Let R be a commutative ring with unity 1 6= 0, and let M be a unitary left module over R. In this paper we introduce the notion of epiform∗ modules. Various properties of this class of modules are given and some relationships between these modules and other related modules are introduced.

Let R be a commutative ring with identity, and let M be a unitary (left) R- modul e. The ideal annRM  = {r E R;rm  = 0 V  mE M} plays a central

role  in  our  work.  In  fact,  we  shall  be  concemed   with  the  case  where annR1i1 = annR(x) for   some   x EM such  modules  will  be  called bounded  modules.[t  htrns out that there are many classes of modules properly contained in the class of bounded modules such as cyclic modules, torsion -G·ee modulcs,faithful  multiplicat

Let  be a commutative ring with 1 and  be left unitary  . In this paper we introduced and studied concept of semi-small compressible module (a     is said to be semi-small compressible module if  can be embedded in every nonzero semi-small submodule of . Equivalently,  is  semi-small compressible module if there exists a monomorphism  , ,     is said to be semi-small retractable module if  , for every non-zero  semi-small sub module in . Equivalently,  is semi-small retractable if there exists a homomorphism  whenever  .     In this paper we introduce and study the concept of semi-small compressible and semi-small retractable s as a generalization of compressible  and retractable  respectively and give some of their adv

Let  be a commutative ring with 1 and  be left unitary  . In this papers we introduced and studied concept P-small compressible  (An     is said to be P-small compressible if  can be embedded in every of it is nonzero P-small submodule of . Equivalently,  is P-small compressible if there exists a monomorphism  , ,     is said to be P-small retractable if  , for every non-zero P-small submodule of . Equivalently,  is P-small retractable if there exists a homomorphism  whenever  as a generalization of compressible  and retractable  respectively and give some of their advantages characterizations and examples.

Temporomandibular disorders (TMDs) were investigated in 143 pretreatment orthodontic patients (43 males and 102 females) whose age ranged between 10-25 years at the College of Dentistry, University of Baghdad, Iraq. The study was undertaken to elucidate the prevalence and severity of TMDs in malocclusion patients and to defme the relationships between malocclusion and TMDs. The clinical signs and subjective symptoms were recorded according to the principles introduced by Helkimo (1974b). Subjective symptoms were reported by 65.7% of the patients with 22.40/0 described as severe, and the most common symptoms were TMJ sounds and feeling offatigue. Clinical signs were observed in 81.8% of the sample with 22.4 and 6.3% described as moderate and

Experimental tests were conducted to investigate the thermal performance (cooling effect) of water mist system consisting of 5μm volume median diameter droplets in reducing the heat gain entering a room through the roof and the west wall by reducing the outside surface temperature due to the evaporative cooling effect during the hot dry summer of Baghdad/Iraq. The test period
was Fifty one days during the months May, June, and July 2012. The single test day consists of 16 test hours starting from 8:00 am to 12:00 pm. The results showed a reduction range of 1.71 to 15.5℃ of the roof outside surface temperature and 21.3 to 76.6% reduction in the daily heat flux entering the room through the roof compared with the case of not using w

    The objective of this paper is, firstly, we study a new concept noted by algebra and discuss the properties of this concept. Secondly, we introduce a new concept related to the algebra such as smallest algebra. Thirdly, we introduce the notion of the restriction of algebra on a nonempty subset  of and investigate some of its basic properties. Furthermore, we present the relationships between field, monotone class, field and algebra. Finally, we introduce the concept of measure relative to the algebra and prove that every measure relative to the   is complete.

The effect of approaching nozzle jet from the deposition surface
on structural, optical and morphology properties of copper oxide thin
films was studied. The film was prepared by homemade fully
computerized CNC spray pyrolysis deposition technique at
preparations speed (3, 4, 5, and 6 mm/sec). The repeated line mode
was used at deposition temperature equal 450 °C whereas the
spraying time was in the range of (15-30 min) according to the
deposition speed. The film exhibit polycrystalline structure with
preferred orientation along (-111), (022) and (011), (002) at a 2θ
value of (35.63o) and (38.8o) respectively. Optical band gaps were
recorded at these speed shows variance in value from (1.53-2.08 eV).
Fi

Let R be a ring and let M be a left R-module. In this paper introduce a small pointwise M-projective module as generalization of small M- projective module, also introduce the notation of small pointwise projective cover and study their basic properties.
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