We establish certain ‘homological properties’ of the stable Higson corona used by Emerson and Meyer to study the Dirac-dual-Dirac approach to the Baum-Connes conjecture [5]. These are used to obtain explicit isomorphisms between the K-theory of the stable Higson corona of certain spaces X and the topological K-theory of natural geometric boundaries of X. This is sufficient to give a simple proo...

Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarisation to the Hilbert scheme. The Baum Fulton Macpherson GRR Theorem enables us to show that on any flat, proper, local complete intersection family the restriction of the extension and the original CM sheaf are isomorphic (under a mild hypothesis on the base). As a consequence the CM stability impl...

Let {Xni , i≥ 1,n≥ 1} be an array of rowwise ρ̃-mixing random variables. Some sufficient conditions for complete convergence for weighted sums of arrays of rowwise ρ̃-mixing random variables are presented without assumptions of identical distribution. As applications, the Baum and Katz type result and the Marcinkiewicz-Zygmund type strong law of large numbers for sequences of ρ̃-mixing random vari...

The complete convergence for pairwise negative quadrant dependent PNQD random variables is studied. So far there has not been the generalmoment inequality for PNQD sequence, and therefore the study of the limit theory for PNQD sequence is very difficult and challenging. We establish a collection that contains relationship to overcome the difficulties that there is no general moment inequality. ...

THIS IS AN UPDATED VERSION OF THE ORIGINAL PAPER Welch and Sidelnikov have obtained lower bounds on the maximum nontrivial correlations of complex signal sets constrained to have uniform signal energy. These results have long been used as a benchmark for testing the merit of signal sets, e.g., in the design of good CDMA sequence families. The Welch lower bound is generalized here to allow for a...

Columnar Oriented Database is an enhance approach to service to service the needs of Business Intelligence. A Columnar Oriented Database Management system that stores content by columns rather than the row. This type of data differs from traditional database with regards to performance, storage requirements and easy to modification of the schema. One of the major advantage of column based datab...

Based on the Cayley, Grothendieck, Knudsen Mumford theory of determinants we extend the CM polarisation to the Hilbert scheme. The Baum Fulton Macpherson GRR Theorem enables us to show that on any flat, proper, local complete intersection family the restriction of the extension and the original CM sheaf are isomorphic (under a mild hypothesis on the base). As a consequence the CM stability impl...

We study several duality isomorphisms between equivariant bivariant K-theory groups, generalising Kasparov’s first and second Poincaré duality isomorphisms. We use the first duality to define an equivariant generalisation of Lefschetz invariants of generalised self-maps. The second duality is related to the description of bivariant Kasparov theory for commutative C∗-algebras by families of elli...

This paper revisits the characteristics of windowing techniques with various window functions involved, and successively investigates spectral leakage mitigation utilizing Welch method. The discrete Fourier transform (DFT) is ubiquitous in digital signal processing (DSP) for spectrum analysis can be efficiently realized by fast (FFT). sampling will result distortion thus may cause unpredictable...