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

Geographic information system (GIS) is utilized in a variety of tasks such as, resource management, urban planning, emergency planning in case of accident, and rapid response etc. The aim of this study is to produce a digital map with the aid of GIS and a survey data. A survey data is conducted with Total Station technique on sanitary planning positions. The campus of Baghdad University is chosen to test the execution and accuracy of the results for sewer manholes locations. During the field survey, Total Station (Nikon Nivo) is used to identify the 3-D coordinates for each location. Finally, Geographical Information System (GIS) are utilized to present the digital map of the network sewer pipe line to the end users. Although Geographic Inf

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

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

One of the most important intellectual issues, which receive attention is the issue of modernity, it has occupied the scholars of all time. However, modern poetry used to have special care in Iraq and in the Arab countries .. it is not strange that the concept of modernity is linked to history .. or having history as the most important dimension of its dimensions .. because Arab poetry is historical and it is moving into an area of ​​the past that is still active in terms of language and literary image .. When some poets found that changing and modernizing poetry became a necessity of evolution, and one of the fundamentals of modernization, the cultural impact did not respond to the desire of poets, and their impulse in modern poetry

The food web is a crucial conceptual tool for understanding the dynamics of energy transfer in an ecosystem, as well as the feeding relationships among species within a community. It also reveals species interactions and community structure. As a result, an ecological food web system with two predators competing for prey while experiencing fear was developed and studied. The properties of the solution of the system were determined, and all potential equilibrium points were identified. The dynamic behavior in their immediate surroundings was examined both locally and globally. The system’s persistence demands were calculated, and all conceivable forms of local bifurcations were investigated. With the aid of MATLAB, a numerical simu

The main objective of present work is to describe the feasibility of friction stir welding (FSW) for
joining of low carbon steel with dimensions (3 mm X 80 mm X 150 mm). A matrix (3×3) of welding
parameters (welding speed and tool rotational speed) was used to see influence of each parameter on
properties of welded joint .Series of (FSW) experiments were conducted using CNC milling machine
utilizing the wide range of rotational speed and transverse speed of the machine. Effect of welding
parameters on mechanical properties of weld joints were investigated using different mechanical tests
including (tensile and microhardness tests ). Micro structural change during (FSW) process was
studied and different welding zones