A submodule Ϝ of an R-module Ε is called small in Ε if whenever , for some submodule W of Ε , implies . In this paper , we introduce the notion of Ζ-small submodule , where a proper submodule Ϝ of an R-module Ε is said to be Ζ-small in Ε if , such that , then , where is the second singular submodule of Ε . We give some properties of Ζ-small submodules . Moreover , by using this concept , we generalize the notions of hollow modules , supplement submodules, and supplemented modules into Ζ-hollow modules, Ζ-supplement submodules, and Ζ-supplemented modules. We study these concepts and provide some of their relations .
Metal-organic frameworks (MOFs) are a relatively new class of materials of unique porous structures and exceptional properties. Currently, more than 110,000 types of MOFs have been reported among the countless possibilities. In this study, we have synthesised a novel MOF using zirconium chloride as the metal source and 4,4'-dicarboxy-2,2'-biquinoline (bicinchoninic acid disodium salt) as the linker, which reacted in N,N-Dimethylformamide (DMF) solvent. Three preparation methods were employed to prepare five types of the MOF, and they were compared to optimize the synthesis conditions. The resulting MOFs, named Zr-BADS, were characterised using scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), microscopy, and
... Show MoreThe compounds 3-[4̄-(4˭-methoxybenzoyloxy) benzylideneamino]-2-thioxo-imidazolidine-4-one(3)aand 4-(1-(5-oxo- 2-thioxoimidazolidin-1-ylimino)ethyl)phenyl acetate(3)b were prepared from the reaction of aromatic aldehyde or ketone(1)a,bwith thiosemicarbazide to give aryl thiosemicarbazones(2)a,b ,followed by cyclization with ethylchloroacetate in the presence of fused sodium acetate. Treatment the compounds(3)a,bwith 4- hydroxybenzenediazoniumchloride yielded the correspondings4-((4-((4-hydroxyphenyl)diazenyl)-5-oxo-2- thioxoimidazolidin-1-ylimino)methyl)phenyl 4-methoxybenzoate(4)aand4-(1-(4-((4-hydroxyphenyl)diazenyl)-5-oxo-2- thioxoimidazolidin-1-ylimino)ethyl)phenyl acetate(4)b.The new 2-thioxo-imidazolidin-4-one with esters (5-7)a,b sy
... Show MoreThe demand for expatriate labor to Iraq increased after 2003 as a result of the openness that Iraq experienced, but this expatriate labor, which was requested at an increasing rate, has had economic, social, and political effects on the Iraqi economy in general, and the Iraqi labor market in particular. This is due to the high rates of unemployment, as most of these expatriate workers cause competition to local labor, and thus cause repercussions on the Iraqi economy as a whole, except for those expatriate workers coming with companies working in the oil sector. Iraq's GDP
The purified prepared compounds were identified through different methods of identification i.e, I.R, UV-vi^ble-spectroscopy in addition to (coloured tests) Calculation of the sum of OH groups. TLC techniques were also used to test the purity and the speed ofthe rate of flow (RF).
Au XIXe siècle, avec l’excès de la passion, le roman français commence à avoir de nouvelles figures. Il tend à être un reflet de la pensée et de la passion. Stendhal et Balzac révèlent ainsi le conflit de l’âme et donnent à leur héros l’impression que tout est permis.
Ces protagonistes doivent, d’une part, subir des fluctuations psychologiques, et d’autre part, ces héros doivent être capables de faire face aux rancunes et aux conflits destructeurs. Les personnages stendhaliens et balzaciens finissent par croire que leur combat ne portera pas ses fruits, parce que toute passion déséquilibrée mènera, soit à la fol
... Show MoreNew, simple and accurate batch and flow injection spectrophotometric
methods have been developed for the determinationsof tetracycline
hydrochloride (TCH) and doxycycline hyclate (DCH) in pharmaceutical
preparations. The methods are based on diazotization of
metchlopramide and coupling reaction with either TCH or DCH in alkaline
medium to form yellow–orange water soluble dye with absorption maxima
at 414 and 436 nm for TCH and DCH, respectively. A graphs of absorbance
versus concentration show that Beer’s law was obeyed over the
concentration ranges of 1 –52 μgmL-1 TCH and DCH for batch method and
of 8 – 240 μg mL-1 TCH and 5 – 350 μgmL-1 DCH for FIA method. The
limits of detection in batchmetho
A load flow program is developed using MATLAB and based on the Newton–Raphson method,which shows very fast and efficient rate of convergence as well as computationally the proposed method is very efficient and it requires less computer memory through the use of sparsing method and other methods in programming to accelerate the run speed to be near the real time.
The designed program computes the voltage magnitudes and phase angles at each bus of the network under steady–state operating conditions. It also computes the power flow and power losses for all equipment, including transformers and transmission lines taking into consideration the effects of off–nominal, tap and phase shift transformers, generators, shunt capacitors, sh