This article will introduce a new iteration method called the zenali iteration method for the approximation of fixed points. We show that our iteration process is faster than the current leading iterations  like Mann, Ishikawa, oor, D- iterations, and *-  iteration for new contraction mappings called  quasi contraction mappings. And we  proved that all these iterations (Mann, Ishikawa, oor, D- iterations and *-  iteration) equivalent to approximate fixed points of  quasi contraction. We support our analytic proof by a numerical example, data dependence result for contraction mappings type  by employing zenali iteration also discussed.

Seeds, beans, leaves, fruit peel and seeds of five plants (Ferula assa-foetida, Coffea robusta, Olea europaea, Punica granatum and Vitis vinifera, respectively) were extracted with four solvents (distilled water, 80% methanol, 80% acetone and a mixed solvent that included methanol, ethanol, acetone and n-butanol at proportions 7:1:1:1). Such manipulation yielded 20 extracts, which were phytochemically analyzed for total polyphenols (TP) and flavonoids (TF). The DPPH (2,2-diphenyl-1-picrylhydrazyl) radical scavenging activity (RSA) and DPP-4 (dipeptidyl peptidase-4) relative inhibition activity (RIA) were also assessed for each extract. The results revealed that mixed solvent extract of V.

A new class of thiadiazole /silica nanocomposites with chemical bonds between thiadiazole monomers and modified nanosilica surface were synthesized by free radical polymerization. Presence silica nanoparticles in the structure of  nanocomposite showed effectively improve the physical and chemical properties of Producing polymers. A nanocomposite material with feature properties comparison with their polymers, The structure and morphology of the synthesis materials were investigated by FT-IR spectrum which display preparation new thiadiazole compounds and polymerization monomers. FT-IR showed disappeared double bond (C=C) of monomers, due to produce long chains of thiadiazole polymers and nanocomposite. X-ray diffraction gave idea ab

Oxygen therapy (OT) is considered    an essential process for

survival for the i nfants with bronchiolitis > However, it may reach the status of being harmful when using it for along beriod . We , here, attempted to shed a light on relations between oxygen therapy duration(OTD)   and each of serum malondialdehyde (MDA) that is used as index for free radical generation , and serum albumin level , in infants with bronchiolitis . Our results   confirmed  that  (OTD) from (1-48) hr. was non effective,  while from 49 was very effective where a grave in crease in serum (MDA)level and a decrease in serum albumin concentration were observed during that time . The relation between age a

      In this study, we prove that let N be a fixed positive integer and R be a semiprime -ring with extended centroid . Suppose that additive maps  such that  is onto,  satisfy one of the following conditions  belong to Г-N- generalized strong commutativity preserving for short; (Γ-N-GSCP) on R   belong to Г-N-anti-generalized strong commutativity preserving for short; (Γ-N-AGSCP)  Then there exists an element  and  additive maps  such that  is of the form  and   when condition (i) is satisfied, and     when condition (ii) is satisfied   

Suppose R has been an identity-preserving commutative ring, and suppose V has been a legitimate submodule of R-module W. A submodule V has been J-Prime Occasionally as well as occasionally based on what’s needed, it has been acceptable: x ∈ V + J(W) according to some of that r ∈ R, x ∈ W and J(W) an interpretation of the Jacobson radical of W, which x ∈ V or r ∈ [V: W] = {s ∈ R; sW ⊆ V}. To that end, we investigate the notion of J-Prime submodules and characterize some of the attributes of has been classification of submodules.

     Suppose that F is a reciprocal ring which has a unity and suppose that H is an F-module. We topologize La-Prim(H), the set of all primary La-submodules of H , similar to that for FPrim(F), the spectrum of fuzzy primary ideals of F, and examine the characteristics of this topological space. Particularly, we will research the relation between La-Prim(H) and La-Prim(F/ Ann(H)) and get some results.

A submodule Ϝ of an R-module Ε is called small in Ε if whenever  , for some submodule W of Ε , implies  . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if  , such that  , then  , where  is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .

         The main goal of this paper is to give  a new generalizations for two important classes in the category of modules, namely the class of small submodules and the class of hollow modules. They are purely small submodules and purely hollow modules respectively. Various properties of these classes of modules are investigated. The relationship between purely small submodules and P-small submodules which is introduced by Hadi and Ibrahim, is studied. Moreover, another characterization of  purely hollow modules is considered.