design of crystal-like lattices can be achieved by using some net operations. hypothetical networks, thus obtained, can be characterized in their topology by various counting polynomials and topological indices derived from them. the networks herein presented are related to the dyck graph and described in terms of omega polynomial and piv polynomials.

for every $1leq s< n$, the $s^{th}$ derivative of a polynomial $p(z)$ of degree $n$ is a polynomial $p^{(s)}(z)$ whose degree is $(n-s)$. this paper presents a result which gives generalizations of some inequalities regarding the $s^{th}$ derivative of a polynomial having zeros outside a circle. besides, our result gives interesting refinements of some well-known results.

in this paper, the concept of canonical representation is proposed to find fuzzy roots of fuzzy polynomial equations. we transform fuzzy polynomial equations to system of crisp polynomial equations, this transformation is perform by using canonical representation based on three parameters value, ambiguity and fuzziness.

conclusions the results of this study in terms of personality disorders and types of used drugs were in accordance with the previous studies results. it is necessary to design appropriate treatment plans for medical treatment of those with personality disorders. results there was a significant correlation between stimulant use and histrionic personality disorder (p < 0.001) and antisocial and n...

We consider multivariate L2-approximation in reproducing kernel Hilbert spaces which are tensor products of weighted Walsh spaces and weighted Korobov spaces. We study the minimal worst-case error eL2−app,Λ(N, d) of all algorithms that use N information evaluations from the class Λ in the d-dimensional case. The two classes Λ considered in this paper are the class Λall consisting of all linear ...

We investigate a simple model that generates random partitions of the leaf set of a tree. Of particular interest is the reconstruction question: what number k of independent samples (partitions) are required to correctly reconstruct the underlying tree (with high probability)? We demonstrate a phase transition for k as a function of the mutation rate, from logarithmic to polynomial dependence o...

We propose a modiŽ cation of local polynomial time series regression estimators that improves efŽ ciency when the innovation process is autocorrelated. The procedure is based on a pre-whitening transformation of the dependent variable that must be estimated from the data. We establish the asymptotic distribution of our estimator under weak dependence conditions. We show that the proposed estima...

In this paper we derive convergence rates for Q-learning. We show an interesting relationship between the convergence rate and the learning rate used in Q-learning. For a polynomial learning rate, one which is 1/t at time t where ω ∈ (1/2, 1), we show that the convergence rate is polynomial in 1/(1− γ), where γ is the discount factor. In contrast we show that for a linear learning rate, one whi...

let $d$ be a digraph with skew-adjacency matrix $s(d)$. then the skew energyof $d$ is defined to be the sum of the norms of all eigenvalues of $s(d)$. denote by$mathcal{o}_n$ the class of digraphs on order $n$ with no even cycles, and by$mathcal{o}_{n,m}$ the class of digraphs in $mathcal{o}_n$ with $m$ arcs.in this paper, we first give the minimal skew energy digraphs in$mathcal{o}_n$ and $mat...