In this work, two different structures are proposed which is fuzzy real normed space (FRNS) and fuzzy real Pre-Hilbert space (FRPHS). The basic concept of fuzzy norm on a real linear space is first presented to construct space, which is a FRNS with some modification of the definition introduced by G. Rano and T. Bag. The structure of fuzzy real Pre-Hilbert space (FRPHS) is then presented which is based on the structure of FRNS. Then, some of the properties and related concepts for the suggested space FRN such as -neighborhood, closure of the set named , the necessary condition for separable, fuzzy linear manifold (FLM) are discussed. The definition for a fuzzy seminorm on is also introduced with the prove that a fuzzy seminorm on is FRNS. The relationship between the -convergent sequence, -Cauchy sequence and -completeness is then investigated in this work. The structure of FRPHS with some important properties concerning on this space are introduced and proved. In addition, the property of orthogonality with some important properties for these spaces is included, for example the annihilator of the set . The relation between FRPHS and FRNS is investigated in the present work. Finally, after introducing the structure of FRPHS, it leads naturally to the definition of the most important class of FRPHS, namely the fuzzy real Hilbert space (FRHS).
The zeolite's textural properties have a significant effect on zeolite's effectiveness in the different industrial processes. This research aimed to study the textual properties of the NaX and FeX zeolites using the nitrogen adsorption-desorption technique at a constant low temperature. According to the International Union of Pure and Applied Chemistry, the adsorption-desorption isotherm showed that the studied materials were mixed kinds I/II isotherms and H3 type hysteresis. The Brunauer-Emmett-Teller isotherm was the best model to describe the nitrogen adsorption-desorption better than the Langmuir and Freundlich isotherms. The obtained adsorption capacity and Brunauer-Emmett-Teller surface area values for NaX were greater than FeX. Ac
... Show MoreHartree-Fock (HF) method relies in the calculations of nonlinear optical properties (NLO) for benzoic acid molecule. Also, another theoretical study is conducted by using the TD-DFT Density Functional Theory through B3LYP/High Base Set 6-311++G (2d,2p) on Gaussian program09. Moreover, an experimental study has been done to obtain the electrons spectrum for benzoic acid with and without ethanol. While the experimental study is done by using UV/VIS. spectrophotometer. Energy gap values of electronic transition between HOMO and LUMO is obtained from theoretical and experimental results. Consequently, the theoretical result for determining the energy gap calculated from EHOMO-LUMO wasvery close to the results of UV / VIS. spectrum. A theoretica
... Show MoreAcid treatment is a widely used stimulation technique in the petroleum industry. Matrix acidizing is regarded as an effective and efficient acidizing technique for carbonate formations that leads to increase the fracture propagation, repair formation damage, and increase the permeability of carbonate rocks. Generally, the injected acid dissolves into the rock minerals and generates wormholes that modify the rock structure and enhance hydrocarbon production. However, one of the key issues is the associated degradation in the mechanical properties of carbonate rocks caused by the generated wormholes, which may significantly reduce the elastic properties and hardness of rocks. There have been several experimental and simulation studies regardi
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That Iraq's dependence on the revenues of the oil product in financing its development programs and growth rates , Making the economy affected by external forces represented by fluctuations in crude oil prices in the global market, Which is directly reflected on the performance and efficiency of the Iraqi economy.
The study adopted its objectives to analyze the time series for the period (1988 - 2015) through the use of standard and statistical methods, Four standard models were estimated to reach those targets, Where the results of the stability test showed instability of most variables at their original level, But to achieve stability when taking the first differences, While the result
... Show MoreBackground: Masseter muscle is one of the most obvious muscles of mastication and considered as one indicator of jaw muscle activity. It has a major influence on the transverse growth of the midface and the vertical growth of the mandible. This study undertaken to determine the role of cephalometric analysis for discrimination between Cl I and Cl III skeletal relationships, determine the role of ultrasonography in determination of masseter muscle thickness, compare masseter muscle thickness between Cl I and Cl III skeletal relationships, and determine the effect of gender on masseter muscle thickness. Material and Method: The sample of the current study consisted of 70 Iraqi subjects 40 males and 30 females with age ranging 18-25 years. The
... Show MoreThe structural, optical and electrical properties of ZnS films prepared by vacuum evaporation technique on glass substrate at room temperature and treated at different annealing temperatures (323, 373, 423)K of thickness (0.5)µm have been studied. The structure of these films is determined by X-ray diffraction (XRD). The X-ray diffraction studies show that the structure is polycrystalline with cubic structure, and there are strong peaks at the direction (111). The optical properties investigated which include the absorbance and transmittance spectra, energy band gab, absorption coefficient, and other optical constants. The results showed that films have direct optical transition. The optical band gab was found to be in the range t
... Show MoreA comprehensive practical study of typical mechanical properties of welded Aluminum alloy AA7020-T6 (Al-Mg-Zn), adopting friction stir welding (FSW) technique and conventional metal inert gas (MIG) technique, is well achieved in this work for real comparison purposes. The essences of present output findings were concentrated upon the FSW samples in respect to that MIG ones which can be summarized in the increase of the ultimate tensile strength for FSW was 340 MPa while it was 232 MPa for MIG welding, where it was for base metal 400 MPa. The minimum microhardness value for FSW was recorded at HAZ and it was 133 HV0.05 while it was 70 HV0.05 for MIG weld at the welding metal. The FSW produce 2470 N higher than MIG welding in the bending t
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