A vector in a separable infinite dimensional Hilbert space is called disk-cyclic for bounded operator if the orbit α : 0, α∈;|∝| 1is dense in. The useful tool used to discover codisk-cyclic operation is called the disk-cyclic Criterion. In this paper we will show that some equivalent conditions of the

Computer modeling has been used to investing the Coulomb coupling parameter ?. The effects of the structure parameter K, grain charge Z, plasma density N, temperature dust grain Td, on the Coulomb coupling parameter had been studied. It was seen that the ? was increasing with increasing Z and N, and decrease with increasing K and T. Also the critical value of ? that the phase transfer of the plasma state from liquid to solid was studied.

The present study included the effect of chronic exposure for two concentrations of NaC? salt on the biology of fresh water zooplankton species Brachionus calyciflorus (from ^otifera). The concentrations 0.5 , 0.75%o were used for chronic exposure to investigate its effects on the life tables, range of the rate of expectation for further life and reproduction. The rotifer B. calyciflorus was sensitive to salinity and may tried to protect the species by increasing the size (2.22 ind./clutch lor control group and 2.9? for 0.5%o concentration) and number of clutches produced ?.1? clutch/female for control group and 2.9 ' ' ' for 0.75 %0 concentration) beside stimulation the animal to produce the first clutch of eggs earlier? ? small reduction

This study investigates the challenges encountered by first-grade intermediate students in learning the Arabic language. It aims to identify specific obstacles that hinder language acquisition and proficiency among this demographic. Through qualitative and quantitative methods, including surveys and interviews with students, teachers, and parents, the research highlights key issues such as limited vocabulary, difficulties in grammar, lack of engagement with the material, and inadequate teaching resources. The findings reveal a complex interplay between cognitive, social, and educational factors that contribute to these challenges. The study underscores the need for targeted interventions, such as enhanced pedagogical strategies and improved

Background: Osteoarthritis (OA) currently seems
inevitable and unavoidable for a large swath of the
population .its etiology relates to a strong ,but
complex ,non mendelian genetic basis ,combined
with mechanical and metabolic factors that cause
molecular alterations the end results of which
affect the whole joint .Glucosamine and
chondrotin sulfate alone or in combination may be
of benefit to a subgroup of individuals who have
knee pain due to OA.
Glucosamine has been shown to alter cartiage turn
over in patients with OA undergoing physical
training
Aim of the study: To find the validity of
glucosamine chondrotin sulfate in treatment of
grade 1 and 2 OA.
Methods: the sample of 280 patients

Distribution of light intensity in the flat photobioreactor for microalgae cultivation as a step design for production of bio-renewable energy was addressed in the current study. Five sizes of bioreactors with specific distances from the main light source were adopted as independent variables in experiential design model. The results showed that the bioreactor’s location according to the light source, determines the nature of light intensity distribution in the reactor body. However, the cross-section area plays an important role in determining the suitable location of reactor to achieve required light homogeneity. This area could change even the expected response of the light passing through the reactor if Beer-Lambert's law is adopted.