This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found the caustic for the certain function with the spreading of the critical points. Finally, as an application, we found the bifurcation solutions for the equation of sixth order with boundary conditions using the Lyapunov-Schmidt method in the variational case.

      This paper is concerned with the controllability of a nonlinear impulsive fractional integro-differential nonlocal control system with state-dependent delay in a Banach space. At first, we introduce a mild solution for the control system by using fractional calculus and probability density function. Under sufficient conditions, the results are obtained by means of semigroup theory and the Krasnoselskii fixed point theorem. Finally, an example is given to illustrate the main results.

The imbalances and economic problems which it face the countries, it is a result of international economic developments or changes or global crises such as deterioration in trade, sharp changes in oil prices, increasing global indebtedness, sharp changes in foreign exchange rates and other changes, all that, they affect the economic features of any country. and These influences vary from one country to another according to the rigidity of its economy and its potential in maneuvering with economic plans and actions that would reduce the impact or avoidance with minimal damage. Therefore, the countries  that  suffer from accumulated economic problems as a result of mismanagement and poor planning or suffe

Background : surface area anatomy is a proportional point to the retention of complete denture, in past there was no quantitative method to evaluate the surface area, nowadays the size and shape of maxillary arch is measured by different electronically and mathematical devices. A study was therefore, undertaken to measure surface area of upper dental cast that was taken by different final impressions. Materials and methods: twenty patients were examined. All of them had a healthy palate with no singe of injury, trauma, or deformity. Casts were taken by three different final impressions; zinc oxide, additional silicon, and poly ether. And two different devices were used; the computerized one and the Aluminum foil measure. Age, se

Background: Identification the relationship of pepsinogen test (pepsinogenI and I /pepsinogen II ratio) and gastric cancer patients make the gastric cancer early diagnosed and prolong the life surviving rate.
Patients and Methods: Serum pepsinogen I and pepsinogen II (PG I and PG I / PG II ratio) measured in 50 patients with gastric cancer ,30 gastritis patients diagnosed , and 16 healthy control by using enzyme immunoassay in those study groups, and the results of PG I and PG I / PG II ratio were comparing to 50 gastric cancer patients whom diagnosed histopathologically according the stomach regions, while the gastritis patients diagnosed endoscopically.
Results: This study showed that the age of pati

Over the last few years, there has been a worldwide increase in the use of composite materials for rehabilitation of deficient reinforced concrete structures. One important application of this technology is the use of Carbon Fiber Reinforced Polymer (CFRP) jacket to provide external confinement of reinforced concrete columns. Square concrete column specimens 100×100×1000 mm with concrete
compressive strength of about 30 and 50 MPa, steel fiber volume fraction 0%, 0.5%, 0.75%, and percentage of longitudinal reinforcement 2.01%, 3.14% and 4.52% were tested until failure in previous research. In this research seven tested columns were repaired and rehabilitated using one layer of CFRP flexible wraps and tested to determine their ultim

FG Mohammed, HM Al-Dabbas, Iraqi journal of science, 2018 - Cited by 6

The Coronavirus Disease (COVID-19) has recently emerged as a human pathogen caused by SARS-CoV-2 virus was first reported from Wuhan, China, on 31 December 2019. Upon study, it has been used molecular docking to binding affinity between COVID-19 protease enzyme and flavonoids with evaluations based on docking scores calculated by AutoDock Vina. Results showed that naringin suppressed COVID-19 protease, as it has the highest binding value than other flavonoids including quercetin, hesperetin, garcina and naringenin. An important finding in this study is that naringin with neighboring poly hydroxyl groups can serve as inhibitors of COVID-19 protease bind to the S pocket of protein, it is shown that residues His163, Glu166, Asn142, His41and