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.

Background: Cancer is a lethal disease that results from a multifactorial process. Progression into carcinogenesis and an abnormal cell proliferation can occur due to the micro and macro environment as well as genetic mutations and modifications. In this review, cancer and the microbiota – mainly bacteria that inhabit the tumour tissue – have been discussed. The positive and negative impacts of the commensal bacteria on tumours being protective or carcinogenic agents, respectively, and their strategies have also been described. Methods: Related published articles written in English language were searched from Google Scholar, PubMed, Mendeley suggestions, as well as Google search using a combination of the keywords ‘Microbiota, commens

Background: The Covid-19 pandemic changed the world; its most important achievement for education was changing the approach from traditional to virtual education. The present study aimed to investigate the role of virtual education networks on mental health of students including personality, beliefs, scientific, and cultural dimensions, in selected countries.Methods: This was an exploratory and applied study. According to the phenomenology strategy, theoretical saturation occurred after 24 semi-structured and targeted qualitative interviews with teachers from Iran, Iraq, Syria and Lebanon, in 2023. Quantitative data was collected through a researcher-made online questionnaire with 423 participants. Teachers with at least a Bachelor’s degr

Understanding of in-situ stress profiles and orientations plays a vital role in designing a successful hydraulic fracturing treatment. This paper is an attempet to examine the effect of lithology and in situ stress on geometery of hydraulic fractures. A hydraulic fracturing design simulator software called FracproPT with various capabilities for designing most of hydraulic fracture was used for  simulate and optimize the hydraulic fracturing. For studying purpose,  three different cases of stress gradient contrast between different formations  are considered in this study (0.4, 0.5 and 0.75 psi/ft). The results obtained from the simulator showed that  lithologies surrounding the pay zone have an effect on the fracture

The presentwork is a theoretical study in the field of charged particle optics. It concentrates on the design of electrostatic enzil lens for focusing charge particles beams, using inverse method in designingthe electrostatic lens. The paraxial ray equation was solved to obtain the trajectory of the particles, the optical properties such as the focal length and spherical and chromatic aberration coefficients were determined. The shape of the electrode of the electrostatic lens were determined by solving poison equation and the results showed low values of spherical and chromatic aberrations, which are considered as good criteria for good design.

The fouling depositions of crude oil stream were studied theoretically in a shell and tube heat exchanger to investigate the effect of depositions on the heat transfer process. The employed heat exchanger was with steam flowing in the inner tubes and crude oil in the shell at different velocities and bulk temperatures. It is assumed that fouling occurs only on the heated stream side (crude oil). The analysis was carried out for turbulent flow heat transfer conditions with wide range of Reynolds number, bulk temperature and time. Many previously proposed models for fouling resistance were employed to estimate a new model for fouling rate. It is found that the fouling rate and consequently the heat transfer coefficient were affected by Rey

The research include a pulsed Nd: YAG Laser with (300µs) pulse duration in the TEM00 mode at (1.06µm) wavelength for energies between (0.5-3) J was employed to drill Brass material which is use in industrial applications. The process of drill was assisted by an electric field. This resulted in an increase in the hole aspect ratio by the value (45%) and decrease in the hole taper by the value (25%) of its value under ordinary drilling conditions using the same input energy.

Flow of water under concrete dams generates uplift pressure under the dam, which may cause the dam to function improperly, in addition to the exit gradient that may cause piping if exceeded a safe value. Cutoff walls usually used to minimize the effect of flow under dams. It is required to
1)minimize the flow quantity to conserve water in the reservoir, it is also required to
2)minimize the uplift pressure under the dam to maintain stability of the dam, and it is required to

3) minimize the exit gradient to prevent quick condition to occur at the toe of the dam where piping may occur and may cause erosion of the soil. Varying the angle of cutoff walls affects its influence on the factors aforementioned that are required to