Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

The article emphasizes that 3D stochastic positive linear system with delays is asymptotically stable and depends on the sum of the system matrices and at the same time independent on the values and numbers of the delays. Moreover, the asymptotic stability test of this system with delays can be abridged to the check of its corresponding 2D stochastic positive linear systems without delays. Many theorems were applied to prove that asymptotic stability for 3D stochastic positive linear systems with delays are equivalent to 2D stochastic positive linear systems without delays. The efficiency of the given methods is illustrated on some numerical examples. HIGHLIGHTS Various theorems were applied to prove the asymptoti

the research ptesents a proposed method to compare or determine the linear equivalence of the key-stream from linear or nonlinear key-stream

In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact

Fourteen morphologically varied Ricinus communis L. seeds were collected from different localities in Egypt, El-Sudan and Saudi Arabia. Seed morphology and ITS barcoding analysis were performed to assess their diversity and phylogenetic relationship. Sequence’s alignment of nrITS region from different accessions display high levels of genetic similarities. Cluster analysis could not group different accessions according to their geographical distribution. Nevertheless, the genetic barcodes are interestingly matched with the morphological features of the Ricinus seeds. In conclusion, seed morphology proved to be a valuable tool in evaluating biodiversity and phylogenetic relationship in plant species with different loca

    The article analyzes the ideological and genre features of L. Ulitskaya's work "The Plague, or OOI in the City", examines the features of building an artistic whole, ways of creating images of characters and their characteristics, stylistic features of the work.

The experiment was carried out in the Department of Biology, College of Education for Pure Science –Ibn AL Haitham, University of Baghdad, Iraq, during the growing season 2017 – 2018. The objective was to find out the effect of foliar spraying of tryptophan and IQ COMBI nano fertilizer on cumin plants. The obtained results show that both tryptophan and IQ COMBI nano fertilizer increased plant height, root length, shoot dry weight, the content of nitrogen, phosphorus, potassium, protein percentage, no. compound umbel.plant-1, wt. seeds. plant-1. The optimum treatment combination was calculated as 30 mg.L-1 tryptophan, 1000mg.L-1 IQ COMBI nano fertilizer, which gave the highest values for most of the parameters studied

Moringa oleifera L. and red pomegranate extracts have been reported to inhibit gram-positive facultative anaerobe growth and inhibit the formation of biofilm on tooth surfaces. The current study aimed to assess the antibacterial effect of M. oleifera L. and red pomegranate extracts and their combinations against Porphyromonas gingivalis. The antimicrobial sensitivity, minimum inhibition concentrations (MIC), and minimum bactericidal concentrations after treatment with the aqueous extracts of M. oleifera L. and red pomegranate as well as their combination against clinically isolated P. gingivalis were determined using agar well diffusion and two-fold serial dilution. The anti-biofilm activity of the extracts and their combination was evaluat

Coupling reaction of 4-nitroaniline with 3-aminobenzoic acid provided the corresponding bidentate azo ligand. The prepared ligand was identified by Microelemental Analysis, 1H-NMR, FT-IR, and UV-Vis spectroscopic techniques. Treatment of the prepared ligand with Y(III) and La(III) metal ions in 1:3 M:L ratio in aqueous ethanol at optimum pH yielded a series of neutral complexes with the general formula of [M(L)3]. The prepared complexes were characterized by flame atomic absorption, Elemental Analysis (C, H, N), FT-IR, and UV-Vis spectroscopic methods, as well as conductivity measurements. The nature of the complexes formed were studied following the mole ratio and continuous variation methods; Beer's law obeyed over a concentration range o