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N∑ ‖Xi‖1,∞.
"... The weak Lp norm of a random variable X is defined as ‖X‖p, ∞ = ( sup t t>0 p P{X > t} ) 1/p, 0 < p < ∞. It is not a norm but equivalent to a norm if p> 1. For p = 1 there is no equivalent norm, see a simple example in [1] where ..."
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The weak Lp norm of a random variable X is defined as ‖X‖p, ∞ = ( sup t t>0 p P{X > t} ) 1/p, 0 < p < ∞. It is not a norm but equivalent to a norm if p> 1. For p = 1 there is no equivalent norm, see a simple example in [1] where
0≤i,j≤n (xi
"... Dedicated to my friend Pier Vittorio Ceccherini on the occasion of his 65th birthday Abstract. As an extension of Cauchy’s double alternant, a general determinant evaluation formula is established. Several interesting determinant identities are derived as consequences by means of divided differences ..."
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Dedicated to my friend Pier Vittorio Ceccherini on the occasion of his 65th birthday Abstract. As an extension of Cauchy’s double alternant, a general determinant evaluation formula is established. Several interesting determinant identities are derived as consequences by means of divided differences. Key words. Cauchy’s double alternant, Divided differences, Symmetric functions. AMS subject classifications. 15A15, 15A18.
Decoding by Linear Programming
, 2004
"... This paper considers the classical error correcting problem which is frequently discussed in coding theory. We wish to recover an input vector f ∈ Rn from corrupted measurements y = Af + e. Here, A is an m by n (coding) matrix and e is an arbitrary and unknown vector of errors. Is it possible to rec ..."
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Cited by 1399 (16 self)
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to recover f exactly from the data y? We prove that under suitable conditions on the coding matrix A, the input f is the unique solution to the ℓ1minimization problem (‖x‖ℓ1:= i xi) min g∈R n ‖y − Ag‖ℓ1 provided that the support of the vector of errors is not too large, ‖e‖ℓ0: = {i: ei ̸= 0}  ≤ ρ · m
∂xi
"... We shall be concerned with smooth functions u: IR m ↦ → IR n. Their graphs thus live on the product space IR m × IR n. The independent and dependent variables will be denoted by x. = (x1,...,xm) and u. = (u1,...,un). 1 Flow of a vector field. Let v be a smooth vector field on the product space IR m ..."
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We shall be concerned with smooth functions u: IR m ↦ → IR n. Their graphs thus live on the product space IR m × IR n. The independent and dependent variables will be denoted by x. = (x1,...,xm) and u. = (u1,...,un). 1 Flow of a vector field. Let v be a smooth vector field on the product space IR
∂xi
"... Abstract. In the present paper we study the transformations for the coefficients of an Nlinear connection (definition 1.1) on the tangent bundle of order two, T 2M, by a transformation of a nonlinear connection in T 2M. We prove that the set T of these transformations together with composition of ..."
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linear connections on tangent bundle of order two Let M be a real C∞manifold with n dimensions and (T 2M,pi,M) its 2tangent bundle, [1]. The local coordinates on 3ndimensional manifold T 2M are denoted by (xi, y(1)i, y(2)i) = (x, y(1), y(2)) = u, (i = 1, 2,...n).
∂xi
, 2005
"... Abstract. We offer a new method of reduction for a system of point vortices on a plane and a sphere. This method is similar to the classical node elimination procedure. However, as applied to the vortex dynamics, it requires substantial modification. Reduction of four vortices on a sphere is given i ..."
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’ motion on a plane. A more complete account can be found in [1, 2], where the hydrodynamic assumptions are also given, under which these equations are valid. The equations of motion of n point vortices with Cartesian coordinates (xi, yi)
∂xi
, 2005
"... We describe the sets on which difference of solutions of the gas dynamics equation satisfy some special conditions. By virtue of nonlinearity of the equation the sets depend on the solution gradient quantity. We show doubleended estimates of the given sets and some properties of these estimates. Co ..."
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. Copyright © 2006 V. A. Klyachin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 1. Main results Consider the gas dynamics equation n
Decoding Reed Solomon Codes beyond the ErrorCorrection Bound
, 1997
"... We present a randomized algorithm which takes as input n distinct points f(xi; yi)g n i=1 from F \Theta F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points in a ..."
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Cited by 274 (18 self)
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We present a randomized algorithm which takes as input n distinct points f(xi; yi)g n i=1 from F \Theta F (where F is a field) and integer parameters t and d and returns a list of all univariate polynomials f over F in the variable x of degree at most d which agree with the given set of points
Towards a Library for
 Process Programming, in Business Process Management. Springer LNCS 2678
, 2003
"... f7oN xi'r o^s IV: ..."
(xi − E)
"... In statistical analysis of measurement results, it is often necessary to compute the range [V, V] of the population variance V = 1 n · n∑ ..."
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In statistical analysis of measurement results, it is often necessary to compute the range [V, V] of the population variance V = 1 n · n∑
Results 1  10
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