This study delves into the properties of the associated act V over the monoid S of sinshT. It examines the relationship between faithful, finitely generated, and separated acts, as well as their connections to one-to-one and onto operators. Additionally, the correlation between acts over a monoid and modules over a ring is explored. Specifically, it is established that functions as an act over S if and only if functions as module, where T represents a nilpotent operator. Furthermore, it is proved that when T is onto operator and is finitely generated, is guaranteed to be finite-dimensional. Prove that for any bounded operator the following, is acting over S if and only if is a module where T is a nilpotent operator, is a faithful act over S, where T is any bounded linear operator, if T is any bounded operator, then is separated, if is separated act over S, Then T is injective, if a basis K = {vj, j} for V, then every element w of can be composed as =(pn (T) + . v, for some v in V, and put T as similar to any operator from to and V as a finite dimensional normed space, then is Noetherian act over S if S is Noetherian.
This study aimed at an analytical comparison of the Internal Auditing Standards issued by the Institute of Internal Auditors (IIA) and the Guidance Manual for Audit Units issued by the Federal Audit Bureau to show the compatibility and differences between them and the possibility of applying the IIA standards to economic units in Iraq. The guideline was generally not covered by all the internal audit units. There is a lack of keeping pace with changes in internal auditing at the international level and there is a need to strengthen the Guideline on Internal Auditing Standards II A), which is characterized by the preparation of an internal document containing the objectives, powers and responsibilities of the internal audit work as well a
... Show MoreBackground: A diverse group of bacteria live in biofilms in the oral cavity. On dental surfaces biofilms form plaque that is potentially involved in caries and periodontal diseases. Periodic studying of plaque microflora and their antimicrobial sensitivity patterns strongly affects the clinical practice in plaque-induced oral diseases. Materials and methods: Dental plaque samples were collected from 22 patients having ages ranged between 33 and 49 years with gingivitis that met the study criteria. Plaque, gingival and gingival bleeding indices (PI, GI, GBI) were measured for each patient. Laboratory procedures included microbiological examination of plaque samples followed by antibiotic sensitivity testing using disc diffusion method were
... Show MoreEffect of copper doping and thermal annealing on the structural and optical properties of Zn0.5Cd0.5S thin films prepared by chemical spray pyrolysis have been studied. Depositions were done at 250°C on glass substrate. The structural properties and surface morphology of deposited films were studied using X-ray diffraction (XRD) and photomicroscope (PHM) techniques. XRD studies reveal that all films are crystalline tetragonal structure. The film crystallinity are increased with 1% Cu-doping concentration and also increased for the films annealed at 300°C than the other studied cases. The lattice constant 'a' and 'c' varies with doping concentrations from 5.487Å to 5.427Å and 10.871Å to 10.757Å respectively. The grain size attained
... Show MoreIn this paper, isobutane (R-600a) is used as a suitable substitute for (R-134a) when changing the length of capillary tube. And the experimental data on capillary tube are obtained under different conditions such as (subcooling and ambient temperatures) on domestic refrigerator (9ft3 size), this data shows that (R-600a) a suitable substitute for (R134a) .The test presented a model for a steady state, two-phase flow in capillary tube for vapour compression system .The numerical model depends on conservation equations (mass, energy and momentum) as wall as the equation of state for refrigerant. The solution methodology was implemented by using finite difference techniques. The system results indicate that it is possible to change the refri
... Show Moreالاحداث السياسية في العراق بعد 2003 وأثر الانتماء والوعي في التشكيل العراقي المعاصر