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The irreducibility of the space of curves of given genus
 Publ. Math. IHES
, 1969
"... Fix an algebraically closed field k. Let Mg be the moduli space of curves of genus g over k. The main result of this note is that Mg is irreducible for every k. Of course, whether or not M s is irreducible depends only on the characteristic of k. When the characteristic s o, we can assume that k ~ ..."
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Cited by 512 (2 self)
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~ (1, and then the result is classical. A simple proof appears in EnriquesChisini [E, vol. 3, chap. 3], based on analyzing the totality of coverings of p1 of degree n, with a fixed number d of ordinary branch points. This method has been extended to char. p by William Fulton [F], using specializations
Dictionary of protein secondary structure: pattern recognition of hydrogenbonded and geometrical features
 Biopolymers
, 1983
"... structure ..."
String theory and noncommutative geometry
 JHEP
, 1999
"... We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero Bfield. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from ..."
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Cited by 801 (8 self)
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counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its Tduality, and Morita equivalence. We also discuss the D0/D4 system, the relation to Mtheory in DLCQ, and a possible noncommutative version of the sixdimensional (2, 0) theory. 8/99
A Structural Approach to Operational Semantics
, 1981
"... Syntax of a very simple programming language called L. What is abstract about it will be discussed a little here and later at greater length. For us syntax is a collection of syntactic sets of phrases; each set corresponds to a different type of phrase. Some of these sets are very simple and can be ..."
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Cited by 1541 (3 self)
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be taken as given: Truthvalues This is the set T = ftt; ffg and is ranged over by (the metavariable) t (and we also happily employ for this (and any other) metavariable sub and superscripts to generate other metavariables: t ; t 0 ; t 1k ).
The Askeyscheme of hypergeometric orthogonal polynomials and its qanalogue
, 1998
"... We list the socalled Askeyscheme of hypergeometric orthogonal polynomials and we give a q analogue of this scheme containing basic hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation, the second order di#erent ..."
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Cited by 580 (6 self)
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3 we list the qanalogues of the polynomials in the Askeyscheme. We give their definition, orthogonality relation, three term recurrence relation, second order di#erence equation, forward and backward shift operator, Rodriguestype formula and generating functions. In chapter 4 we give the limit
Lag length selection and the construction of unit root tests with good size and power
 Econometrica
, 2001
"... It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We conside ..."
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Cited by 534 (14 self)
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It is widely known that when there are errors with a movingaverage root close to −1, a high order augmented autoregression is necessary for unit root tests to have good size, but that information criteria such as the AIC and the BIC tend to select a truncation lag (k) that is very small. We
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 5350 (67 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 long time, ‘variational ’ problems have been identified mostly with the ‘calculus of variations’. In that venerable subject, built around the minimization of integral functionals, constraints were relatively simple and much of the focus was on infinitedimensional function spaces. A major theme was the exploration of variations around a point, within the bounds imposed by the constraints, in order to help characterize solutions and portray them in terms of ‘variational principles’. Notions of perturbation, approximation and even generalized differentiability were extensively investigated. Variational theory progressed also to the study of socalled stationary points, critical points, and other indications of singularity that a point might have relative to its neighbors, especially in association with existence theorems for differential equations.
Monitoring the future: National survey results on drug use
 I: Secondary school students (NIH Publication No. 055726). Bethesda, MD: National Institute on Drug Abuse
, 2005
"... by ..."
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