The cheif aim of the present investigation is to develop Leslie Gower type three species food chain model with prey refuge. The intra-specific competition among the predators is considered in the proposed model. Besides the logistic growth rate for the prey species, Sokol Howell functional response for predation is chosen for our model formulation. The behaviour of the model system thoroughly analyses near the biologically significant equilibria. The linear stability analysis of the equilibria is carried out in order to examine the response of the system. The present model system experiences Hopf bifurcation depending on the choice of suitable model parameters. Extensive numerical simulation reveals the validity of the proposed model.

Abstract Planetary nebulae (PN) represents the short phase in the life of stars with masses (0.89-7) M☉. Several physical processes taking place during the red giant phase of low and intermediates-mass stars. These processes include :1) The regular (early ) wind and the envelope ejection, 2) The thermal pulses during Asymptotic Giant Branch (AGB ) phase. In this paper it is briefly discussed how such processes affect the mass range of Planetary Nebulae(PN) nuclei(core) and their evolution, and the PN life time, and fading time for the masses which adopted. The Synthetic model is adopted. The envelope mass of star (MeN ) and transition time (ttr) calculated respectively for the parameter (MeR =1.5,2, 3×10-3 M☉). Another time scale is o

This paper shews how to estimate the parameter of generalized exponential Rayleigh (GER) distribution by three estimation methods. The first one is maximum likelihood estimator method the second one is moment employing estimation method (MEM), the third one is rank set sampling estimator method (RSSEM)The simulation technique is used for all these estimation methods to find the parameters for generalized exponential Rayleigh distribution. Finally using the mean squares error criterion to compare between these estimation methods to find which of these methods are best to the others

A simple, environmental friendly and selective sample preparation technique employing porous membrane protected micro-solid phase extraction (μ-SPE) loaded with molecularly imprinted polymer (MIP) for the determination of ochratoxin A (OTA) is described. After the extraction, the analyte was desorbed using ultrasonication and was analyzed using high performance liquid chromatography. Under the optimized conditions, the detection limits of OTA for coffee, grape juice and urine were 0.06 ng g−1, 0.02 and 0.02 ng mL−1, respectively while the quantification limits were 0.19 ng g−1, 0.06 and 0.08 ng mL−1, respectively. The recoveries of OTA from coffee spiked at 1, 25 and 50 ng g−1, grape juice and urine samples at 1, 25 and 50 ng mL

Islamic shrines architecture is one of the Islamic Architectural building types. It is called (Thresholds); (Atabat) in Arabic. Thoroughbred throughout the Islamic world from the east to west. In addition, it carries the style features and peculiarities of uniqueness from the rest of the types of Islamic architecture. By virtue of the particularity of its function as tomb for important person in Islamic history. Islamic shrines architecture has grown and evolved in started from the small shrines, and then taken to widen with the evolution of time in line with the value of the event and the rituals associated with it. Some of them to became centers of large cities of the largest in many parts of the Islamic world.

The paper deals with the study of the sciences of the Qur’an according to the interpreter, Ayatollah Sayyid Mahmoud al-Talaqani, a religious jihadist figure from Iran. He is the author of the exegesis (Ishraq from Al-Quran), which consists of six parts, which he wrote inside the prisons of the Shah and in exile. Mr. Al-Talaqani agreed with some of the commentators in his positions on the sciences of the Qur’an, and some of them disagreed with others.

The study included three topics, the definition of the personality of Imam al-Bazazi, his scientific biography, his elders, his writings, his students and his death, selected issues of his weightiness related to purity, and the Imam al-Bazazi is Muhammad ibn Muhammad ibnShihabibn Yusuf, known in al-Kardari al-Hanafi al-Balzazi. The other doctrines, the author relied in his book on the sources of the previous scholars of the Hanafis, and make them the basis in his book, the author did not adopt the definitions of language and terminology, and rarely mention the evidence Shariah adopted by scientists in their opinions, and limited to mention only opinions, In front of the first issue spotlessly water user, and the second issue that sleep l

In the present study, free convection heat and mass transfer of fluid in a square packed bed enclosure is numerically investigated. For the considered geometrical shape, the left vertical wall of enclosure was assumed to be kept at high temperature and concentration while the opposite wall was kept at low temperature and concentration with insulating both the top and bottom walls of enclosure. The Brinkman– Forchheimer extended Darcy model was used to solve the momentum equations, while the energy equations for fluid and solid phases were solved by using the local thermal non-equilibrium (LTNE) model.Computations are performed for a range of the Darcy number from 10-5 to 10-1, the porosity from 0.5 to 0.9, and buoyancy ratio from -15 t

In this study, the spreading of the pandemic coronavirus disease (COVID-19) is formulated mathematically. The objective of this study is to stop or slow the spread of COVID-19. In fact, to stop the spread of COVID-19, the vaccine of the disease is needed. However, in the absence of the vaccine, people must have to obey curfew and social distancing and follow the media alert coverage rule. In order to maintain these alternative factors, we must obey the modeling rule. Therefore, the impact of curfew, media alert coverage, and social distance between the individuals on the outbreak of disease is considered. Five ordinary differential equations of the first-order are used to represent the model. The solution properties of the system ar

Global warming has a serious impact on the survival of organisms. Very few studies have considered the effect of global warming as a mathematical model. The effect of global warming on the carrying capacity of prey and predators has not been studied before. In this article, an ecological model describing the relationship between prey and predator and the effect of global warming on the carrying capacity of prey was studied. Moreover, the wind speed was considered an influencing factor in the predation process after developing the function that describes it. From a biological perspective, the nonnegativity and uniform bounded of all solutions for the model are proven. The existence of equilibria for the model and its local stability is inves