‎Let $p(z)$ be a polynomial of degree $n$ and for a complex number $alpha$‎, ‎let $D_{alpha}p(z)=np(z)+(alpha-z)p'(z)$ denote the polar derivative of the polynomial p(z) with respect to $alpha$‎. ‎Dewan et al proved‎ ‎that if $p(z)$ has all its zeros in $|z| leq k, (kleq‎ ‎1),$ with $s$-fold zeros at the origin then for every‎ ‎$alphainmathbb{C}$ with $|alpha|geq k$‎, ‎begin{align*}‎ ‎max_{|z|=...

In 1993 Stanley showed that if a simplicial complex is acyclic over some field, then its face poset can be decomposed into disjoint rank \(1\) boolean intervals whose minimal faces together form subcomplex. further conjectured complexes with higher notion of acyclicity could in similar way using rank. We provide an explicit counterexample to this conjecture. also prove version the conjecture fo...

due to the presence of polyphenols and phthalides in kelussia odoratissima mozzaf (umbelliferae; k. odoratissima hereafter), this medicinal plant might be a robust in-feed additive to modulate lipid peroxidation in meat-type chickens. the present study evaluates antioxidative, antihyperlipidemic, and growth-promoting effects of k. odoratissima in meat-type chickens. in a 37-day trial (5-42 days...

Abstract. Given an undirected graph G, the classical Cheeger constant, hG, measures the optimal partition of the vertices into 2 parts with relatively few edges between them based upon the sizes of the parts. The wellknown Cheeger’s inequality states that 2λ1 ≤ hG ≤ √ 2λ1 where λ1 is the minimum nontrivial eigenvalue of the normalized Laplacian matrix. Recent work has generalized the concept of...

Cross-validation type of methods have been widely used to facilitate model estimation and variable selection. In this work, we suggest a new K-fold cross validation procedure to select a candidate 'optimal' model from each hold-out fold and average the K candidate 'optimal' models to obtain the ultimate model. Due to the averaging effect, the variance of the proposed estimates can be significan...