Relationship between Pollen Counts and Weather Variables in East-Mediterranean Coast of Turkey

Background: Aeroallergen sampling provides information regarding the onset, duration and severity of the pollen season that clinicians use to guide allergen selection for skin testing and treatment

GENERALIZATIONS OF SOME RESULTS ON GENERALIZED POLYNOMIAL IDENTITIES

In this work, our aim is to generalize some of the results in [1] and [5]. Precisely, we extend the result in [1] on commuting values of the same generalized derivations to the different generalized derivations case by a short proof. Also as an application, we extend a result in [5] on images of a linear map with derivations to generalized derivations case

Generalized skew derivations with centralizer conditions on multilinear polynomials

Let R be a noncommutative prime ring of characteristic not 2 with extended centroid C, the maximal right ring of quotients Q and a nonzero generalized skew derivation d. Assume that f (X-1, center dot center dot center dot ,X-n) is amultilinear polynomial over C that is not central-valued on R and f (R) is the set of all evaluations of the multilinear polynomial f (X-1, center dot center dot center dot ,X-n) in R. Denote the set S := {delta(u)u | u is an element of f (R)}. The goal of the paper is to study C-R(S), the centralizer of S in R. To be precise, given a noncentral element b is an element of R it is proved that if b is an element of C-R(S), i.e.

Noncommutative higher commutators

Let A be a unital algebra over a field of characteristic different from 2. The main goal of this work is to characterize higher commutators of A. In particular, we show that if H is a noncommutative higher commutator of A and contains the unity, then H is equal to either A or [A, A]. As a result, we prove that if there exist x, y is an element of A such that 1 = [x, y], then the only higher commutators of A are A and [A, A]. We also consider the structure of noncommutative Lie ideals of the form [U, A], where U is a Lie ideal of A, and show that if L = [U, A] is noncommutative and contains the unity, then L = [A, A] and [A, A] subset of U.(c) 2021 Published by Elsevier Inc