In this paper we define and study new concepts of fibrewise topological spaces over B namely, fibrewise Lindelöf and locally Lindelöf topological spaces, which are generalizations of will-known concepts: Lindelöf topological space (1) "A topological space X is called a Lindelöf space if for every open cover of X has a countable subcover" and locally Lindelöf topological space (1) "A topological space X is called a locally Lindelöf space if for every point x in X, there exist a nbd U of x such that the closure of U in X is Lindelöf space". Either the new concepts are: "A fibrewise topological space X over B is called a fibrewise Lindelöf if the projection function p : X→B is Lindelöf" and "The fibrewise topological space X over B is called a fibrewise locally Lindelöf if for each point x of Xb, where bÎB, there exist a nbd W of b and a nbd UÌXW of x such that the closure of U in XW (i.e., XW∩cl(U) ) is fibrewise Lindelöf space over W". Moreover, we study relationships between fibrewise Lindelöf (locally Lindelöf) spaces and some fibrewise separation axioms.
In the present study benzofuran based chalcones 1 (a, b) are synthesized by condensing aromatic aldehydes with 2-acetylbenzofuran in the presence suitable base. These chalcones are very useful precursors for the synthesis of pyrazoline, isoxazoline, pyrmidine, cyclohexenone and indazole derivatives. All these compounds are characterized by their melting points, FTIR and 1 HMNR (for some of them) spectral dat
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The ground-state properties of exotic 18N and 20F nuclei, including the neutron, proton and matter densities and related radii are investigated using the two-body model of within Gaussian (GS) and Woods Saxon (WS) wave functions. The long tail is evident in the computed neutron and matter densities of these nuclei. The plane wave Born approximation (PWBA) is calculate the elastic form factors of these exotic nuclei. The variation in the proton density distributions due to the presence of the extra neutrons in 18N and 20F leads to a major difference between the elastic form factors of these exotic nuclei and their stable isotopes 14N and 19F. The reaction c
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Background: During acrylic resin processing, the mold must be separated from the surface of the gypsum to prevent liquid resin from penetrating into the gypsum, and water from the gypsum seeping into the acrylic resin. For many years, tin foil was the most acceptable separating medium, and because it's difficult to apply, a tin-foil substitute is used. In this study, olive oil is used as an alternative to tin foil separating medium for first time, and evaluating its effect as a separating medium on some mechanical properties such as (indentation hardness and transverse strength) of acrylic resins denture base comparing it with those processed using tin-foil and tin foil substitute such as (cold mold seal) separating medium. Materials and M
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The aim of the current research is to prepare an integrated learning program based on mathematics standards for the next generation of the NYS and to investigate its impact on the development of the teaching performance of middle school mathematics teachers and the future thinking skills of their students. To achieve the objectives of the research, the researcher prepared a list of mathematics standards for the next generation, which were derived from a list of standards. He also prepared a list of the teaching competencies required for middle school mathematics teachers in light of the list of standards, as well as clarified the foundations of the training program and its objectives and the mathematical
... Show MoreObjective: preparing exercises for the third intensity zone for strength and speed for the legs, and identifying their effect on some physiological and biochemical indicators for (the level of lactic acid concentration, the concentration of sodium bicarbonate, the concentration level of (potassium K+) and (sodium Na+) in the blood, and the number of breathing times (RF) Research methodology: the experimental research method was adopted by designing the experimental and control groups on a sample of Army Sports Club players amounting to (16) players, deliberately selected (100%) from their community using a comprehensive enumeration method, and then divided into two groups of equal number, After determining the tests for physiologica
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The experiment was conducted to study the effect of sodium chloride (NaCl) at the concentrations of 0.0, 0.5, 1.0 and 1.5% on the callus cells. The Iraq wheat variety was grown in vitro for the purpose of knowing the effect of salt stress on some indicators and cellular components of callus by using a randomized complete design, at the laboratories of tissue culture propagation date palm unit in the College of Agriculture / University of Kufa during the period 2014-2015. Fresh and dry weight, the rate of absolute growth, percentage of dry matter of callus, content of the callus cells of proline, total soluble carbohydrates, sodium and potassium ions, effectiveness of the enzymes catalase and peroxidase study shock salt proteins in callus we
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In this research, the preparation of bidentate Schiff base was carried out via the condensation reaction of both the salicylaldehyde with 1-phenyl-2,3-dimethyl-4-amino-5-oxo-pyrazole to form the ligand (L). The mentioned ligand was used to prepare complexes with transition metal ions Mn(II), Co(II), Ni(II), Cu(II) and Zn(II). The resulting complexes were separated and characterized by FTIR and UV-Vis spectroscopic technique. Elemental analysis for Carbon, Hydrogen and Nitrogen elements, electronic spectra of the ligand and complexes were obtained, and the magnetic susceptibility tests were also achieved to measure the dipole moments. The molar conductivities were also measured and determination of chlorine content in the complexes and
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