About the space $∩l_{p}$, p > 0

On the Performance of Sparse Recovery via L_p-minimization (0<=p <=1)

It is known that a high-dimensional sparse vector x∗ in R can be recovered from low-dimensional measurements y = Ax∗ where Am×n(m < n) is the measurement matrix. In this paper, we investigate the recovering ability of `p-minimization (0 ≤ p ≤ 1) as p varies, where `p-minimization returns a vector with the least `p “norm” among all the vectors x satisfying Ax = y. Besides analyzing the performan...

THE SPACE Hp WITH 0<p<l

Comonotone Polynomial Approximation in L_p[-1, 1], 0 < p &le; &infin;

Let a function f 2 L p ?1; 1], 0 < p 1 have 1 r < 1 changes of monotonicity. For all suuciently large n, we construct algebraic polynomials p n of degree n which are comonotone with f, and such that kf ? p n k Lp?1; 1] C(r)! ' 2 (f; n ?1) p , where ! ' 2 (f; n ?1) p denotes the Ditzian-Totik second modulus of smoothness in L p metric.

0 Se p 20 02 GEOMETRY OF THE TETRAHEDRON SPACE

Let X be the space of all labeled tetrahedra in P. In [1] we constructed a smooth symmetric compactification X̃ of X. In this article we show that the complement X̃ r X is a divisor with normal crossings, and we compute the cohomology ring H(X̃ ;Q).

0 Se p 20 04 GEOMETRODYNAMICS : SPACETIME OR SPACE ?

The work in this thesis concerns the split of Einstein field equations (EFE’s) with respect to nowhere-null hypersurfaces, the GR Cauchy and Initial Value problems (CP and IVP), the Canonical formulation of GR and its interpretation, and the Foundations of Relativity. I address Wheeler’s question about the why of the form of the GR Hamiltonian constraint “from plausible first principles”. I con...