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)

Background: The bond strength of the root canal sealers to dentin is very important property for maintaining the integrity and the seal of root canal filling. The aim of this study was to evaluate and compare the push-out bond strength of root filled with total fill Bioceramic, AH Plus and Gutta-flow®2 sealers using GuttaFusion®obturation system versus single cone obturation technique. Materials and method: sixty of mandibular premolars teeth with straight roots were used in this study, these roots were instrumented using Reciproc system, instrumentation were done with copious irrigation of 3 mL 5.25% sodium hypochlorite solution (NaOCl) during all the steps of preparation, and smear layer will be removed with 1 ml of 17% EDTA kept in

Background: The bond strength of the root canal sealers to dentin is very important property for maintaining the integrity and the seal of root canal filling. The aim of this study was to evaluate and compare the push-out bond strength of root filled with total fill Bioceramic, AH Plus and Gutta-flow®2 sealers using GuttaFusion®obturation system versus single cone obturation technique. Materials and method: sixty of mandibular premolars teeth with straight roots were used in this study, these roots were instrumented using Reciproc system, instrumentation were done with copious irrigation of 3 mL 5.25% sodium hypochlorite solution (NaOCl) during all the steps of preparation, and smear layer will be removed with 1 ml of 17% EDTA kept in

Abstract:                                        

   We can notice cluster data in social, health and behavioral sciences, so this type of data have a link between its observations and we can express these clusters through the relationship between measurements on units within the same group.

    In this research, I estimate the reliability function of cluster function by using the seemingly unrelate

The main work of this paper is devoted to a new technique of constructing approximated solutions for linear delay differential equations using the basis functions power series functions with the aid of Weighted residual methods (collocations method, Galerkin’s method and least square method).

Three cohesionless free flowing materials of different density were mixed in an air fluidized bed to study the mixing process by calculating performance of mixing index according to Rose equation (1959) and to study the effect of four variables (air velocity, mixing time, particle size of trace component and concentration of trace component) on the mixing index and as well as on mixing performance. It was found that mixing index increases with increasing the air velocity, mixing time and concentration of trace component until the optimum value. Mixing index depends on the magnitude of difference in particle size The first set of experiments (salt then sand then cast iron) give higher mixing index and better performance of mixing than the

Nonlinear differential equation stability is a very important feature of applied mathematics, as it has a wide variety of applications in both practical and physical life problems. The major object of the manuscript is to discuss and apply several techniques using modify the Krasovskii's method and the modify variable gradient method which are used to check the stability for some kinds of linear or nonlinear differential equations. Lyapunov function is constructed using the variable gradient method and Krasovskii’s method to estimate the stability of nonlinear systems. If the function of Lyapunov is positive, it implies that the nonlinear system is asymptotically stable. For the nonlinear systems, stability is still difficult even though

Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is a basic pri

Hygienic engineering has dedicated a lot of time and energy to studying water filtration because of how important it is to human health. Thorough familiarity with the filtration process is essential for the design engineer to keep up with and profit from advances in filtering technology and equipment as the properties of raw water continue to change. Because it removes sediment, chemicals, odors, and microbes, filtration is an integral part of the water purification process. The most popular technique for treating surface water for municipal water supply is considered fast sand filtration, which can be achieved using either gravity or pressure sand filters. Predicting the performance of units in water treatment plants is

In this paper investigate the influences of dissolved CO₂/H₂S gases, crude oil velocity and temperature on the rate of corrosion of crude oil transmission pipelines of Maysan oil fields southern Iraq. The Potentiostatic corrosion test technique was conducted into two types of carbon steel pipeline (materials API 5L X60 and API 5L X80). The computer software ECE electronic corrosion engineer was used to predict the influences of CO₂ partial pressure, the composition of crude oil, flow velocity of crude oil and percentage of material elements of carbon steel on the rate of corrosion. As a result, the carbon steel API 5L X80 indicates good and appropriate resistance to corrosion compared to carbon steel API