Let R be associative ring with identity and M is a non- zero unitary left module over R. M is called M- hollow if every maximal submodule of M is small submodule of M. In this paper we study the properties of this kind of modules.

The main purpose of this paper is to study some results concerning reduced ring with another concepts as semiprime ring ,prime ring,essential ideal ,derivations and homomorphism ,we give some results a bout that.

Background: The world health organization estimates that worldwide 2 billion people still have iodine deficiency Objectives: Is to make comparison between the effect of identification of recurrent laryngeal nerve (RLN) and non-identification of the nerve on incidence of recurrent laryngeal nerve injury (RLNI) in different thyroidectomy procedures.

Type of the study: cross –sectional study.

Methods: 132 patients with goiters underwent thyroidectomy .Identification of RLN visually by exposure were done for agroup of them and non-identification of the nerves for the other group. The outcomes of RLNI in the two groupsanalyzed statistically for the effect of

Image steganography is undoubtedly significant in the field of secure multimedia communication. The undetectability and high payload capacity are two of the important characteristics of any form of steganography. In this paper, the level of image security is improved by combining the steganography and cryptography techniques in order to produce the secured image. The proposed method depends on using LSBs as an indicator for hiding encrypted bits in dual tree complex wavelet coefficient DT-CWT. The cover image is divided into non overlapping blocks of size (3*3). After that, a Key is produced by extracting the center pixel (pc) from each block to encrypt each character in the secret text. The cover image is converted using DT-CWT, then the p

Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be approximately pure submodule of an R-module, if for each ideal I of R. The main purpose of this paper is to study the properties of the following concepts: approximately pure essentialsubmodules, approximately pure closedsubmodules and relative approximately pure complement submodules. We prove that: when an R-module M is an approximately purely extending modules and N be Ap-puresubmodulein M, if M has the Ap-pure intersection property then N is Ap purely extending.

This paper deals with the F-compact operator defined on probabilistic Hilbert space and gives some of its main properties.

Abstract

Research title: The legal ruling of advice.

This research deals with the topic of advice, as the research included the following:

Preamble: I explained in it the meaning of advice in the Qur’an and Sunnah, and that what is meant by it is a good performance of the duty, then explaining its importance, importing it, and the difference between advice and what is similar to it, from enjoining good, denial, reproach and reprimand, backbiting and the will.

The first topic: It dealt with the ruling on advice, whether it is recommended or disliked, or forbidden, because what is meant by it is to give advice to others may be an obligation in kind, or it may be desirable or dislike

The investor needs to a clear strategy for the purpose of access to the financial market, that is, has a plan to increase The share of the profits thinking entrepreneur and new, and highlights the importance of this in that it sets for the investor when it goes to the market, and when it comes out of it, and at what price to buy or sell the stock, and what is the the amount of money it starts. Fortunately, he does not need to invent his own investment strategy, because over the years the development of effective methods of buying and selling, and once you understand how to work these methods investor can choose the most appropriate methods and adapted image that fit his style investment .

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Background: With the increasing demands for adult orthodontics, a growing need arises to bond attachments to porcelain surfaces. Optimal adhesion to porcelain surface should allow orthodontic treatment without bond failure but not jeopardize porcelain integrity after debonding.The present study was carried out to compare the shear bond strength of metal bracket bonded to porcelain surface prepared by two mechanical treatments and by using different etching systems (Hydrofluoric acid 9% and acidulated phosphate fluoride 1.23%). Materials and Methods: The samples were comprised of 60 models (28mm *15mm*28mm) of metal fused to porcelain (feldspathic porcelain). They were divided as the following: group I (control): the porcelain surface left u