A non-zero module M is called hollow, if every proper submodule of M is small. In this work we introduce a generalization of this type of modules; we call it prime hollow modules. Some main properties of this kind of modules are investigated and the relation between these modules with hollow modules and some other modules are studied, such as semihollow, amply supplemented and lifting modules.

      In this paper, we introduce the notion of a 2-prime module as a generalization of prime module E over a ring R, where E is said to be prime module if (0) is a prime submodule. We introduced the concept of the 2-prime R-module. Module E is said to be 2-prime if (0) is 2-prime submodule of E. where a proper submodule K of module E is 2-prime submodule if, whenever rR, xE, E, Thus xK or [K: E].

In this paper we investigated some new properties of π-Armendariz rings and studied the relationships between π-Armendariz rings and central Armendariz rings, nil-Armendariz rings, semicommutative rings, skew Armendariz rings, α-compatible rings and others. We proved that if R is a central Armendariz, then R is π-Armendariz ring. Also we explained how skew Armendariz rings can be ?-Armendariz, for that we proved that if R is a skew Armendariz π-compatible ring, then R is π-Armendariz. Examples are given to illustrate the relations between concepts.

It is commonly known that Euler-Bernoulli’s thin beam theorem is not applicable whenever a nonlinear distribution of strain/stress occurs, such as in deep beams, or the stress distribution is discontinuous. In order to design the members experiencing such distorted stress regions, the Strut-and-Tie Model (STM) could be utilized. In this paper, experimental investigation of STM technique for three identical small-scale deep beams was conducted. The beams were simply supported and loaded statically with a concentrated load at the mid span of the beams. These deep beams had two symmetrical openings near the application point of loading. Both the deep beam, where the stress distribution cannot be assumed linear, and the ex

Samples of Bi1.6Pb0.4Sr2Ca2Cu3O10+δ superconductor were prepared by solid-state reaction method to study the effects of gold nanoparticles addition to the superconducting system, Nano-Au was introduced by small weight percentages (0.25, 0.50, 0.75, 1.0, and 1.25 weight %). Phase identification and microstructural
characterization of the samples were investigated using XRD and SEM. Moreover, DC electrical resistivity as a function of the temperature, critical current density Jc, AC magnetic susceptibility, and DC magnetization measurements were carried to evaluate the relative performance of samples. x-ray diffraction analysis showed that both (Bi,Pb)-2223 and Bi-2212 phases coexist in the samples having an orthorhombic crystal struct

In this work, the superconducting CuBa2LaCa2Cu4O11+δ compound was prepared by citrate precursor method and the electrical and structural properties were studied. The electrical resistivity has been measured using four probe test to find the critical temperature Tc(offset) and Tc(onset). It was found that Tc (offset) at zero resistivity has 101 K and Tc (onset) has 116 K. The X-ray diffraction (XRD) analysis exhibited that a prepared compound has a tetragonal structure. The crystal size and microscopic strain due to lattice deformation of CuBa2LaCa2Cu4O11+δ were estimated by four methods, namely Scherer(S), Halder-Wagner(H-W), size-strain plot (SSP) and Williamson-Hall, (W-H) methods. Results of crystal sizes obtained by these meth

In this study, we made a comparison between LASSO & SCAD methods, which are two special methods for dealing with models in partial quantile regression. (Nadaraya & Watson Kernel) was used to estimate the non-parametric part ;in addition, the rule of thumb method was used to estimate the smoothing bandwidth (h). Penalty methods proved to be efficient in estimating the regression coefficients, but the SCAD method according to the mean squared error criterion (MSE) was the best after estimating the missing data using the mean imputation method

Twelve compounds containing a sulphur- or oxygen-based heterocyclic core, 1,3- oxazole or 1,3-thiazole ring with hydroxy, methoxy and methyl terminal substituent, were synthesized and characterized. The molecular structures of these compounds were performed by elemental analysis and different spectroscopic tequniques. The liquid crystalline behaviors were studied by using hot-stage optical polarizing microscopy and differential scanning calorimetry. All compounds of 1,4- disubstituted benzene core with oxazole ring display liquid crystalline smectic A (SmA) mesophase. The compounds of 1,3- and 1,4-disubstituted benzene core with thiazole ring exhibit exclusively enantiotropic nematic liquid crystal phases.

Background: Juvenile idiopathic arthritis (JIA) is a chronic disease of childhood. Increased prevalence of periodontal disease and dental caries in juvenile idiopathic arthritis is due to difficulties in executing good oral hygiene. This study was conducted to assess oral health status in patients with Juvenile idiopathic arthritis according to age and duration of illness. Materials and methods: A research was conducted among Juvenile idiopathic arthritis patients attending Baghdad Teaching Hospital with different age and both gender, underwent a clinical evaluation of their dental and oral condition. Diagnosis of dental caries was done according to the criteria of WHO (1997). Dental plaque, gingival condition, calculus were assessed by PI/