This is a review article regarding the new types of Mucopolysacharidose disease and re­lated diagnostic tests. Recently has been found that Hurler's and Scheie's diseases are due to the deficiency of Alpha-Iduronidase and San­filippo's disease is due to Heparan-N-Sulphatase and N-Acetyl-Alpha-D-Glucosaminidase defici­ency. 

In this paper we study positive solutions to the following nonlocal system of equations: \begin{equation*} \left\{\begin{aligned} &(-\Delta)^s u = \frac{\alpha}{2_s^*}|u|^{\alpha-2}u|v|^{\beta}+f(x)\;\;\text{in}\;\mathbb{R}^{N}, v \frac{\beta}{2_s^*}|v|^{\beta-2}v|u|^{\alpha}+g(x)\;\;\text{in}\;\mathbb{R}^{N}, & \qquad u, \, >0\, \mbox{ in }\,\mathbb{R}^{N}, \end{aligned} \right. \end{equation*...

Defining a scale of $k$-modes the quantum fluctuations during inflation through dynamical horizon crossing condition $k = aH$ we go from physical $t$ variable to $k$ and solve equations cosmological first-order perturbations self consistently, with chaotic $\alpha$-attractor type potentials. This enables us study behaviour $n_{s}$, $r$, $n_{t}$ $N$ in $k$-space. Comparison our results low-$k$ r...

We give necessary and sufficient conditions for an orthogonal series to converge in the mean-squares a nonnegative function. present many examples applications, analysis probability. In particular, we Lancaster-type of expansion $% \sum_{n\geq 0}c_{n}\alpha _{n}(x)\beta _{n}(y)$ with two sets polynomials $\left\{ \alpha _{n}\right\} $ \beta means-squares bivariate study properties set $C(\alpha...