We prove a “local” Tb Theorem for square functions, in which we assume only Lq control of the pseudo-accretive system, with q > 1. We then give an application to variable coefficient layer potentials for divergence form elliptic operators with bounded measurable non-symmetric coefficients.

In this paper, we develop a general classification framework called Kullback-Leibler Boosting, or KLBoosting. KLBoosting has following properties. First, classification is based on the sum of histogram divergences along corresponding global and discriminating linear features. Second, these linear features, called KL features, are iteratively learnt by maximizing the projected Kullback-Leibler d...

We establish a strong comparison principle, as well as a weak comparison principle and a Hopf-type lemma, for elliptic solutions of the self-similar potential flow equation. A major difference from the steady case is that the coefficients of the equation depend on the potential function itself, besides its gradient. We employ the divergence structure and other features of the equation to derive...

A numerical homogenization procedure for elliptic differential equations is presented. It is based on wavelet decompositions of discrete operators in fine and coarse scale components followed by the elimination of the fine scale contributions. If the operator is in divergence form, this is preserved by the homogenization procedure. For periodic problems, results similar to classical effective c...

The linearization of products of wavefunctions of exactly solvable potentials often reduces to the generalized linearization problem for hypergeometric polynomials (HPs) of a continuous variable, which consists of the expansion of the product of two arbitrary HPs in series of an orthogonal HP set. Here, this problem is algebraically solved directly in terms of the coefficients of the second-ord...

Let Pn denote the set of all algebraic polynomials of degree at most n with real coefficients. Associated with a set of poles {a1, a2, . . . , an} ⊂ R\ [−1, 1] we define the rational function spaces Pn(a1, a2, . . . , an) := 8< : : f(x) = b0 + n X j=1 bj x− aj , b0, b1, . . . , bn ∈ R 9= ; . Associated with a set of poles {a1, a2, . . . } ⊂ R\[−1, 1] , we define the rational function spaces P(a...

Using direct numerical simulations, we calculate the rate of divergence of neighboring magnetic-field lines in different types of strong magnetohydrodynamic turbulence. In the static-magnetic-field approximation, our results imply that tangled magnetic fields in galaxy clusters reduce the electron diffusion coefficient and thermal conductivity by a factor of approximately 5-10, relative to thei...

ABSTRACT The domain partition for the construction of a natural base is presented in order to solve the inverse problem of absorption coefficient estimation from the available measurements (experimental noisy data) of transmitted radiation. Within the framework of Lebesgue measure, a family of reconstruction algorithms is constructed based on Bregman distances using a q-discrepancy functional. ...

We consider an N-dimensional real integral, indexed by a parameter that specifies the power of a Vandermonde determinant. For two particular values of the parameter, this integral arises from matrix integrals, over real symmetric and complex Hermitian N × N matrices. When it is normalized, it gives the expectation of an arbitrary power of the determinant. The results are given as finite summati...

We have reanalyzed the published optical absorption coefficient data for a-Si:H and introduced a divergence temperature, a new concept in the physics of these materials. Copyright © 1989 The American Physical Society URL: http://link.aps.org/abstract/PRB/v39/p1953 DOI: 10.1103/PhysRevB.39.1953 PACS: 78.50.Ge, 72.80.Ng