In this work, byemploying the Leggett-Williams fixed point theorem, we study theexistence of at least three positive solutions of boundary valueproblems for system of third-order ordinary differential equationswith $(p_1,p_2,ldots,p_n)$-Laplacianbegin{eqnarray*}left { begin{array}{ll} (phi_{p_i}(u_i''(t)))'  +  a_i(t) f_i(t,u_1(t), u_2(t), ldots, u_n(t)) =0 hspace{1cm} 0  leq t leq 1, alpha_i u...

Let$ P_{n}(x)= sum_{i=0}^{n} A_{i}x^{i}$ be a random algebraicpolynomial, where $A_{0},A_{1}, cdots $ is a sequence of independent random variables belong to the domain of attraction of the normal law. Thus $A_j$'s for $j=0,1cdots $ possesses the characteristic functions $exp {-frac{1}{2}t^{2}H_{j}(t)}$, where $H_j(t)$'s are complex slowlyvarying functions.Under the assumption that there exist ...

We prove that given a measure preserving system \begin{document}$ (X,\mathcal{B},\mu,T_1,\dots, T_d) $\end{document} with commuting, ergodic transformations id="M2">\begin{document}$ T_i such id="M3">\begin{document}$ T_iT_j^{-1} are for all id="M4">\begin{document}$ i \neq j $\end{document}</i...

In this paper we develop a method to transfer density results for primitive automatic sequences logarithmic-density general sequences. As an application show that the logarithmic densities of any sequence along squares $(n^2)_{n\geq 0}$ and primes $(p_n)_{n\geq 1}$ exist are computable. Furthermore, give these subsequences criterion decide whether exist, in which case they also particular prime...

Let $P=(p_1, p_2, \dots, p_n)$ be a polygonal chain in $\mathbb{R}^d$. The stretch factor of $P$ is the ratio between total length and distance its endpoints, $\sum_{i = 1}^{n-1} |p_i p_{i+1}|/|p_1 p_n|$. For parameter $c \geq 1$, we call $c$-chain if $|p_ip_j|+|p_jp_k| \leq c|p_ip_k|$, for every triple $(i,j,k)$, $1 i<j<k n$. global property: it measures how close to straight line, involves al...

The purpose of this paper is to investigate the properties spectral and tiling subsets cyclic groups, with an eye towards set conjecture in one dimension, which states that a bounded measurable subset $\mathbb{R}$ accepts orthogonal basis exponentials if only it tiles by translations. This strongly connected its discrete counterpart, namely every finite group, tile. tools presented herein are r...