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)

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

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

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

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

New Azo compounds containing an 1,8-naphthalimide moiety were synthesized from 1, 8-naphthalic anhydride by a reaction with p-phenylenediamine or benzidine to produce 1,8-naphthalimide derivatives (1 or 2), which were converted to diazonium salt derivatives by using sodium nitrite and acetic acid at 0-5 áµ’C. The diazonium salt was subjected to a coupling reaction with different substituted phenol in alkaline media at 0-5 áµ’c to produce azo compound derivatives (3-14).

The New Azo compound derivatives (3-14) were identified by ¹H-NMR, ¹³C-NMR, and FTIR and by measuring characteristic physical properties and specific reactions. Also, the ability of the prepared azo compounds to work as acid-

When searching for an answer to the following question: What are the reasons for the reluctance of female physical education teachers in secondary schools to referee sports competitions according to the variable of years of service? It was found that the research aimed to reveal the differences between the opinions of the research sample of physical education teachers in secondary schools (girls) about refereeing sports competitions according to the variable of years of service. To achieve the research goal, it is assumed that there are significant differences between the average opinions of the research sample of female teachers and their reluctance and the reasons for the differences in the practice of refereeing sports competitions accor

The objective of this study is to evaluate the efficacy and safety of rowatinex and tamsulosin in the treatment of patients with ureteric stone.

Forty patients with ureteric stone ranged (4- 12) mm, were included in this study. They were randomized into two groups where the first group includes twenty patients treated with Rowatinex three times daily (Group 1), and the second group includes twenty patients treated with tamsulosin 0.4mg/day (Group 2). All patients were randomly assigned to receive the designed standard medical therapy for a maximum of 3 weeks.

Each group was given an antibiotic as prophylaxis and an injectable non-steroidal anti-inflammatory drug used on demand. At the outpatient clinic all subjects were a

The goal of this paper is to study dynamic behavior of a sporadic model (prey-predator). All fixed points of the model are found. We set the conditions that required to investigate the local stability of all fixed points. The model is extended to an optimal control model. The Pontryagin's maximum principle is used to achieve the optimal solutions. Finally, numerical simulations have been applied to confirm the theoretical results.