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.

The role of email is becoming more and more important and email is considered one of the most effective tools of communication and correspondence nowadays. This research paper investigates the use of etiquette by Libyan EFL postgraduate students in writing formal emails. The aim is to shed light on the situation and determine to what extent Libyan EFL postgraduate students adhere to the rules of etiquette in their formal emails. Another aim is to try to find out if there are any problems, they face in this respect in order to find better ways that may help in dealing with them. To fulfill these aims, 39 students were asked to send a formal email to their instructor (the researcher) of subjects of their own choice. However, only 34 emails were received. The results have shown that the majority of the students who have participated in the study are aware of the overall structure and organization of emails written in formal style. However, examining details have shown that students face some problems that are not only related to style, but also to language and culture. It was apparent from the emails investigated that students lack practice and experience in writing formal emails. To overcome these difficulties, teachers are advised to raise their students’ awareness of the importance of using formal emails as a means of communication and to provide them with sufficient practice by regularly using formal email in their correspondence with their teachers. Students also need to be aware of the inter-linguistic and cultural differences; what might be acceptable and favorable in Arabic may lead to miscommunication problems when used in English.

This coursebook is designed to satisfy the need for a coursebook that is suitable for the university level. It is a practical book which introduces syntactic concepts in a simple way and which gives a chance to students of syntax to understand these concepts through practice by doing related exercises. It is based on my experience of teaching syntax to university students for several years. 

The sequencing and the grading of material from simple topics to more difficult ones makes it easier to understand and grasp the ideas discussed. For example, Unit One is an introductory unit where syntax as a subject is clarified and where analysis approaches and methods of representations that will be used throughout the book are introduced and explained. Unit Two discusses the internal structure of clauses and phrases. It is only after a thorough understanding of these constituents has been ensured through illustrations and practice that the functions of these constituents are introduced in a separate unit, i.e. Unit three.  

   This book has been written to satisfy the need for a practical guide for MA Libyan students which takes them step by step in the process of writing a research proposal. It is the outcome of years of experience in teaching a ‘proposal writing seminar’ subject to postgraduates in the English department in the University of Zawia. However, we believe it will be useful for all MA students in the Libyan academic institutions who write their proposals in the English language.

    The book is not meant to teach the students the methodology of writing research which is presumably should have been dealt with in a separate subject and which is considered a prerequisite for writing a proposal. Thus, in order for students to benefit much from this book, they should be first acquainted with the terminology, procedure and methodology of writing their research which will facilitate their understanding of the process of writing their proposals. 

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.