We consider multipoint Padé approximation to Cauchy transforms of complex measures. We show that if the support of a measure is an analytic Jordan arc and if the measure itself is absolutely continuous with respect to the equilibrium distribution of that arc with Dini-smooth non-vanishing density, then the diagonal multipoint Padé approximants associated with appropriate interpolation schemes c...

The existing proofs of the Fundamental theorem of calculus for Lebesgue integration typically rely either on the Vitali–Carathéodory theorem on approximation of Lebesgue integrable functions by semi-continuous functions (as in [3, 9, 12]), or on the theorem characterizing increasing functions in terms of the four Dini derivates (as in [6, 10]). Alternatively, the theorem is derived using the Pe...

Local Regularity of the Complex Monge-Ampère Equation Yu Wang In this thesis, we study the local regularity of the complex Monge-Ampère equation, (√ −1∂∂̄u )n = fdx where √ −1∂∂̄u stands for the complex Hessian form and dx the Lebesgue measure. The underline idea of our work is to consider this equation as a full-nonlinear equation and apply modern theory and techniques of elliptic PDEs. Our main...

The trigonometric interpolants to a periodic function f in equispaced points converge if f is Dini-continuous, and the associated quadrature formula, the trapezoidal rule, converges if f is continuous. What if the points are perturbed? With equispaced grid spacing h, let each point be perturbed by an arbitrary amount ≤ αh, where α ∈ [0, 1/2) is a fixed constant. The Kadec 1/4 theorem of samplin...

1077-3142/$ see front matter 2011 Elsevier Inc. A doi:10.1016/j.cviu.2011.01.004 ⇑ Corresponding author. E-mail addresses: [email protected] (A. Del Bim Dini). In many real world applications, tracking must be performed reliably in real-time for sufficiently long periods where target appearance and motion may sensibly change from one frame to the following. In such non ideal conditions this...

A signed k-partite graph (signed multipartite graph) is a k-partite graph in which each edge is assigned a positive or a negative sign. If G(V1, V2, · · · , Vk) is a signed k-partite graph with Vi = {vi1, vi2, · · · , vini}, 1 ≤ i ≤ k, the signed degree of vij is sdeg(vij) = dij = d + ij − d − ij , where 1 ≤ i ≤ k, 1 ≤ j ≤ ni and d + ij(d − ij) is the number of positive (negative) edges inciden...

We consider inverse boundary value problems in Rn, n ≥ 3, for operators which may be written as first order perturbations of the Laplacian. The purpose is to obtain global uniqueness theorems for such problems when the coefficients are nonsmooth. We use complex geometrical optics solutions of Sylvester-Uhlmann type to achieve this. A main tool is an extension of the Nakamura-Uhlmann intertwinin...

and Applied Analysis 3 Definition 2.1. The trivial solution of system 2.2 is said to be globally exponentially stable, if there exist numbers λ > 0 and M 1 such that ∣∣x(t, t0, φ )∣∣ M∥∥φ∥∥e−λt, t 0, 2.3 whenever φ ∈ PC. Definition 2.2. V : −τ,∞ ×Rn → R is said to belong to the class ν0, ifV is continuous on each of the sets tk−1, tk × R, lim t,y → t− k ,x V t, y V tk, x exists, V t, x is local...

Downloading software via Web is a major solution for publishers to deliver their software products. In this context, user interfaces for software downloading play a key role. Actually, they have to allow usable interactions as well as support users in taking conscious and coherent decisions about whether to accept to download a software product or not. This paper presents different design alter...