This paper contains two results related to the material in [2]. Suppose/is a one-one transformation of the open unit interval /" (where n^2) onto /". 1. If/ is absolutely measureable and £>0, then there is an absolutely measurable homeomorphism ç»t of /" onto /" such that m({x:f(x)^(pc(x) or f~'(x)^ 9'J1W})<£. where m denotes /»-dimensional Lebesgue measure. 2. Suppose p is either (1) a nonatom...

The fully developed speckle (multiplicative noise) naturally appears in coherent imaging systems, such as synthetic aperture radar. Since the speckle is multiplicative, it is difficult to interpret observed data. Total variation (TV) based variational models have recently been used in the removal of the speckle because of the strong edge preserving property of TV and reasonable computational co...

The Normalization transformation plays a key role in the compilation of Diderot programs. The transformations are complicated and it would be easy for a bug to go undetected. To increase our confidence in normalization part of the compiler we provide a formal analysis on the rewriting system. We proof that the rewrite system is type preserving, value preserving (for tensor-valued expressions), ...

On the one hand, we prove that the spaces of C 1 symplectomor-phisms and of C 1 volume-preserving diffeomorphisms both contain residual subsets of diffeomorphisms whose centralizers are trivial. On the other hand, we show that the space of C 1 diffeomorphisms of the circle and a non-empty open set of C 1 diffeomorphisms of the two-sphere contain dense subsets of diffeomorphisms whose centralize...

Privacy has become an important issue in the progress of data mining techniques. Many laws are being enacted in various countries to protect the privacy of data. This privacy concern has been addressed by developing data mining techniques under a framework called privacy preserving data mining. Presently there are two main approaches popularly used -data perturbation and secure multiparty compu...