It is well known that the spread of cancer or tumor growth increases in polluted environments. In this paper, the dynamic behavior of the cancer model in the polluted environment is studied taking into consideration the delay in clearance of the environment from their contamination. The set of differential equations that simulates this epidemic model is formulated. The existence, uniqueness, and the bound of the solution are discussed. The local and global stability conditions of disease-free and endemic equilibrium points are investigated. The occurrence of the Hopf bifurcation around the endemic equilibrium point is proved. The stability and direction of the periodic dynamics are studied. Finally, the paper is ended with a numerical simul

This study has contributed to understanding a delayed prey-predator system involving cannibalism. The system is assumed to use the Holling type II functional response to describe the consuming process and incorporates the predator’s refuge against the cannibalism process. The characteristics of the solution are discussed. All potential equilibrium points have been identified. All equilibrium points’ local stability analyses for all time delay values are investigated. The system exhibits a Hopf bifurcation at the coexistence equilibrium, which is further demonstrated. The center manifold and normal form theorems for functional differential equations are then used to establish the direction of Hopf bifurcation and the stability of the per

Stylistics represents a modern approach in understanding the literary text through the linguistic patterns that form it. The distinctive phenomena that the text includes constitute special features in it. As well as exploring its aesthetic aspects through description and analysis at the same time. The close link between stylistics and linguistics made stylistics occupy a prominent place in modern literary criticism.
In this regard, we do not want to dwell on the different directions of stylistics. Rather, we will prolong the discussion in the study of the style as a (deviation. Aversion) from the original. Because this trend plays on the chord of the paradox between the surface structure and the deep structure, especially when the sur

A case of angiolymphoid hyperplasia with eosinophilia (ALH) is reported in a 42-year-old woman who developed multiple nodules behind the ear. Angiolymphoid hyperplasia with eosinophilia usually occurs on the head and neck of young adults and is more common in women than in men. Characteristic histologic features of ALH present in this case included proliferation of thick-walled blood vessels lined by prominent endothelial cells, infiltration of the interstitium by chronic inflammatory cells (mainly eosinophils), and presence of lymphoid follicles with germinal centers. The patient referred for surgeon for complete excision. in this context , cases previously described in the literature, and the differential diagnosis of ALH are discussed

A particular solution of the two and three dimensional unsteady state thermal or mass diffusion equation is obtained by introducing a combination of variables of the form,
η = (x+y) / √ct , and η = (x+y+z) / √ct, for two and three dimensional equations
respectively. And the corresponding solutions are,
θ (t,x,y) = θ₀ erfc (x+y)/√8ct and θ( t,x,y,z) =θ₀ erfc (x+y+z/√12ct)

Every body has a size and mass that distinguishes it from others and makes it different from others. Some of these bodies are huge and large in size, and some are small and light in weight. Among these masses and bodies are some that are dealt with by their size and weight, each according to its quantity, weight, and cheapness. This is why they created quantities by which these weights and quantities could be estimated, so they used measures and weights for that. Objectives: The research aims to know some measures and weights, such as the wife’s maintenance, the amount of zakat, etc.I found it to be a widely spread topic, and widely used in the folds of jurisprudence. During my reading of jurisprudence books, I found jurists using many qu

The research aims to develop physical exercises with auxiliary training tools that work to develop the explosive power of the arms and legs, and then find out their effect on the accuracy of shooting from free throw and correction from jumping of advanced basketball players, as the researchers found a problem that these players have weakness in the skill of throwing Free throwing and shooting by jumping calculated with two points as a result of adopting unhealthy physical and technical positions, which led to a lack of focus and accuracy, and thus negatively affected the performance technique of free throw and jump shot, as most teams use traditional exercises without the use of auxiliary training tools, and this topic gave researchers the

Polish Academy of Sciences

In this study, low cost biosorbent ̶inactive biomass (IB) granules (dp=0.433mm) taken from drying beds of Al-Rustomia Wastewater Treatment Plant, Baghdad-Iraq were used for investigating the optimum conditions of Pb(II), Cu(II), and Ni(II) biosorption from aqueous solutions. Various physico-chemical parameters such as initial metal ion concentration (50 to 200 mg/l), equilibrium time (0-180 min), pH (2-9), agitation speed (50-200 rpm), particles size (0.433 mm), and adsorbent dosage (0.05-1 g/100 ml) were studied. Six mathematical models describing the biosorption equilibrium and isotherm constants were tested to find the maximum uptake capacities: Langmuir, Freundlich, Redlich–Peterson, Sips, Khan, and Toth models. The best fit to the P