This article examines and proposes a dietary chain model with a prey shelter and alternative food sources. It is anticipated that mid-predators' availability is positively correlated with the number of refuges. The solution's existence and exclusivity are examined. It is established that the solution is bounded. It is explored whether all potential equilibrium points exist and are locally stable. The Lyapunov approach is used to investigate the equilibrium points' worldwide stability. Utilizing a Sotomayor theorem application, local bifurcation is studied. Numerical simulation is used to better comprehend the dynamics of the model and define the control set of parameters.

The necessary optimality conditions with Lagrange multipliers  are studied and derived for a new class that includes the system of Caputo–Katugampola fractional derivatives to the optimal control problems with considering the end time free. The formula for the integral by parts has been proven for the left Caputo–Katugampola fractional derivative that contributes to the finding and deriving the necessary optimality conditions. Also, three special cases are obtained, including the study of the necessary optimality conditions when both the final time  and the final state  are fixed. According to convexity assumptions prove that necessary optimality conditions are sufficient optimality conditions.

     The scientific and technological developments and their practical applications in all fields of life in general and in the education field in specific have led to the emergence of variables in the educational structure, teaching methods and in education in their modern form which is consistent in its entirety with    the spirit of the age. We today live the age of knowledge increase full of wide ranging scientific and technological developments. Thus life demands human capabilities of a special kind able to develop and innovate. Here the increasing significance emerges for taking care of the human powers through educational systems much different from those current traditional systems.  System

In this work, study the optical properties of composites consisting of poly Methyl Methacrylate and Berry Paper Mulberry. The samples of composites were prepared using casting method .The Berry Paper Mulberry (BPM) was added by different concentrations are (0, 2, 4 and 6)wt.%. The optical properties of composites have been studied in the wavelength range (200-800)nm. The absorption coefficient ,energy gap, refractive index, extinction coefficient and dielectric constants have been determined. The results show that the optical constants change with increase of BPM concentrations .

The hydatid materials were collected and studied, so they were contained 50 fertile human hydatid cases {33 (66%) females and 17 (34%) males}. They were collected from Al-Ramadi General Hospital during the period from December, 2003 to July, 2004 .Cysts were observed in 40 (80%) from the liver, 5 (10%) from the lungs, 3 (6%) from the kidney and 2 (4%) cysts from urinary bladder. The specimens were taken from patients of different ages. The in vitro viability of protoscoleces was assessed on the basis of flame cell activity and eosein exclusion, which were considered as criteria to determine the death or viability of protoscoleces. In addition to this movement (flame cell activity), another motility like constriction – relaxatio

The local authority represented by the Provincial Council and the administrative units thereof has legislative and supervisory functions which are in the administration and supervision of the local public utilities as provided for by the laws in force. The subject of the interactive relationship between the federal authority and the provincial councils not organized in one of the main problems that accompanied the emergence and application of decentralized system Iraq after 2003, which began since the writing of the Constitution in force for the year 2005 and the law of the provinces No. 21 of 2008 This law has been subjected to political recordings that eventually led to the appearance of this consensus image. The weakness of the legisl

This study concerns the removal of a trihydrate antibiotic (Amoxicillin) from synthetically contaminated water by adsorption on modified bentonite. The bentonite was modified using hexadecyl trimethyl ammonium bromide (HTAB), which turned it from a hydrophilic to a hydrophobic material. The effects of different parameters were studied in batch experiments. These parameters were contact time, solution pH, agitation speed, initial concentration (C0) of the contaminant, and adsorbent dosage. Maximum removal of amoxicillin (93 %) was achieved at contact time = 240 min, pH = 10, agitation speed = 200 rpm, initial concentration = 30 ppm, and adsorbent dosage = 3 g bentonite per 1L of pollutant solution. The characterization of the adsorbent, modi

Endophytic fungi live inside plants or any part of them without creating any visible pathogenic signs. Endophytic fungi are found within medicinal plants and have shown strong biologic activity, such as anticancer and antioxidant activities, as well as producing extracellular enzymes. In this study, different fungal strains were isolated from the leaves of the medicinal plant Ziziphus spina, including Aspergillus flavus, Aspergillus fumigatus, Aspergillus niger, Cladosporium sp., Rhizopus sp., and Mucor sp. Extracellular enzymes have been quantified using agar plate-based methods in which fungi were grown in specified growth media to detect the enzymes produced. The results showed that A. niger has the highest ability to produce amy

problems with its unobvious effect on scientific creativity and information. Problem solving is one of main goals of researchers because it develops their right logical thinking methods. The present study aims at measuring logical thinking among female it structures in the university mea swing problem solving among them ,identifying statically differences significance in logical thinking among female instructors in the university according to (Specialization Variable), identifying differences significance in problem Solving among female instructions in the university according to ( Specialization Variable) and identifying the Correlation between logical thinking and problem solving among female instructors in the university. The sample c