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The mathematics of infectious diseases
 SIAM Review
, 2000
"... Abstract. Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R0, the contact number σ, and the replacement number R are reviewed for the classic SIR epidemic a ..."
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Cited by 489 (4 self)
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Abstract. Many models for the spread of infectious diseases in populations have been analyzed mathematically and applied to specific diseases. Threshold theorems involving the basic reproduction number R0, the contact number σ, and the replacement number R are reviewed for the classic SIR epidemic
Mathematical Control Theory: Deterministic Finite Dimensional Systems
 of Texts in Applied Mathematics
, 1990
"... The title of this book gives a very good description of its contents and style, although I might have added “Introduction to ” at the beginning. The style is mathematical: precise, clear statements (i.e., theorems) are asserted, then carefully proved. The book covers many of the key topics in contro ..."
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Cited by 485 (121 self)
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The title of this book gives a very good description of its contents and style, although I might have added “Introduction to ” at the beginning. The style is mathematical: precise, clear statements (i.e., theorems) are asserted, then carefully proved. The book covers many of the key topics
An axiomatic basis for computer programming
 COMMUNICATIONS OF THE ACM
, 1969
"... In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference w ..."
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Cited by 1753 (4 self)
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In this paper an attempt is made to explore the logical foundations of computer programming by use of techniques which were first applied in the study of geometry and have later been extended to other branches of mathematics. This involves the elucidation of sets of axioms and rules of inference
Singularity Detection And Processing With Wavelets
 IEEE Transactions on Information Theory
, 1992
"... Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales of their wavele ..."
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Cited by 604 (13 self)
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Most of a signal information is often found in irregular structures and transient phenomena. We review the mathematical characterization of singularities with Lipschitz exponents. The main theorems that estimate local Lipschitz exponents of functions, from the evolution across scales
Convex Analysis
, 1970
"... In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a lo ..."
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Cited by 5396 (68 self)
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In this book we aim to present, in a unified framework, a broad spectrum of mathematical theory that has grown in connection with the study of problems of optimization, equilibrium, control, and stability of linear and nonlinear systems. The title Variational Analysis reflects this breadth. For a
Methodologies in spectral analysis of large dimensional random matrices, a review
 STATIST. SINICA
, 1999
"... In this paper, we give a brief review of the theory of spectral analysis of large dimensional random matrices. Most of the existing work in the literature has been stated for real matrices but the corresponding results for the complex case are also of interest, especially for researchers in Electri ..."
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Cited by 454 (39 self)
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in Electrical and Electronic Engineering. Thus, we convert almost all results to the complex case, whenever possible. Only the latest results, including some new ones, are stated as theorems here. The main purpose of the paper is to show how important methodologies, or mathematical tools, have helped to develop
Recursive Functions of Symbolic Expressions and Their Computation by Machine, Part I
, 1960
"... this paper in L a T E Xpartly supported by ARPA (ONR) grant N000149410775 to Stanford University where John McCarthy has been since 1962. Copied with minor notational changes from CACM, April 1960. If you want the exact typography, look there. Current address, John McCarthy, Computer Science Depa ..."
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Cited by 457 (3 self)
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applications of our recursive function formalism to mathematical logic and to the problem of mechanical theorem proving. 2 Functions and Function Definitions
Formal Methods: State of the Art and Future Directions
 ACM Computing Surveys
, 1996
"... ing with credit is permitted. To copy otherwise, to republish, to post on servers, to redistribute to lists, or to use any component of this work in other works, requires prior specific permission and/or a fee. Permissions may be requested from Publications Dept, ACM Inc., 1515 Broadway, New York, N ..."
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Cited by 425 (6 self)
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, NY 10036 USA, fax +1 (212) 8690481, or permissions@acm.org. 2 \Delta E.M. Clarke and J.M. Wing About ProgramsMechanical verification, Specification techniques; F.4.1 [Mathematical Logic and Formal Languages]: Mathematical LogicMechanical theorem proving General Terms: Software engineering
Model Checking Java Programs Using Java PathFinder
, 1998
"... . This paper describes a translator called Java PathFinder (Jpf), from Java to Promela, the modeling language of the Spin model checker. Jpf translates a given Java program into a Promela model, which then can be model checked using Spin. The Java program may contain assertions, which are translated ..."
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Cited by 387 (32 self)
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. This work should be seen in a broader attempt to make formal methods applicable within NASA's areas such as space, aviation, and robotics. The work is a continuation of an effort to formally analyze, using Spin, a multithreaded operating system for the DeepSpace 1 space craft, and of previous work
Digraphs  Theory, Algorithms and Applications
, 2007
"... Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. As a research area, graph theory is still relatively young, but it is maturing rapidly with many deep results having been discovered o ..."
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Cited by 378 (48 self)
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Graph theory is a very popular area of discrete mathematics with not only numerous theoretical developments, but also countless applications to practical problems. As a research area, graph theory is still relatively young, but it is maturing rapidly with many deep results having been discovered
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