 publications in 2 languages and 2,412 library holdings 

Roles:  Author 
Classifications:  QA377, 517.383 
Publication Timeline
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Most widely held works about
Paul Garabedian
 Garabedian, Paul Roesel : applied mathematics( )
 Sonata in F sharp minor for cello and piano by Paul Garabedian( )
 Rotating figures of equilibrium by Paul Garabedian( )
Most widely held works by
Paul Garabedian
Partial differential equations by
Paul Garabedian(
Book
)
33 editions published between 1964 and 2007 in English and Undetermined and held by 1,129 WorldCat member libraries worldwide
This book is intended to fill the gap between the standard introductory material on partial differential equations: separation of variables, the basics of the secondorder equations from mathematical physics and the advanced methods such as Sobolev spaces and fixed point theorems
33 editions published between 1964 and 2007 in English and Undetermined and held by 1,129 WorldCat member libraries worldwide
This book is intended to fill the gap between the standard introductory material on partial differential equations: separation of variables, the basics of the secondorder equations from mathematical physics and the advanced methods such as Sobolev spaces and fixed point theorems
A theory of supercritical wing sections, with computer programs and examples by
Frances Bauer(
Book
)
15 editions published in 1972 in English and German and held by 286 WorldCat member libraries worldwide
15 editions published in 1972 in English and German and held by 286 WorldCat member libraries worldwide
A computational method in plasma physics by
Frances Bauer(
Book
)
10 editions published in 1978 in English and held by 213 WorldCat member libraries worldwide
In this book, we report on research in methods of computational magneto hydrodynamics supported by the United States Department of Energy under Contract EY76C023077 with New York University. The work has re sulted in a computer code for mathematical analysis of the equilibrium and stability of a plasma in three dimensions with toroidal geometry but no sym metry. The code is listed in the final chapter. Versions of it have been used for the design of experiments at the Los Alamos Scientific Laboratory and the Max Planck Institute for Plasma Physics in Garching. We are grateful to Daniel Barnes, Jeremiah Brackbill, Harold Grad, William Grossmann, Abraham Kadish, Peter Lax, Guthrie Miller, Arnulf Schliiter, and Harold Weitzner for many useful discussions of the theory. We are especially indebted to Franz Herrnegger for theoretical and pedagogical comments. Constance Engle has provided outstanding assistance with the typescript. We take pleasure in acknowledging the help of the staff of the Courant Mathematics and Com puting Laboratory at New York University. In particular we should like to express our thanks to Max Goldstein, Kevin McAuliffe, Terry Moore, Toshi Nagano and Tsun Tam. Frances Bauer New York Octavio Betancourt September 1978 Paul Garabedian v Contents Chapter 1. Introduction 1 1. 1 Formulation of the Problem 1 1. 2 Discussion of Results 2 Chapter 2. The Variational Principle 4 4 2. 1 The Magnetostatic Equations 6 2. 2 Flux Constraints in the Plasma . 7 2. 3 The Ergodic Constraint
10 editions published in 1978 in English and held by 213 WorldCat member libraries worldwide
In this book, we report on research in methods of computational magneto hydrodynamics supported by the United States Department of Energy under Contract EY76C023077 with New York University. The work has re sulted in a computer code for mathematical analysis of the equilibrium and stability of a plasma in three dimensions with toroidal geometry but no sym metry. The code is listed in the final chapter. Versions of it have been used for the design of experiments at the Los Alamos Scientific Laboratory and the Max Planck Institute for Plasma Physics in Garching. We are grateful to Daniel Barnes, Jeremiah Brackbill, Harold Grad, William Grossmann, Abraham Kadish, Peter Lax, Guthrie Miller, Arnulf Schliiter, and Harold Weitzner for many useful discussions of the theory. We are especially indebted to Franz Herrnegger for theoretical and pedagogical comments. Constance Engle has provided outstanding assistance with the typescript. We take pleasure in acknowledging the help of the staff of the Courant Mathematics and Com puting Laboratory at New York University. In particular we should like to express our thanks to Max Goldstein, Kevin McAuliffe, Terry Moore, Toshi Nagano and Tsun Tam. Frances Bauer New York Octavio Betancourt September 1978 Paul Garabedian v Contents Chapter 1. Introduction 1 1. 1 Formulation of the Problem 1 1. 2 Discussion of Results 2 Chapter 2. The Variational Principle 4 4 2. 1 The Magnetostatic Equations 6 2. 2 Flux Constraints in the Plasma . 7 2. 3 The Ergodic Constraint
Supercritical wing sections III by
Frances Bauer(
Book
)
14 editions published between 1972 and 1977 in 3 languages and held by 187 WorldCat member libraries worldwide
14 editions published between 1972 and 1977 in 3 languages and held by 187 WorldCat member libraries worldwide
Magnetohydrodynamic equilibrium and stability of stellarators by
Frances Bauer(
Book
)
9 editions published in 1984 in English and held by 160 WorldCat member libraries worldwide
In this book, we describe in detail a numerical method to study the equilibrium and stability of a plasma confined by a strong magnetic field in toroidal geometry without twodimensional symmetry. The principal appli cation is to stellarators, which are currently of interest in thermonuclear fusion research. Our mathematical model is based on the partial differential equations of ideal magnetohydrodynamics. The main contribution is a computer code named BETA that is listed in the final chapter. This work is the natural continuation of an investigation that was presented in an early volume of the Springer Series in Computational Physics (cf. [3]). It has been supported over a period of years by the U.S. Department of Energy under Contract DEAC0276ER03077 with New York University. We would like to express our gratitude to Dr. Franz Herrnegger for the assistance he has given us with the preparation of the manuscript. We are especially indebted to Connie Engle for the high quality of the final typescript. New York F. BAUER October 1983 O. BETANCOURT P. GARABEDIAN Contents 1. Introduction 1 2. Synopsis of the Method 3 1. Variational principle 3 2. Coordinate system 6 3. Finite Difference Scheme 8 1. Difference equations ..." 8 2. Island structure ... 10 3. Accelerated iteration procedure ... .. 12 Nonlinear Stability 15 4. 1. Second minimization ... ... . . 15 ... 2. Test functions and convergence studies ... .. . . 17 . 3. Comparison with exact solutions ... 19 5. The Mercier Criterion 22 1. Local mode analysis ... ... . . 22 ... 2. Computational method ... ... . 23
9 editions published in 1984 in English and held by 160 WorldCat member libraries worldwide
In this book, we describe in detail a numerical method to study the equilibrium and stability of a plasma confined by a strong magnetic field in toroidal geometry without twodimensional symmetry. The principal appli cation is to stellarators, which are currently of interest in thermonuclear fusion research. Our mathematical model is based on the partial differential equations of ideal magnetohydrodynamics. The main contribution is a computer code named BETA that is listed in the final chapter. This work is the natural continuation of an investigation that was presented in an early volume of the Springer Series in Computational Physics (cf. [3]). It has been supported over a period of years by the U.S. Department of Energy under Contract DEAC0276ER03077 with New York University. We would like to express our gratitude to Dr. Franz Herrnegger for the assistance he has given us with the preparation of the manuscript. We are especially indebted to Connie Engle for the high quality of the final typescript. New York F. BAUER October 1983 O. BETANCOURT P. GARABEDIAN Contents 1. Introduction 1 2. Synopsis of the Method 3 1. Variational principle 3 2. Coordinate system 6 3. Finite Difference Scheme 8 1. Difference equations ..." 8 2. Island structure ... 10 3. Accelerated iteration procedure ... .. 12 Nonlinear Stability 15 4. 1. Second minimization ... ... . . 15 ... 2. Test functions and convergence studies ... .. . . 17 . 3. Comparison with exact solutions ... 19 5. The Mercier Criterion 22 1. Local mode analysis ... ... . . 22 ... 2. Computational method ... ... . 23
Computational methods for the problems of the tip vortex final technical report by
Paul Garabedian(
Book
)
1 edition published in 1988 in English and held by 71 WorldCat member libraries worldwide
1 edition published in 1988 in English and held by 71 WorldCat member libraries worldwide
The NYU inverse swept wing code by
Frances Bauer(
Book
)
1 edition published in 1983 in English and held by 70 WorldCat member libraries worldwide
1 edition published in 1983 in English and held by 70 WorldCat member libraries worldwide
Papers in mathematics by
Paul Garabedian(
Book
)
2 editions published in 1963 in English and held by 32 WorldCat member libraries worldwide
2 editions published in 1963 in English and held by 32 WorldCat member libraries worldwide
Extremal methods in cavitational flow by
Paul Garabedian(
Book
)
1 edition published in 1951 in English and held by 6 WorldCat member libraries worldwide
1 edition published in 1951 in English and held by 6 WorldCat member libraries worldwide
Convexity of domain functionals by
Paul Garabedian(
Book
)
2 editions published in 1953 in English and held by 6 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
2 editions published in 1953 in English and held by 6 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
A complex tensor calculus for Kähler manifolds by
Paul Garabedian(
Book
)
5 editions published in 1951 in English and held by 5 WorldCat member libraries worldwide
5 editions published in 1951 in English and held by 5 WorldCat member libraries worldwide
On subsonic flow of a compressible fluid by
Paul Garabedian(
Book
)
2 editions published in 1953 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1953 in English and held by 5 WorldCat member libraries worldwide
Axially symmetric cavitational flow by
P. R Garabedian(
Book
)
2 editions published in 1952 in English and held by 5 WorldCat member libraries worldwide
2 editions published in 1952 in English and held by 5 WorldCat member libraries worldwide
On solution of partial differential equations by the HahnBanach theorem by
Paul Garabedian(
Book
)
2 editions published in 1953 in English and held by 4 WorldCat member libraries worldwide
A means of construction is presented for the Green's and Neuman n's functions of a linear ellipitc partial differential equation by a method based on linear functionals. The construction depends essentially on the HahnBanach extension theorem (Theorle des Operations Lineaires, Warsaw, 1932) which was used in a similar connection by Lax (Proc. Amer. Math. Soc. 3:526531, 1952). Lax's approach differs in that, while his proof centers about a bounded linear functional based on inhomogeneous boundary conditions, this proof centers about a functional based on the solution of an inhomogeneous differential equation. This latter point of view has the advantage that in constructing the Green's and Neumann's functions only a fundamental solution of the differential equation is needed in specific instances, and success is possible with merely a parametrix. These considerations are also advantageous for domains with general boundaries and for Riemannian manifolds. The proof of the HahnBanach theorem in the form used does not require transfinite induction, since the Banach space of continous functions is separable
2 editions published in 1953 in English and held by 4 WorldCat member libraries worldwide
A means of construction is presented for the Green's and Neuman n's functions of a linear ellipitc partial differential equation by a method based on linear functionals. The construction depends essentially on the HahnBanach extension theorem (Theorle des Operations Lineaires, Warsaw, 1932) which was used in a similar connection by Lax (Proc. Amer. Math. Soc. 3:526531, 1952). Lax's approach differs in that, while his proof centers about a bounded linear functional based on inhomogeneous boundary conditions, this proof centers about a functional based on the solution of an inhomogeneous differential equation. This latter point of view has the advantage that in constructing the Green's and Neumann's functions only a fundamental solution of the differential equation is needed in specific instances, and success is possible with merely a parametrix. These considerations are also advantageous for domains with general boundaries and for Riemannian manifolds. The proof of the HahnBanach theorem in the form used does not require transfinite induction, since the Banach space of continous functions is separable
The onequarter theorem for mean univalent functions by
Paul Garabedian(
Book
)
2 editions published in 1953 in English and held by 3 WorldCat member libraries worldwide
The class of mapping functions of Spencer (Ann. Math. 42:61463 2, 1941) (i) w  f(z) = z sub p + a sub p+1 z p+1 + sub a sub p+2 sub z p+2 ..., regular in the unit circle (z) <1, is considered which transform the unit circle into a Riemann surface R over the wplane so that, for each r> 0, the area of the sheets of R covering the circle (w) <r does not exceed p pi r squared. These functions are called mean pvalent, and mean univalent when p = 1. The analytic functions w = f(z) are considered of the form (i) in the unit circle, with p = 1, which map the unit circle onto a Riemann surface R over the wplane satisfying the condition integral from r to 0 (integral alpha phi  2 pi) 1/p dp <or equal to 0 for each r>), where the integration with respect to phi is extended over all sheets of R covering the circle (w) = pho. For this class of weakly mean univalent functions, any omitted value d is shown to satisfy the sharp inequality (ii) (d)> or = 1/4, where d is any value which f(z) does not assume in the unit circle. The first part of the proof of (ii) is based on the work of Hayman (J. d'Analyse Mathematique 1:155179, 1951) who gave elegant sharp estimates for the distortion of pvalent mappings by using the concept of circular symmetrization due to Polya (Compt. rend. 230:2527, 1950). The later part of the proof depends on the polygonal Hadamard variations of Garabedian and Royden (Proc. Nat. Acad. Sci. 38:5761, 1952) and closes with an inequality from the theory of free streamline flows
2 editions published in 1953 in English and held by 3 WorldCat member libraries worldwide
The class of mapping functions of Spencer (Ann. Math. 42:61463 2, 1941) (i) w  f(z) = z sub p + a sub p+1 z p+1 + sub a sub p+2 sub z p+2 ..., regular in the unit circle (z) <1, is considered which transform the unit circle into a Riemann surface R over the wplane so that, for each r> 0, the area of the sheets of R covering the circle (w) <r does not exceed p pi r squared. These functions are called mean pvalent, and mean univalent when p = 1. The analytic functions w = f(z) are considered of the form (i) in the unit circle, with p = 1, which map the unit circle onto a Riemann surface R over the wplane satisfying the condition integral from r to 0 (integral alpha phi  2 pi) 1/p dp <or equal to 0 for each r>), where the integration with respect to phi is extended over all sheets of R covering the circle (w) = pho. For this class of weakly mean univalent functions, any omitted value d is shown to satisfy the sharp inequality (ii) (d)> or = 1/4, where d is any value which f(z) does not assume in the unit circle. The first part of the proof of (ii) is based on the work of Hayman (J. d'Analyse Mathematique 1:155179, 1951) who gave elegant sharp estimates for the distortion of pvalent mappings by using the concept of circular symmetrization due to Polya (Compt. rend. 230:2527, 1950). The later part of the proof depends on the polygonal Hadamard variations of Garabedian and Royden (Proc. Nat. Acad. Sci. 38:5761, 1952) and closes with an inequality from the theory of free streamline flows
Complex boundary value problems : prepared under constract N6ORI106 task order 5 < NR043992 > for Office of Naval Research by
Paul Garabedian(
Book
)
3 editions published in 1951 in English and held by 3 WorldCat member libraries worldwide
3 editions published in 1951 in English and held by 3 WorldCat member libraries worldwide
Calculation of axially symmetric cavities and jets by
Paul Garabedian(
Book
)
2 editions published in 1955 in English and held by 3 WorldCat member libraries worldwide
2 editions published in 1955 in English and held by 3 WorldCat member libraries worldwide
Partial differential equations with more than two independent variables in the complex domain by
Paul Garabedian(
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
Supercritical wing sections II : a handbook by
Frances Bauer(
Book
)
2 editions published in 1975 in English and held by 1 WorldCat member library worldwide
2 editions published in 1975 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Bauer, Frances Author
 Betancourt, Octavio 1945
 Korn, D.
 Korn, David
 United States National Aeronautics and Space Administration
 United States National Aeronautics and Space Administration Scientific and Technical Information Branch
 McFadden, G.
 Jameson, Antony
 Mackey, George W. (George Whitelaw) 19162006
 Mac Lane, Saunders 19092005
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Associated Subjects
Aerodynamics, SupersonicComputer programs Aerodynamics, Transonic AerodynamicsComputer programs AerofoilsComputer programs AirplanesWings Boundary layer Canada Cavitation Complex manifolds Differential equations, Partial Economics EducationCurricula Fluid dynamics Functions Garabedian, Paul Harvard University Hydrodynamics JetsFluid dynamics Kählerian structures Mathematical models Mathematical physics Mathematics Music NavierStokes equationsNumerical solutions Oscillating wings (Aerodynamics) Physics Plasma (Ionized gases)Data processing Plasma confinementData processing Plasma confinementMathematical models Scientists Sonatas (Cello and piano)Scores and parts StellaratorsData processing StellaratorsMathematical models Symmetry (Physics) United States Whirlwinds
Alternative Names
Garabedian, P.
Garabedian, P. 19272010
Garabedian, P. (Paul)
Garabedian, P. R.
Garabedian, P. R. 19272010
Garabedian, Paul.
Garabedian, Paul R.
Garabedian, Paul R. 19272010
Garabedian, Paul Roesel 19272010
Paul Garabedian Amerikaans wiskundige (19272010)
Paul Garabedian mathématicien américain
Paul Garabedian USamerikanischer Mathematiker
Пол Гарабедян
Փոլ Գարաբեդյան հայ մաթեմատիկոս
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