The Internet is the hallmark of the age of technology and this technology is complemented by the presence of software which is one of the basic components of the operation of the network and it is used in almost all daily life aspects such as industry, commerce and others. Because the digital documents and objects can be easily replicated and distributed at an economically low cost and as the software is a type of digital object, the problem of software watermarking risen as related to how to protect data from piracy. Therefore, various techniques have been developed to protect codes from misusing and unauthorized alteration. Each of them is known as watermarking technology that protects data by inserting secret information into software

Our active aim in this paper is to prove the following Let Ŕ be a ring having an
idempotent element e(e  0,e 1) . Suppose that R is a subring of Ŕ which
satisfies:
(i) eR  R and Re  R .
(ii) xR  0 implies x  0 .
(iii ) eRx  0 implies x  0( and hence Rx  0 implies x  0) .
(iv) exeR(1 e)  0 implies exe  0 .
If D is a derivable map of R satisfying D(R )  R ;i, j 1,2. ij ij Then D is
additive. This extend Daif's result to the case R need not contain any non-zero
idempotent element.

This article dealt with the evolutionary interpretation in three parts: First, it focused on the conceptual framework of evolutionary interpretation of International Treaties, its philosophical and legal foundation and its determinants. As for the second topic, it dealt with the position of the International Court of Justice from the evolutionary interpretation, studying and analyzing its precedents in this aspect and the resulting proposed and adopted criteria. The third topic dealt with the position of the judiciary of human rights through analyzing the rulings of the European Court of Human Rights and the Inter - American Court of Human Rights based on the criteria that were produced by the judicial practices, which varied according t

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

The research sought to know the educational goals of Quranic proverbs, The first chapter: includes general terms of research, its problem, its importance, its objectives, its methodology, and the definition of terms. In the second chapter: Proverbs in Quranic usage such as simple and complex proverbs, standard proverbs, In the third chapter, the educational objectives of the Quranic proverbs include: bringing the meaning, persuasion, thought provoking ..... the educational characteristics of the Koranic verses, including: accuracy of photography, and the truth of similar, and included the lesson applied lesson, Chapter fourth : Conclusions and Recommendations with abstra

Let
be a dynamical system,
is said to be topological transitive if for every pair of non-empty open set
, there exists
such that
. We introduce and investigate a new definition of topological transitive by using the nation N-open subset and we called N-transitive and prove the equivalent definitions of this new definition.

     Let  be any connected graph with vertices set  and edges set .  For any two distinct vertices  and , the detour distance between  and  which is denoted by  is a longest path between  and  in a graph . The detour polynomial of a connected graph  is denoted by ;  and is defined by . In this paper, the detour polynomial of the theta graph and the uniform theta graph will be computed.

      Let R be a commutative ring with unity. And let E be a unitary R-module. This paper introduces the notion of 2-prime submodules as a generalized concept of 2-prime ideal, where proper submodule H of module F over a ring R is said to be 2-prime if , for r R and x F implies that  or . we prove many properties for this kind of submodules, Let H is a submodule of module F over a ring R then H is a 2-prime submodule if and only if [N ] is a 2-prime submodule of E, where r R. Also, we prove that if F is a non-zero multiplication module, then [K: F] [H: F] for every submodule k of F such that H K. Furthermore, we will study the basic properties of this kind of submodules.

In this work, we present the notion of a multiplier on AT-algebra and investigate several properties. Also, some theorems and examples are discussed.  The notions of the kernel and the image of multipliers are defined. After that, some propositions related to isotone and regular multipliers are proved. Finally, the Left and the Right derivations of the multiplier are obtained