The recursive algorithm of a (fast) discrete wavelet transform, as well as its generalizations, can be described as repeated applications of block-Toeplitz operators or, in the case of periodized wavelets, multiplications by block circulant matrices. Singular values of a block circulant matrix are the singular values of some matrix trigonometric series evaluated at certain points. The norm of a...

Recently 4-point correlation functions of axion and dilaton fields in type IIB SUGRA on AdS5 × S 5 were computed [1]. We reproduce from a CFT point of view all power law singular terms in these AdS 4-point amplitudes. We also calculate a corresponding 4-point function in the weak coupling limit, g YMN → 0. Comparison reveals the existence of a primary operator that contributes to these same sin...

We explore the connections between singular Weyl–Titchmarsh theory and the single and double commutation methods. In particular, we compute the singular Weyl function of the commuted operators in terms of the original operator. We apply the results to spherical Schrödinger operators (also known as Bessel operators). We also investigate the connections with the generalized Bäcklund–Darboux trans...

We show the existence of positive solutions for a class of singular elliptic systems with convection term. The approach combines sub and supersolution method with the pseudomonotone operator theory and perturbation arguments involving singular terms. 2000 Mathematics Subject Classi…cation: 35J50, 35J60, 35J75

Consistent with a holistic perspective emphasizing the integration of multiple individual characteristics within child systems, it was hypothesized that subgroups of anxious solitary (AS) children characterized by agreeableness, behavioral normality, attention-seeking-immaturity, and externalizing behaviors would demonstrate heterogeneity in peer relations and dyadic friendships. Sociometrics w...

The topic of this paper is formal solutions of linear dierential equations with formal power series coeecients. The method proposed for computing these solutions is based on factorization of diierential operators. The notion of exponential parts is introduced to give a description of factorization properties and to characterize the formal solutions. The algorithms will be described and their im...

Microlocal analysis of a seismic linearized inverse problem. Abstract: The seismic inverse problem is to determine the wavespeed c(x) in the interior of a medium from measurements at the boundary. In this paper we analyze the linearized inverse problem in general acoustic media. The problem is to nd a left inverse of the linearized forward map F, or, equivalently, to nd the inverse of the norma...

In this paper, the dierential transform method (DTM) is applied to the Fisherequation. This method can be used to obtain the exact solutions of Fisherequation. Finally, we give some examples to illustrate the suciency of themethod for solving such nonlinear partial dierential equations. These resultsshow that this technique is easy to apply.

In this paper, a technique generally known as meshless numerical scheme for solving fractional dierential equations isconsidered. We approximate the exact solution by use of Radial Basis Function(RBF) collocation method. This techniqueplays an important role to reduce a fractional dierential equation to a system of equations. The numerical results demonstrate the accuracy and ability of this me...

Let b ∈ BMO(Rn) and T be the Calderón–Zygmund singular integral operator. The commutator [b,T ] generated by b and T is defined by [b,T ] f (x) = b(x)T f (x)−T (b f )(x). By a classical result of Coifman et al [6], we know that the commutator is bounded on Lp(Rn) for 1 < p < ∞. Chanillo [1] proves a similar result when T is replaced by the fractional integral operators. In [9], the boundedness ...