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CURVATURE PINCHING ESTIMATE AND SINGULARITIES OF THE RICCI FLOW
SINGULARITIES CURVATURE PINCHING ESTIMAT
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2015/8/17
In this paper, we first derive a pinching estimate on the traceless Ricci
curvature in term of scalar curvature and Weyl tensor under the Ricci flow. Then
we apply this estimate to study...
THE CONJUGATE HEAT EQUATION AND ANCIENT SOLUTIONS OF THE RICCI FLOW
ANCIENT SOLUTIONS CONJUGATE HEAT EQUATION
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2015/8/17
We prove Gaussian type bounds for the fundamental solution of the conjugate heat equation evolving under the Ricci flow. As a consequence, for dimension 4 and
higher, we show that the backward ...
Fading memory and the problem of approximating nonlinear operators with Volterra series
Continuous nonlinear operator volterra series operator nonlinear dynamic system
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2015/8/13
Using the notion of fading memory, very strong versions of two theorems are proved. The first is that any time-invariant (TI) continuous nonlinear operator can be approximated by a Volterra series ope...
Efficient distance computation using best ellipsoid fit
ellipsoid fi t geometric approximation collision detection
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2015/8/12
This paper describes a method for estimating the distance between a robot and its surrounding environment using best ellipsoid fit. The method consists of the following two stages. First we approximat...
A polynomial-time algorithm for determining quadratic Lyapunov functions for nonlinear systems
Nonlinear systems quadratic lyapunov function and convex programming function
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2015/8/12
We consider nonlinear systems dx/dt=f(x(t)) where Df(x(t)) is known to lie in the convex hull of L n times n matrices A_1,ldots,A_L. For such systems, quadratic Lyapunov functions can be determined us...
Obstacle collision detection using best ellipsoid fit
ellipsoid fit geometric approximation collision detection
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2015/8/11
This paper describes a method for estimating the distance between a robot and its surrounding environment using best ellipsoid fit. The method consists of the following two stages. First we approximat...
Efficient nonlinear optimization of queueing systems
Systems nonlinear optimization computational tools transition mode network the performance optimization
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2015/8/11
We present a systematic treatment of efficient nonlinear optimization of queuing systems. The suite of formulations uses the computational tool of convex optimization, with fast polynomial time algori...
An ellipsoidal approximation to the Hadamard product of ellipsoids
Computational efficiency ellipsoid signal
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2015/8/11
This paper introduces a computationally efficient outer approximation to the Hadamard, i.e., element-wise, product of two ellipsoids. This element-wise product corresponds to multiplicative uncertaint...
Designing fast distributed iterations via semidefinite programming
Iteration markov chain the transition probability mixing ratio the monte carlo markov chain
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2015/8/11
The general setting we consider involves a process, iteration, or method in which the computation or communication at each step is local, determined by a given graph, and involves some parameters or c...
Curvelets and Wave Atoms for Mirror-Extended Images
Curvelets Wave Atoms Mirror-Extended Images
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2015/7/15
We present variants of both the digital curvelet transform, and the digital wave atom transform, which handle the image boundaries by mirror extension. Previous versions of these transforms treated im...
FAST DISCRETE CURVELET TRANSFORMS
two-dimensional and three-dimensional curvelet transforms fast Fourier transforms unequally spaced fast Fourier transforms smooth partitioning interpolation digital shear filtering wrapping
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2015/7/14
This paper describes two digital implementations of a new mathematical transform, namely, the second generation curvelet transform in two and three dimensions. The first digital transformation is base...
Discrete Symbol Calculus
sublinear complexity inversion of elliptic operators square root of elliptic operators
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2015/7/14
This paper deals with efficient numerical representation and manipulation of differential and integral operators as symbols in phase-space, i.e., functions of space x and frequency ξ. The symbol smoot...
Fast construction of hierarchical matrix representation from matrix–vector multiplication
Fast algorithm Hierarchical matrix construction Randomized singular value decomposition Matrix–vector multiplication Elliptic operator Green’s function
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2015/7/14
We develop a hierarchical matrix construction algorithm using matrix–vector multiplications, based on the randomized singular value decomposition of low-rank matrices. The algorithm uses Oelog nT appl...
A fast direct solver for elliptic problems on general meshes in 2D
Elliptic equations Fast algorithms Multifrontal methods Hierarchical matrices Sparse matrix
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2015/7/14
We present a fast direct algorithm for solutions to linear systems arising from 2D elliptic equations. We follow the approach in Xia et al. (2009) on combining the multifrontal method with hierarchica...
A fast nested dissection solver for Cartesian 3D elliptic problems using hierarchical matrices
Elliptic equations Fast algorithms Nested dissection Hierarchical matrices Sparse matrix
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2015/7/14
We present a fast algorithm for solutions to linear systems arising from three dimensional elliptic problems on a regular Cartesian mesh. We follow the approach of Schmitz and Ying (2012) on combining...