Suppose that the inverse image of the zero vector by a continuous map f : R → R has an isolated point P . The existence of a continuous map g which approximates f but is nonvanishing near P is equivalent to a topological property we call “locally inessential,” generalizing the notion of index zero for vector fields, the q = n case. For dimensions n, q where πn−1(Sq−1) is trivial, every isolated...

In this note we give an extended version of Combinatorial Nullstellensatz, with weaker assumption on nonvanishing monomial. We also present an application of our result in a situation where the original theorem does not seem to work.

In this note it is observed that nonvanishing of a generalized LittlewoodRichardson coefficient of any type can be decided in polynomial time assuming the conjecture in [2, 6] that the coefficients of the associated stretching quasi-polynomial are nonnegative.

how to cite this article: fayyazi a, kheizrian l, kheradmand z, damadi s, khajeh a. evaluation of the young children with neurodevelopmental disability: a prospective study at hamadan university of medical sciences clinics. iran j child neurol. 2013 winter; 7 (1):29-33.   objective developmental impairment is a common problem in children health that occurs in approximately 5–10% of the childhoo...

Inspired by Sun’s breakthrough in establishing the nonvanishing hypothesis for Rankin-Selberg convolutions for the groups GLn(R)×GLn−1(R) and GLn(C)×GLn−1(C), we confirm it for GLn(C)×GLn(C) at the central critical point.