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Nonlinear Neural Networks: Principles, Mechanisms, and Architectures
, 1988
"... An historical discussion is provided of the intellectual trends that caused nineteenth century interdisciplinary studies of physics and psychobiology by leading scientists such as Helmholtz, Maxwell, and Mach to splinter into separate twentiethcentury scientific movements. The nonlinear, nonstatio ..."
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Cited by 263 (21 self)
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Schuster models. A Liapunov functional method is described for proving global limit or oscillation theorems for nonlinear competitive systems when their decision schemes are globally consistent or inconsistent, respectively. The former case is illustrated by a model of a globally stable economic market
Local stable reduction of plane curve singularities, Journal fur die Reine und Angewandte Mathematik 520
, 2000
"... Consider a family of curves over the disc, with smooth bers except for the central ber over the origin. By the local stable reduction theorem, after suitable blowups and base changes we obtain a family such that the central ber has reduced normal crossings. This stable central ber has two parts: th ..."
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Cited by 16 (2 self)
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Consider a family of curves over the disc, with smooth bers except for the central ber over the origin. By the local stable reduction theorem, after suitable blowups and base changes we obtain a family such that the central ber has reduced normal crossings. This stable central ber has two parts
Modular verification of software components in C
 IEEE TRANSACTIONS ON SOFTWARE ENGINEERING
, 2003
"... We present a new methodology for automatic verification of C programs against finite state machine specifications. Our approach is compositional, naturally enabling us to decompose the verification of large software systems into subproblems of manageable complexity. The decomposition reflects the mo ..."
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Cited by 233 (23 self)
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, simulation is checked via a reduction to Boolean satisfiability. MAGIC is able to interface with several publicly available theorem provers and SAT solvers. We report experimental results with procedures from the Linux kernel and the OpenSSL toolkit.
Asymptotic stability and feedback stabilization
 Differential Geometric Control Theory
, 1983
"... Abstract. We consider the loca1 behavior of control problems described by ( * = dx/dr) i=f(x,u) ; f(x,0)=0 o and more specifically, the question of determining when there exists a smooth function u(x) such that x = xo is an equilibrium point which is asymPtotically stable. Our main results are form ..."
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Cited by 224 (0 self)
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Abstract. We consider the loca1 behavior of control problems described by ( * = dx/dr) i=f(x,u) ; f(x,0)=0 o and more specifically, the question of determining when there exists a smooth function u(x) such that x = xo is an equilibrium point which is asymPtotically stable. Our main results
The structure of complete stable minimal surfaces in 3manifolds of nonnegative scalar curvature.
 Comm. Pure Appli. Math.
, 1980
"... The purpose of this paper is to study minimal surfaces in threedimensional manifolds which, on each compact set, minimize area up to second order. If M is a minimal surface in a Riemannian threemanifold N, then the condition that M be stable is expressed analytically by the requirement that o n a ..."
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Cited by 192 (1 self)
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stable minimal surface M is a plane (Corollary 4). The earliest result of this type was due to S. Bernstein [2] who proved this in the case that M is the graph of a function (stability is automatic in this case). The Bernstein theorem was generalized by R. Osserman [lo] who showed that the statement
Strongly Equivalent Logic Programs
 ACM Transactions on Computational Logic
, 2000
"... A logic program 1 is said to be equivalent to a logic program 2 in the sense of the answer set semantics if 1 and 2 have the same answer sets. We are interested in the following stronger condition: for every logic program , 1 [ has the same answer sets as 2 [ . The study of strong equival ..."
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Cited by 231 (36 self)
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equivalence is important, because we learn from it how one can simplify a part of a logic program without looking at the rest of it. The main theorem shows that the verication of strong equivalence can be accomplished by checking the equivalence of formulas in a monotonic logic, called the logic of here
Stable
"... trimorphic coexistence in a lattice model of spatial competition with two site types ..."
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trimorphic coexistence in a lattice model of spatial competition with two site types
The symplectic nature of fundamental groups of surfaces
 ADV. MATH
, 1984
"... A symplectic structure on a manifold is a closed nondegenerate exterior 2form. The most common type of symplectic structure arises on a complex manifold as the imaginary part of a Hermitian metric which is Klhler. Many moduli spaces associated with Riemann surfaces have such Kahler structures: the ..."
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Cited by 223 (8 self)
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: the Jacobi variety, Teichmüller space, moduli spaces of stable vector bundles and even the first real cohomology group have such structures. In all of these examples the topology of the associated spaces depends, remarkably, only on the topology of the Riemann surface, while often their complex structures
Results 11  20
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1,050,461