For a compact subset K of the complex plane C, let C(K) denote algebra continuous functions on K. an open U?K, A(K,U)?C(K) be that are analytic in U. We show there exists ??A(K,U) so each f?A(K,U) can uniformly approximated by {pn+qn?} K, where pn and qn polynomials z. In particular, ? chosen as Cauchy transform finite positive measure ? compactly supported C?U. Recent developments capacity pro...

partial frames provide a rich context in which to do pointfree structured and unstructured topology. a small collection of axioms of an elementary nature allows one to do much traditional pointfree topology, both on the level of frames or locales, and that of uniform or metric frames. these axioms are sufficiently general to include as examples bounded distributive lattices, $sigma$-frames, $ka...

Hashing, which involves learning binary codes to embed high-dimensional data into a similarity-preserving low-dimensional Hamming space, is often formulated as linear dimensionality reduction followed by binary quantization. Linear dimensionality reduction, based on maximum variance formulation, requires leading eigenvectors of data covariance or graph Laplacian matrix. Computing leading singul...