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)

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

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

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

One of the main causes for concern is the widespread presence of pharmaceuticals in the environment, which may be harmful to living things. They are often referred to as emerging chemical pollutants in water bodies because they are either still unregulated or undergoing regulation. Pharmaceutical pollution of the environment may have detrimental effects on ecosystem viability, human health, and water quality. In this study, the amount of remaining pharmaceutical compounds in environmental waters was determined using a straightforward review. Pharmaceutical production and consumption have increased due to medical advancements, leading to concerns about their environmental impact and potential harm to living things due to their increa

The present study investigates the use of intensifiers as linguisticdevices employed by Charles Dickens in Hard Times. For ease of analysis, the data are obtained by a rigorous observation of spontaneously occurring intensifiers in the text. The study aims at exploring the pragmatic functions and aesthetic impact of using intensifiers in Hard Times.The current study is mainly descriptive analytical and is based on analyzing and interpreting the use of intensifiers in terms ofHolmes (1984) andCacchiani’smodel (2009). From the findings, the novelist overuses intensifiers to the extent that 280 intensifiers are used in the text. These intensifiers(218) are undistinguished

The anatomic characteristics of the leaves of 22 taxa of Stachys L. representing seven of the currently recognized sections distributed in northern Iraq, were examined. The study did not found any variations in the characteristics of the stomata system of the leaves.Therewere variations with a good taxonomic value in other anatomic characteristics.Thevariations in characters of the mesophyll tissue in S.kurdica var.brevidens Bom ex Bhattacharjeewas bifacial but in S.kurdica var.kurdica Boiss. & Hohen.was unifacial .The study also found that the taxa S.benthamiana Bioss., S.lanigera (Bornm.) Rech.f. andS.kotscyi Bioss. with 3 vascular bundles in the middle vein while the taxa S.ballotiformis Vatke., S.megalodonta Hausskn. &Bornm.exP.H.Davis

Background: The use of electronic apex locators for working length determination eliminates many of the problems associated with the radiographic measurements (interference of anatomical structures, errors in projection such as elongation or shortening, and lack of three-dimensional representation). Its most important advantage over radiography is that it measures the length of the root canal to the apical constriction, not to the radiographic apex. The aim of this study was to assess the accuracy of a new fifth generation apex locator (Joypex 5) in recording the apical constriction and comparing it with a third generation apex locator (Root ZX) in vitro. Materials and method: Twenty four single-rooted sound human premolars, extracted for t