The aim of this modest study was to shed some light on one of

the useful tools of complex analysis, which is the method of conformal

mapping (Also called conformal transformation). Conformal

transformations are optimal for solving various physical and

engineering problems that are difficult to solve in their original form

and in the given domain. This work starts by introducing the meaning

of a ''Conformal Mapping'', then introducing its basic Properties. In the

second part, it deals with a set of various examples that explain the

behavior of these mappings and show how they map a given domain

from its original form into a simpler one. Some of these examples

mentioned in this study showed that conformal transformations could

be used to determine harmonic functions, that is, to solve Laplace's

equation in two dimensions, which is the equation that governs a variety

of physical phenomena such as the steady-state temperature distribution

in solids, electrostatics and inviscid and irrotational flow (potential

flow). Other mathematical problems are treated. All problems that are

dealt with in this work became easier to solve after using this technique.

In addition, they showed that the harmonicity of a function is preserved

under conformal maps and the forms of the boundary conditions change

accordingly

Contamination of wastewater by toxic metals is a global environmental concern. In this study, the possibility of using inactive (dead) Sargassum bacilluria powder as a natural adsorbent was investigated in the removal of cadmium from aqueous solutions. The biosorption process was found to be highly dependent on a set of variables such as pH, temperature, contact time, shaking speed and initial metal concentration. The results showed an optimum pH value, (6.0) for cadmium, where was the biosorption capacity (842.15±0.252) for cadmium, and the lowest biosorption value for Cd was found at pH 2.0. The optimum temperature in this study was 30 °C. The time required for equilibrium was investigated over a period of 360 min and found to be 180 min. The capacity of biosorption increased with increasing shaking speed, and the highest uptake value was found at 120 rpm. The maximum removal of Cd+2 was found at 20 mg/l. The models Freundlich and Langmuir were used to study the equilibrium process of these systems. The Langmuir model was found to be more suitable for the interpretation of these systems by the value of the correlation coefficients higher than 0.99. Brown seaweed powder is an effective, low-cost, .and environmentally friendly adsorbent for removing metals from aqueous solutions, according to the results obtained.

In this paper we want to describe the algorithm to find all good starting points for

iteration of 𝑁𝑝(𝑧) to find all the roots of 𝑝(𝑧) by quick and easy way. So in this paper

we have proved that all critical points go to the roots under iteration of Newton’s

function then it will be the good starting points for iteration of 𝑁𝑝(𝑧) .

This work is focused on nucleation stages during isothermal austenite decomposition in two medium carbon Vanadium Ti / Ti free micro alloyed steels. Isothermal treatment was carried out in the temperature range 350 to 600οC. Metallographic evaluation using optical and scanning electron microscopy (SEM) enabled determination of the nucleation onset phases of isothermally decomposed austenite. Mainly three phases are found to be relevant to this initiation stage of transformation: first is related to grain boundary nucleated ferrite (GBF), second is related to intra-granularly nucleated ferrite (IGF) and the third to pearlite (P). GBF and IGF are divided into the high temperature and the low temperature segments as consequence of either displacive or diffusion nature of transformation. Addition of titanium to V – micro alloyed steel in this work seems to be balanced by a slightly higher C and Mn content, leading to limited effect on nucleation stage of austenite decomposition. The results show that during continuous cooling, onset of pearlite phase can take place. It occurs at temperatures ≥ 500 C°, followed by an incomplete reaction phenomenon. The main characteristics of pearlite is always nucleated on the surface between proeutectoid ferrite and austenite. Incubation time for onset of pearlite decrease with decrease of temperature.

This paper aims to demonstrate the application of two different control techniques, namely the Linear Quadratic Regulator (LQR) and a neural network-based controller to evaluate and control the vibrations that occurred in the car's suspension system. When the car suspension is designed, a quarter car model with 1-DOF is used. A complete control system is needed to provide the desired suspension performance and characteristics such as passenger comfort, road handling, and suspension deflection, this control system performed by using the Matlab software and includes three parts: input signals (actuator force and road profile), Controller, and the suspension system model. The simulation results show a comparison between the uncontrolled suspension system and the suspension system with a neural network-based controller and the active suspension system of the car based on the linear-quadratic regulator, and it is explained thoroughly.

Vehicle safety and control is attracting attention increasingly in an attempt to improve the stability and manoeuvrability of vehicles. Three degrees of freedom vehicle dynamic model (called planar vehicle model) is established. Based on theories of fuzzy PID control and neural network based-Controller, controller of vehicle stability is designed by using the method of direct yaw rate control and the two different control strategies. The controllers were compared under one road condition which is a lane change of manoeuvre. By comparing and analyzing the control effect of fuzzy PID control and neural network based-Controller, the result shows as follows: the two controllers improved the yaw rate to follow the reference yaw rate but, using the fuzzy PID controller gave a better and closer path for the desired path of yaw rate compared to using of the neural network controller.