We show that, on the Riemann hypothesis, lim supX→∞I(X)/X2⩽0.8603, where I(X)=∫X2X(ψ(x)−x)2dx. This proves (and improves on) a claim by Pintz from 1982. also unconditionally that 1.86⋅10−4⩽I(X)/X2 for sufficiently large X, and I(X)/X2 has no limit as X→∞.

We consider the problem of estimating a function ( ) on the unit disk ( ): 2 + 2 1 , given a discrete and noisy data recorded on a regular square grid. An estimate of ( ) based on a class of orthogonal and complete functions over the unit disk is proposed. This class of functions has a distinctive property of being invariant to rotation of axes about the origin of coordinates yielding therefore...

We have already developed three kinds of time-varying complex AR (TV-CAR) parameter estimation algorithms for analytic speech signal, which are based on minimizing mean square error (MMSE), Huber's robust Mestimation and Instrumental Variable (IV) method. This paper presents novel robust TV-CAR model parameter estimation algorithms on the basis of a Generalized Least Square (GLS) and Extended L...

As processors evolve from simple scalar machines to more advanced designs using dynamic instruction scheduling, speed critical algorithms should be reexamined to ensure that the optimal strategy is being used. One important example of this class of algorithms is MPEG encoding. Although the Mean Absolute Distance approach is recognized in the literature as more eecient in terms of speed, our res...

In this paper, we propose a damage identification method based on minimum mean square error estimation for wind tunnel flexible plate condition monitoring system. Critical structural members of important equipment are large in size, and the measurement systems used to monitor their often complex. The proposed is squared estimator generalized likelihood ratio test. It introduced activation funct...