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)
In this paper, some necessary and sufficient conditions are obtained to ensure the oscillatory of all solutions of the first order impulsive neutral differential equations. Also, some results in the references have been improved and generalized. New lemmas are established to demonstrate the oscillation property. Special impulsive conditions associated with neutral differential equation are submitted. Some examples are given to illustrate the obtained results.
A systematic approach is presented to achieve the stable grasping of objects through a two-finger robotic hand, in which each finger cavity was filled with granular media. The compaction of the latter, controlled by vacuum pressure, was used to adjust the structural and contact stiffness of the finger. The grasping stability was studied under the concurrent effect of an external torque and applied vacuum pressure. Stable grasping was defined as the no slippage condition between the grasped object and the two fingers. Three control schemes were adopted and applied experimentally to ensure the effectiveness of the grasping process. The results showed that stable and unstable grasping regions exist for each combination of applied torqu
... Show MoreIn this study three reactive dyes (blue B, red R and yellow Y) in single , binary and ternary solution were adsorbed by activated carbon AC in equilibrium and kinetic experiments. Surface area, Bulk and real density, and porosity were carried out for the activated carbon.
Batch Experiments of pH (2.5-8.5) and initial concentration (5-100) mg/l were carried out for single solution for each dye. Experiments of adsorbent dosage effect (0.1-1)g per 100 ml were studied as a variable to evaluate uptake% and adsorption capacity for single dyes(5, 10) ppm, binary and ternary (10) ppm of mixture solutions solution of dyes. Langmuir, and Freundlich, models were used as Equilibrium isotherm models for single solution. Extended Langmuir and Freun
This article suggests and explores a three-species food chain model that includes fear effects, refuges depending on predators, and cannibalism at the second level. The Holling type II functional response determines food consumption between stages of the food chain. This study examined the long-term behavior and impacts of the suggested model's essential elements. The model's solution properties were studied. The existence and stability of every probable equilibrium point were examined. The persistence needs of the system have been determined. It was discovered what conditions could lead to local bifurcation at equilibrium points. Appropriate Lyapunov functions are utilized to investigate the overall dynamics of the system. To support the a
... Show MoreCorrosion rate tests were carried out on carbon steel under concentration cells conditions of oxygen and sodium chloride. The effect of aeration in one compartment on the corrosion rate of both coupled metals was determined. In addition, the effects of time and temperatures on the corrosion rate of both coupled metals and galvanic currents between them were investigated. Corrosion potentials for the whole range of operating conditions under concentration cell conditions were also studied. The results showed that under aeration condition, the formation of concentration cell caused a considerable corrosion rate of the Carbon steel specimens coupled in different concentrations of O2 and NaCl due to the galvanic effect
... Show MoreThe aim of this paper is to describe an epidemic model when two SI-Type of diseases are transmitted vertically as well as horizontally through one population. The population contains two subclasses: susceptible and infectious, while the infectious are divided into three subgroups: Those infected by AIDS disease, HCV disease, and by both diseases. A nonlinear mathematical model for AIDS and HCV diseases is Suggested and analyzed. Both local and global stability for each feasible equilibrium point are determined theoretically by using the stability theory of differential equations, Routh-Hurwitz and Gershgorin theorem. Moreover, the numerical simulation was carried out on the model parameters in order to determine their impact on the disease
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