Robert Edmund O'Malley | Academic Influence

Robert Edmund O'Malley's AcademicInfluence.com Rankings

Robert Edmund O'Malley

Mathematics

#2092

World Rank

#3283

Historical Rank

#836

USA Rank

Group Theory

#125

World Rank

#153

Historical Rank

#26

USA Rank

Number Theory

#210

World Rank

#270

Historical Rank

#40

USA Rank

Algebra

#236

World Rank

#344

Historical Rank

#53

USA Rank

mathematics Degrees

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Mathematics

Robert Edmund O'Malley's Degrees

PhD Mathematics Princeton University
Masters Mathematics Stanford University

Why Is Robert Edmund O'Malley Influential?

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According to Wikipedia, Robert Edmund O'Malley Jr. is an American mathematician. O'Malley studied electrical engineering and mathematics at the University of New Hampshire, where he received his baccalaureate degree in 1960 and his master's in 1961. He then studied differential equations and singular perturbations at Stanford University, where he received his doctorate in mathematics in 1966. After brief appointments at the University of North Carolina , Bell Telephone Laboratories, the Courant Institute , and the Mathematics Research Center , O'Malley returned to New York University in 1968. He remained there, doing research on asymptotic methods and singular perturbations with Joseph Keller and a number of other stimulating colleagues and students. O'Malley spent a year at the University of Edinburgh, where his lecture notes formed the basis of his book, Introduction to Singular Perturbations . In 1973, he moved to the University of Arizona where he later organized a successful interdisciplinary program in applied mathematics, and where he applied singular perturbation ideas in control theory. After a sabbatical at Stanford University, O'Malley moved to Rensselaer Polytechnic Institute in 1981. At Rensselaer, he headed a mathematical sciences department which emphasized applied mathematics and computer science. There, he was active in campus affairs and served as the chairman of the faculty and the Ford Foundation Professor. Soon after a sabbatical at the Technical University of Vienna, where O'Malley studied asymptotic methods in semiconductor modeling, he moved to the University of Washington, Seattle.

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Robert Edmund O'Malley's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Singular perturbations and order reduction in control theory - An overview (1975) (911)
The Statistical Inevitability of Stability‐Diversity Relationships in Community Ecology (1998) (714)
Introduction to singular perturbations (1974) (687)
Theory and Applications of Stochastic Differential Equations (1980) (576)
Analyzing Multiscale Phenomena Using Singular Perturbation Methods (1999) (115)
Singular perturbations and singular arcs. I (1973) (90)
Boundary Layer Problems Exhibiting Resonance (1970) (79)
Cheap control of the time-invariant regulator (1975) (79)
Shock Layer Movement for Burgers' equation (1995) (70)
Topics in singular perturbations (1968) (69)
Phase-plane solutions to some singular perturbation problems (1976) (67)
Singular perturbations and optimal control (1978) (62)
The Singularly Perturbed Linear State Regulator Problem. II (1972) (60)
The numerical solution of boundary value problems for stiff differential equations (1977) (58)
Singular Perturbations and Hysteresis (2005) (52)
Nonlinear singular perturbation phenomena: Theory and application (1986) (47)
On the Asymptotic Solution of a Two-Parameter Boundary Value Problem of Chemical Reactor Theory (1974) (43)
Boundary Layer Methods for Nonlinear Initial Value Problems (1971) (43)
Singularly Perturbed Linear Two-Point Boundary Value Problems (2008) (38)
On the motion of viscous shocks and the supersensitivity of their steady-state limits (1994) (36)
Analytical and Numerical Methods for Nonlinear Singular Singularly-Perturbed Initial Value Problems (1980) (33)
Singular perturbations of boundary value problems for linear ordinary differential equations involving two parameters (1967) (32)
Historical Developments in Singular Perturbations (2014) (31)
Boundary layer methods for certain nonlinear singularly perturbed optimal control problems (1974) (31)
On singular singularly perturbed initial value problems (1989) (29)
Introduction to Perturbation Methods (M. H. Holmes) (1996) (28)
Loss of boundary conditions in the asymptotic solution of linear ordinary differential equations, II boundary value problems (1968) (27)
Singular perturbation of the time-invariant linear state regulator problem☆ (1972) (26)
Singular Perturbation Theory: A Viscous Flow out of Göttingen (2010) (22)
On singular singularly-perturbed initial value problems (1978) (21)
A New Renormalization Method for the Asymptotic Solution of Weakly Nonlinear Vector Systems (2003) (21)
On initial value problems for nonlinear systems of differential equations with two small parameters (1971) (21)
On the Asymptotic Solution of the Singularly Perturbed Boundary Value Problems Posed by Bohé (2000) (21)
On the matrix Riccati approach to a singularly perturbed regulator problem (1974) (20)
Singular perturbation analysis for ordinary differential equations (1977) (18)
Singular perturbations of semilinear second order systems (1980) (18)
Deriving amplitude equations for weakly-nonlinear oscillators and their generalizations (2006) (17)
Singular perturbations of a boundary value problem for a system of nonlinear differential equations (1970) (17)
Numerical Methods for Stiff Systems of Two-Point Boundary Value Problems (1984) (15)
Regularization of nonlinear differential-algebraic equations (1994) (15)
Supersensitive Boundary Value Problems (1993) (15)
Quantum Fields and Strings: A Course for Mathematicians, Volumes I and 2. (2016) (15)
On Multiple Solutions of Singularly Perturbed Systems in the Conditionally Stable Case (1980) (14)
Singularly perturbed boundary value problems for nonlinear systems, including a challenging problem for a nonlinear beam (1982) (14)
The Motion of Internal Layers in Singularly Perturbed Advection‐Diffusion‐Reaction Equations * (2004) (13)
Variation of Parameters and the Renormalization Group Method (2015) (13)
A boundary value problem for certain nonlinear second order differential equations with a small parameter (1968) (12)
On the computation of singular controls (1977) (12)
The regularization of linear differential-algebraic equations (1996) (12)
Viscous shock motion for advection-diffusion equations (1995) (12)
High gain feedback systems as singular singular-perterbation problems (1977) (11)
Exponential Asymptotics, Boundary Layer Resonance, and Dynamic Metastability (1996) (11)
Singular singular-perturbation problems (1977) (11)
Thinking about Ordinary Differential Equations (1997) (11)
The asymptotic solution semiconductor device problem involving reverse bias (1990) (9)
Review: J. Kevorkian and J. D. Cole, Perturbation methods in applied mathematics, and Ali Hasan Nayfeh, Introduction to perturbation techniques (1982) (9)
NAIVE SINGULAR PERTURBATION THEORY (2001) (8)
International Workshop on Multi-Rate Processes and Hysteresis (2006) (8)
A Survey in Mathematics for Industry: Two-timing and matched asymptotic expansions for singular perturbation problems (2011) (8)
Singular Perturbations, Asymptotic Evaluation of Integrals, and Computational Challenges (1991) (7)
Time-scale modeling of dynamic networks with applications to power systems: J. H. Chow (1985) (7)
On the asymptotic solution of boundary value problems for nonhomogeneous ordinary differential equations containing a parameter (1969) (6)
Analyzing multiscale phenomena using singular perturbation methods : American Mathematical Society short course, January 5-6, 1998, Baltimore, Maryland (1999) (6)
Working with multiscale asymptotics (2005) (6)
A Non-linear Singular Perturbation Problem Arising in the Study of Chemical Flow Reactors (1970) (6)
Boundary layer methods for ordinary differential equations with small coefficients multiplying the highest derivatives (1974) (5)
Singular Perturbations, Order Reduction, and Decoupling of Large Scale Systems. (1978) (5)
Partially Singular Control Problems as Singular Singular-Perturbation Problems (1978) (5)
THE SINGULAR PERTURBATION APPROACH TO SINGULAR ARCS (1975) (5)
Thinking About Ordinary Differential Equations: Frontmatter (1997) (4)
Ludwig Prandtl’s Boundary Layer Theory (2014) (4)
Slow/Fast Decoupling — Analytical and Numerical Aspects (1982) (4)
On the Numerical Integration of Two-Point Boundary Value Problems for Stiff Systems of Ordinary Differential Equations. (1980) (4)
On solving boundary value problems for multi-scale systems using asymptotic approximations and multiple-shooting (1984) (4)
Asymptotic and Numerical Methods for Vector Systems of Singularly-Perturbed Boundary Value Problems. (1982) (4)
Boundary value problems for differential-algebraic equations (1995) (3)
The Numerical Solution of a Challenging Class of Turning Point Problems (2003) (3)
Examples Illustrating the Connection between Singular Perturbations and Singular Arcs. (1973) (3)
The slow motion of shock layers for advection--diffusion--reaction equations (2005) (3)
Give Your ODEs a Singular Perturbation (2000) (3)
On Singular Perturbations, Especially Matching (1994) (3)
Two-Timing, Geometric, and Multi-scale Methods (2014) (3)
Metastable travelling-wave solutions of singularly-perturbed reaction-diffusion equations (1998) (3)
Thinking About Ordinary Differential Equations: Preface (1997) (2)
Cheap Control, Singular Arcs, and Singular Perturbations (1974) (2)
Decoupling and Order Reduction for Linear Time-Varying Two-Time-Scale Systems. (1980) (2)
On multiple solutions of a singular perturbation problem (1972) (2)
Solving weakly nonlinear oscillator equations on long-time intervals (2005) (2)
Time-scale decoupling and order reduction for linear time-varying systems† (2007) (2)
Amplitude modulation for the Swift-Hohenberg and Kuramoto-Sivashinski equations (2014) (2)
Mahony's intriguing stiff equations (1999) (2)
Examples Illustrating Regular and Singular Perturbation Concepts (1991) (2)
ICIAM 91 : proceedings of the Second International Conference on Industrial and Applied Mathematics (1993) (2)
Multiple solutions of a singularly perturbed boundary value problem arising in chemical reactor theory (1972) (2)
Book Review: Perturbation methods in applied mathematics (1982) (1)
The first boundary value problem for certain linear elliptic differential equations involving two small parameters (1967) (1)
Analytic Methods for the Approximate Solution of Singularly Perturbed Systems (1981) (1)
Book Reviews Featured Review: Two Perspectives on Recent Books on Ordinary Differential Equations Formal Power Series and Linear Systems of Meromorphic Ordinary Differential (2001) (1)
Singularly Perturbed Boundary Value Problems (1991) (1)
On the asymptotic solution of multi-point boundary value problems (1970) (1)
ON EXORCISING SECULAR TERMS (2000) (1)
Singularly Perturbed Initial Value Problems (1991) (1)
Book Reviews (2014) (0)
Book Reviews (2013) (0)
Holmes, M. H.: Introduction to Perturbation Methods. New York etc., Springer‐Verlag 1995. XIII, 337 pp., DM 68.–. ISBN 0‐387‐94203‐3 (Texts in Applied Mathematics 20) (1996) (0)
Asymptotic and Numerical Methods for Singularly Perturbed Differential Equations with Applications to Impact Problems. (1986) (0)
Book Reviews Embedded Robotics: Mobile Robot De- Sign and Applications with Embedded Systems. Second Edition (2007) (0)
Thinking About Ordinary Differential Equations: First-order equations (1997) (0)
Singular Perturbations I. Spaces and Singular Perturbations on Manifolds without Boundaries (L. S. Frank) (1992) (0)
The Numerical Solution of Singular Singulary-Perturbed Initial Value Problems. (1978) (0)
Book Reviews (2014) (0)
Wendepunkts and Canards (Turning Points and Delayed Bifurcations) (2014) (0)
The numerical solution of boundary value problems for still differential equations (1976) (0)
Thinking About Ordinary Differential Equations: Stability concepts (1997) (0)
Further Results on Singular Perturbations and Singular Arcs. (1974) (0)
Singular Perturbations and Slow-Mode Approximations for Large Scale Linear Systems. (1978) (0)
Book Reviews (2013) (0)
Book Reviews (2013) (0)
Thinking About Ordinary Differential Equations: General References (1997) (0)
Book Reviews (2014) (0)
On Nonlinear Optimal Control Problems (1982) (0)
International Workshop on Hysteresis & Multi-scale Asymptotics (2005) (0)
Featured Review : Diffusion and Ecological Problems : Modern Perspectives (2003) (0)
Perturbation Methods. By A. H. NAYFEH. Wiley, 1973. 425 pp. £9 (hardback) or £3.75 (paperback). (1974) (0)
Book Review: Analysis and Simulation of Chaotic Systems. By F. C. Hoppensteadt (2002) (0)
Featured Review: Textbooks on Linear Algebra Practical Linear Algebra: A Geometric Toolbox. By Gerald Farin and Dianne Hansford (2006) (0)
Book Review: ICIAM 99. By J. M. Ball and J. C. R. Hunt (2002) (0)
Thinking About Ordinary Differential Equations: Systems of linear differential equations (1997) (0)
SINGULAR PERTURBATIONS AND THE LINEAR STATE REGULATOR PROBLEM (1972) (0)
Book Reviews (2007) (0)
Thinking About Ordinary Differential Equations: Singular perturbation methods (1997) (0)
Thinking About Ordinary Differential Equations: Power series solutions and special functions (1997) (0)
Thinking About Ordinary Differential Equations: Linear second-order equations (1997) (0)
A singular perturbations approach to reduced-order modeling and decoupling for large scale linear systems (1982) (0)
Rationality, frustration minimisation, hysteresis and the El Farol problem (2005) (0)
Grid Approximations of Multis ale Problems Arising inSingularly Perturbed Paraboli Rea tion-Di usionEquations in an Unbounded Domain (0)
Book Reviews (2007) (0)
Asymptotic methods and singular perturbations : [proceedings of the Symposium in Applied Mathematics of the American Mathematical Society and the Society for Industrial and Applied Mathematics held in New York City, April 11-12, 1976 (1976) (0)
Book Reviews How Does This Book Relate to Other Visualization Work? Intuition vs. Experimentation. the Visual Display of Quantitative Information (2002) (0)
The Method of Matched Asymptotic Expansions and Its Generalizations (2014) (0)
A Simple Multi-scale Procedure for Both Oscillatory and Boundary Layer Problems (2014) (0)
Lectures on ordinary differential equations (1970) (0)
Singularly Perturbed Boundary Value Problems Viewed in the Liénard Plane (2020) (0)
Book Reviews (2013) (0)

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