We get an upper bound of O(x 5=14+o(1)) on the numberof Carmichael numbers x with exactly three prime factors.

The aim of the present work is to introduce the concept of $lambda _{r}$-almost convergence of sequences. We define the spaces $fleft( lambda _{r}right) $ and $f_{0}left( lambda _{r}right) $ of $ lambda _{r}$-almost convergent and $lambda _{r}$-almost null sequences. We investigate some inclusion relations concerning those spaces with examples and we determine the $beta $- and $gamma $-duals of...

The temporal waveform of neural activity is commonly estimated by low-pass filtering spike train data through convolution with a gaussian kernel. However, the criteria for selecting the gaussian width sigma are not well understood. Given an ensemble of Poisson spike trains generated by an instantaneous firing rate function lambda(t), the problem was to recover an optimal estimate of lambda(t) b...

We get an upper bound ofO(x5/14+o(1)) on the number of Carmichael numbers ≤ x with exactly three prime factors.

Numerical evidence relevant to the evaluation of the constant κ3 in the conjectural distribution of three-prime Carmichael numbers of Granville and Pomerance (2001) is summarised.

We prove that when (a, m) = 1 and a is a quadratic residue mod m, there are infinitely many Carmichael numbers in the arithmetic progression a mod m. Indeed the number of them up to x is at least x1/5 when x is large enough (depending on m). 2010 Mathematics subject classification: primary 11N25; secondary 11A51.

‎This paper deals with the singular Sturm-Liouville expressions‎ ‎$ ‎ell y =‎ -‎y''+q(x)y=lambda y‎ ‎$‎ ‎on a finite interval‎, ‎where the potential function $q$ is real and‎ ‎has a singularity inside the interval‎. ‎Using the asymptotic estimates of a‎ ‎spectral fundamental system of solutions of Sturm-Liouville‎ ‎equation‎, ‎the asymptotic form of the solution of the‎ ‎equation (0.1) and the ...

in this paper, we investigate the existence of positive solutions for the ellipticequation $delta^{2},u+c(x)u = lambda f(u)$ on a bounded smooth domain $omega$ of $r^{n}$, $ngeq2$, with navier boundary conditions. we show that there exists an extremal parameter$lambda^{ast}>0$ such that for $lambda< lambda^{ast}$, the above problem has a regular solution butfor $lambda> lambda^{ast}$, the probl...