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Discrete Integrable Systems and Geometry
 In: XII International Congress on Mathematical Physics, ICMP'97
, 1997
"... Introduction Long before the theory of solitons, geometers used integrable equations to describe various special curves, surfaces etc. Nowadays this field of research takes advantage of using both geometrical intuition and methods of soliton theory in order to study integrable geometries, i.e. geom ..."
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Cited by 5 (1 self)
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transformation etc.) are used to study local properties of integrable geometries. Recently it was found that integrable discretizations (i.e. those described by discrete integrable systems) of integrable geometries have natural properties. Looking for proper definitions of integrable nets and investigation
Coresets for Discrete Integration and Clustering
 In proceedings of FSTTCS
, 2006
"... The problem received the title of `Buridan's sheep. ' The biological code was taken from a young merino sheep, by the CasparoKarpov method, at a moment when the sheep was between two feeding troughs full of mixed fodder. This code, along with additional data about sheep in general, was fe ..."
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Cited by 8 (1 self)
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, we investigate the problem of nding a small (weighted) subset S ⊆ P, such that for any f ∈ F, we have that f(P) is a (1 ± ε)approximation to f(S). Here, f(Q) = ∑ q∈Q w(q)f(q) denotes the weighted discrete integral of f over the point set Q, where w(q) is the weight assigned to the point q. We study
Discretized integral hydrodynamics
 Phys. Rev. E
, 1998
"... Using an interpolant form for the gradient of a function of position, we write an integral version of the conservation equations for a fluid. In the appropriate limit, these become the usual conservation laws of mass, momentum, and energy. We also discuss the special cases of the NavierStokes equa ..."
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Cited by 1 (0 self)
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Stokes equations for viscous flow and the Fourier law for thermal conduction in the presence of hydrodynamic fluctuations. By means of a discretization procedure, we show how the integral equations can give rise to the socalled ''particle dynamics'' of smoothed particle hydrodynamics
On discrete integrable equations of higher order
, 2013
"... We study 2D discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund– Darboux transformations f ..."
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We study 2D discrete integrable equations of order 1 with respect to one independent variable and m with respect to another one. A generalization of the multidimensional consistency property is proposed for this type of equations. The examples are related to the Bäcklund– Darboux transformations
Finite state Markovchain approximations to univariate and vector autoregressions
 Economics Letters
, 1986
"... The paper develops a procedure for finding a discretevalued Markov chain whose sample paths approximate well those of a vector autoregression. The procedure has applications in those areas of economics, finance, and econometrics where approximate solutions to integral equations are required. 1. ..."
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Cited by 493 (0 self)
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The paper develops a procedure for finding a discretevalued Markov chain whose sample paths approximate well those of a vector autoregression. The procedure has applications in those areas of economics, finance, and econometrics where approximate solutions to integral equations are required. 1.
Discrete integrable systems in projective geometry
, 2008
"... The notion of integrability is one of the central notions in mathematics. Starting from Euler and Jacobi, the theory of integrable systems is among the most remarkable applications of geometric ideas to mathematics and physics in general. Discrete integrable systems is a new and actively developing ..."
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The notion of integrability is one of the central notions in mathematics. Starting from Euler and Jacobi, the theory of integrable systems is among the most remarkable applications of geometric ideas to mathematics and physics in general. Discrete integrable systems is a new and actively developing
Control of Systems Integrating Logic, Dynamics, and Constraints
 Automatica
, 1998
"... This paper proposes a framework for modeling and controlling systems described by interdependent physical laws, logic rules, and operating constraints, denoted as Mixed Logical Dynamical (MLD) systems. These are described by linear dynamic equations subject to linear inequalities involving real and ..."
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Cited by 413 (50 self)
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and integer variables. MLD systems include constrained linear systems, finite state machines, some classes of discrete event systems, and nonlinear systems which can be approximated by piecewise linear functions. A predictive control scheme is proposed which is able to stabilize MLD systems on desired
Discrete moving frames and discrete integrable systems
 Foundations of Computational Mathematics, Volume 13, Issue 4 (2013), Page 545582
"... Group based moving frames have a wide range of applications, from the classical equivalence problems in differential geometry to more modern applications such as computer vision. Here we describe what we call a discrete group based moving frame, which is essentially a sequence of moving frames with ..."
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Cited by 2 (0 self)
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integrable systems. We demonstrate that the discrete analogues of some curvature flows lead naturally to Hamiltonian pairs, which generate integrable differentialdifference systems. In particular, we show that in the centroaffine plane and the projective space, the Hamiltonian pairs obtained can
GEOMETRY OF DISCRETE INTEGRABILITY. THE CONSISTENCY APPROACH
"... Long before the theory of solitons, geometers used integrable equations to describe various special curves, surfaces etc. At that time no relation to mathematical physics was known, and quite different geometries appeared in this context (we will call them integrable) were unified by their common ge ..."
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Long before the theory of solitons, geometers used integrable equations to describe various special curves, surfaces etc. At that time no relation to mathematical physics was known, and quite different geometries appeared in this context (we will call them integrable) were unified by their common
Results 1  10
of
9,351