Abstract In this article, we have mainly focused on the uniqueness problem of an L-function L with an L-function or a meromorphic function f under the condition of sharing the sets, generated from the zero set of some strong uniqueness polynomials. We have introduced two new definitions, which extend two existing important definitions of URSM and UPM in the literature and the same have been used to prove one of our main results. As an application of the result, we have exhibited a much improved and extended version of a recent result of Khoai-An-Phuong [13]. Our remaining results are about the uniqueness of L-function under weighted sharing of sets generated from the zeros of a suitable strong uniqueness polynomial, which improve and extend some results in [12].

Resumen En este artículo nos hemos enfocado principalmente en el problema de unicidad de una L-función L con una L-función o una función meromorfa f bajo la condición de compartir los conjuntos, generados a partir del conjunto de ceros de algunos polinomios de unicidad fuerte. Hemos introducido dos definiciones nuevas, que extienden dos importantes definiciones existentes en la literatura de URSM y UPM, y las mismas han sido usadas para probar uno de nuestros resultados principales. Como una aplicación del resultado, exhibimos una versión mejorada y extendida de un resultado reciente de Khoai-An-Phuong [13]. Nuestros resultados restantes son sobre la unicidad de una L-función bajo la condición de compartir conjuntos pesados generados a partir de los ceros de un polinomio de unicidad fuerte apropiado, que mejora y extiende algunos resultados en [12].

Zn-ferrite nanoparticles were synthesized at room temperature by mechanical alloying the stoichiometric (1:1 mol%) mixture of ZnO and α-Fe2O3 powder under open air. Formation of both normal and inverse spinel ferrite phases was noticed after 30 minutes and 2.5 hours ball milling respectively and the content of inverse spinel phase increased with increasing milling time. The phase transformation kinetics towards formation of ferrite phases and microstructure characterization of ball milled ZnFe2O4 phases was primarily investigated by X-ray powder diffraction pattern analysis. The relative phase abundances of different phases, crystallite size, r.m.s. strain, lattice parameter change etc. were estimated from the Rietveld powder structure refinement analysis of XRD data. Positron annihilation lifetime spectra of all ball milled samples were deconvoluted with three lifetime parameters and their variation with milling time duration was explained with microstructural changes and formation of different phases with increase of milling time duration.

With the help of the notion of weighted sharing we investigate the uniqueness of meromorphic functions concerning three set sharing and significantly improve two results of Zhang [16] and as a corollary of the main result we improve a result of the present author [2] as well.

Con la ayuda del concepto de peso repartido, investigamos la unicidad de funciones meromorfas sobre un conjunto compartido y mejoramos significativamente dos resulta- dos de Zhang [16] y como corolario del resultado principal que mejoramos también el resultado de la autora [2]