by the method of weight coefficients, techniques of real analysis andhermite-hadamard's inequality, a half-discrete hardy-hilbert-type inequalityrelated to the kernel of the hyperbolic cosecant function with the best possibleconstant factor expressed in terms of the extended riemann-zeta function is proved.the more accurate equivalent forms, the operator expressions with the norm,the reverses a...

By the method of weight coefficients, techniques of real analysis and Hermite-Hadamard's inequality, a half-discrete Hardy-Hilbert-type inequality related to the kernel of the hyperbolic cosecant function with the best possible constant factor expressed in terms of the extended Riemann-zeta function is proved. The more accurate equivalent forms, the operator expressions with the norm, the rever...

The relation of the Al-Alaoui pattern recognition algorithm to the boosting and bagging approaches to pattern recognition is delineated. It is shown that the Al-Alaoui algorithm shares with bagging and boosting the concepts of replicating and weighting instances of the training set. Additionally it is shown that the Al-Alaoui algorithm provides a Mean Square Error, MSE, asymptotic Bayesian appr...

In this paper, an efficient method to obtain the elements current distribution for a non uniformly spaced array is presented. For a given far field pattern, after sampling the array factor the proposed method uses the least mean square error technique to solve the system of equations rather than solving the previously published Legendre function method. It’s shown that the average side lob leve...

A new design for a double-tuned dynamic-angle-spinning (DAS) probe that employs a RF coil wrapped directly around the stator is presented. The increased filling factor of this design and the smaller RF coil result in improved sensitivity and facilitate the incorporation of ‘H decoupling capabilities. Since the RF coil is reoriented with the spinning sample, the pulse lengths and sensitivity var...

Special finite sums of the even powers of the cosecant and of the secant are studied, ∑ k csc (kπ/N) and ∑ k sec (kπ/N), with positive integers N ≥ 3,m and 1 ≤ k < N/2 . The main result of this article is that these power sums are even polynomials in N , of order 2m, whose coefficients are rational. The approach is based on new differential identities for the functions cscz and secz. The Mittag...

Many models have been developed to study the role of branching actin networks in motility. One important component of those models is the distribution of filament orientations relative to the cell membrane. Two mean-field models previously proposed are generalized and analyzed. In particular, we find that both models uniquely select for a dominant orientation pattern. In the linear case, the pa...