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296,118
Blowup of Smooth Solutions for an Aggregation Equation
"... We study the blowup criterion of smooth solutions for an inviscid aggregation equation in R . By means of the losing estimates and the logarithmic Sobolev inequality, we establish an improved blowup criterion of smooth solutions. ..."
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We study the blowup criterion of smooth solutions for an inviscid aggregation equation in R . By means of the losing estimates and the logarithmic Sobolev inequality, we establish an improved blowup criterion of smooth solutions.
Learning with local and global consistency.
- In NIPS,
, 2003
"... Abstract We consider the general problem of learning from labeled and unlabeled data, which is often called semi-supervised learning or transductive inference. A principled approach to semi-supervised learning is to design a classifying function which is sufficiently smooth with respect to the intr ..."
Abstract
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Cited by 673 (21 self)
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to the intrinsic structure collectively revealed by known labeled and unlabeled points. We present a simple algorithm to obtain such a smooth solution. Our method yields encouraging experimental results on a number of classification problems and demonstrates effective use of unlabeled data.
SMOOTH SOLUTIONS FOR THE DYADIC MODEL
"... ABSTRACT. We consider the dyadic model, which is a toy model to test issues of well–posedness and blow–up for the Navier–Stokes and Euler equations. We prove well–posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier–Stokes. Likewise we prov ..."
Abstract
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Cited by 8 (5 self)
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ABSTRACT. We consider the dyadic model, which is a toy model to test issues of well–posedness and blow–up for the Navier–Stokes and Euler equations. We prove well–posedness of positive solutions of the viscous problem in the relevant scaling range which corresponds to Navier–Stokes. Likewise we
Topology of the Set of Smooth Solutions to the Liouville Equation
, 2008
"... We prove that the space of smooth initial data and the set of smooth solutions of the Liouville equation are homeomorphic. 1 1 ..."
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We prove that the space of smooth initial data and the set of smooth solutions of the Liouville equation are homeomorphic. 1 1
Smooth Solution to the 1-Dimensional Spin Equations
"... Abstract In this paper, the global existence and uniqueness of a smooth solution to the periodic initial-value problem of the spin equations of antiferromagnets in 1 dimension are proved. ..."
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Abstract In this paper, the global existence and uniqueness of a smooth solution to the periodic initial-value problem of the spin equations of antiferromagnets in 1 dimension are proved.
New results in linear filtering and prediction theory
- TRANS. ASME, SER. D, J. BASIC ENG
, 1961
"... A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary sta ..."
Abstract
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Cited by 607 (0 self)
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A nonlinear differential equation of the Riccati type is derived for the covariance matrix of the optimal filtering error. The solution of this "variance equation " completely specifies the optimal filter for either finite or infinite smoothing intervals and stationary or nonstationary
Shape and motion from image streams under orthography: a factorization method
- INTERNATIONAL JOURNAL OF COMPUTER VISION
, 1992
"... Inferring scene geometry and camera motion from a stream of images is possible in principle, but is an ill-conditioned problem when the objects are distant with respect to their size. We have developed a factorization method that can overcome this difficulty by recovering shape and motion under orth ..."
Abstract
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Cited by 1094 (38 self)
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uses the singular-value decomposition technique to factor the measurement matrix into two matrices which represent object shape and camera rotation respectively. Two of the three translation components are computed in a preprocessing stage. The method can also handle and obtain a full solution from a
A Signal Processing Approach To Fair Surface Design
, 1995
"... In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing, or fai ..."
Abstract
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Cited by 654 (15 self)
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In this paper we describe a new tool for interactive free-form fair surface design. By generalizing classical discrete Fourier analysis to two-dimensional discrete surface signals -- functions defined on polyhedral surfaces of arbitrary topology --, we reduce the problem of surface smoothing
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