A numerical simulation is made on the thermal lensing effect in an laser diode end-pumped Nd:YAG laser rod. Based on finite element method (FEM), the laser rod temperature distribution is calculated and the focal length is deduced for a Gaussian and super-Gaussian pump beam profiles.

At the pump power of 20W, the highest temperature located at the center of end-pumped face was 345K, and the thermal lens focal length was 81.4mm along the x-z axis. 

The results indicate that the thermal lensing effect sensitively depend on the pump power, waist radius of the pump beam and the pump distribution in a laser rod geometry.

There is a theoretical controversy in the books of Usul al-Fiqh, in the past and the present, about whether the ruling should be attached to its reason (al-Hikmah), or its apparent and stable cause (al-Illah). Looking at the practical cases of the jurists, we found them sometimes attaching rulings to its reason, and sometimes to its cause, so there is a need to know the factors that affect their choices. By extrapolation, the researcher reached at nine factors that affect referring the ruling to its cause or to its reason in jurisprudential cases.

This work, in fact, is an English language teaching study (henceforth, ELT) which may provide the inspiration for much –needed research on issues such as testing students' level of achievement in articulatory phonetics at the university level. It attempts to answer two questions: 1)What is college students' level of achievement in articulatory phonetics? 2- Are there any statistical significant differences in the achievement of college students in articulatory phonetics between the production and recognition testing techniques? This research falls into three sections: Section one indicates the problem, the aims, the hypotheses, the procedures, the limits and the value of the study. Section two provides a general overview of the articul

Abstract

Toady technology Nano since it launched human Alivia third interest and anticipation unusual and that by the decision-makers in the world's governments and its institutions and research departments productivity, especially after the US Congress enact a law (the National Initiative for Tknlojba nanotechnology in the United States of America) and the allocation of large sums of money To support this initiative, the research aims to shed light on the concept of technology nanotechnology, which is technology atheist and the twentieth century, and reflect its economic importance and in order to reach the objectives of the research has been the division of research into several axes has been allocated

The subject of multi- ethnics is one of the most important subjects in the study of political
geography, as multi- ethnics and its consequent problems are global geopolitical phenomena
that started early and reached its peak with the beginning of the twentieth century, because of
major changes in the political landscape that resulted by wars and led to the collapse of many
empires and major powers, a matter which led to put new political maps according to certain
considerations of the colonial powers, especially in Africa and Asia. All these things led to
the most serious challenges based on ethnic and sectarian conflict and led to the development
of geopolitical problems. Among the examples what most countries in th

In this paper we generalize Jacobsons results by proving that any integer  in   is a square-free integer), belong to . All units of  are generated by the fundamental unit  having the forms

Our generalization build on using the conditions

This leads us to classify the real quadratic fields  into the sets  Jacobsons results shows that  and Sliwa confirm that  and  are the only real quadratic fields in .

0