This paper is concerned with introducing an explicit expression for orthogonal Boubaker polynomial functions with some important properties. Taking advantage of the interesting properties of Boubaker polynomials, the definition of Boubaker wavelets on interval [0,1) is achieved. These basic functions are orthonormal and have compact support. Wavelets have many advantages and applications in the theoretical and applied fields, and they are applied with the orthogonal polynomials to propose a new method for treating several problems in sciences, and engineering that is wavelet method, which is computationally more attractive in the various fields. A novel property of Boubaker wavelet function derivative in terms of Boubaker wavelet themselves is also obtained. This Boubaker wavelet is utilized along with a collocation method to obtain an approximate numerical solution of singular linear type of Lane-Emden equations. Lane-Emden equations describe several important phenomena in mathematical science and astrophysics such as thermal explosions and stellar structure. It is one of the cases of singular initial value problem in the form of second order nonlinear ordinary differential equation. The suggested method converts Lane-Emden equation into a system of linear differential equations, which can be performed easily on computer. Consequently, the numerical solution concurs with the exact solution even with a small number of Boubaker wavelets used in estimation. An estimation of error bound for the present method is also proved in this work. Three examples of Lane-Emden type equations are included to demonstrate the applicability of the proposed method. The exact known solutions against the obtained approximate results are illustrated in figures for comparison
Treatises concerning analyzing the interior spaces multiplied and their directions varied, that some of them analyzed the interior space on the basis of the intellectual and philosophical affiliation or the historical period and others in the light of the concept and mechanisms of the shape. The researcher has not been able to find a research that dealt with analyzing the space within the systems of shape generation, thus it is possible to determine the research problem with the following question: to what extent is it possible to analyze the interior space based on systems of shape generation? As far as the importance of the research is concerned, it sheds light on five of the systems of the shape generation which are: Syntax, shape gra
... Show Moresynthesis, Composition, Spectral, Geometry and Antibacterial Applications ofMn(||),Ni(||),Co(||),Cu(||) and Hg(||) schiff Base complexes of N2O2 mixed donor with 1,10-phenanthroline
A series of liquid crystals comprising a heterocyclics dihydro pyrrole and 1,2,3-triazole rings [VII]-[X] were synthesized by many steps starting from a reaction of 3,3'-dimethyl-[1,1'-biphenyl]- 4,4'-diamine with chloroacetyl chloride in a mixture of solutions DMF and TEA to synthesise the compounds [I], then the compounds [I] reacted with malononitrile in 1,4-dioxane and TEA solutions to produce compounds [II], then the first step is repeated with compound [II] where it reacted with chloroacetyl chloride in mixture of DMF and TEA to give compound [III], this compound reacted with sodium azide in the presence of sodium chloride and DMF as solvent to produce the compound [IV], which reacted with acrylic acid by a 1.3 dipolar reaction in sol
... Show MoreBackground: Moringa peregrina is widely used in the traditional medicine of the Arabian Peninsula to treat various ailments, because it has many pharmacologically active components with several therapeutic effects. Objective: This study aimed to investigate the inhibitory effect of Moringa peregrina seed ethanolic extract (MPSE) against key enzymes involved in human pathologies, such as angiogenesis (thymidine phosphorylase), diabetes (α-glucosidase), and idiopathic intracranial hypertension (carbonic anhydrase). In addition, the anticancer properties were tested against the SH-SY5Y(human neuroblastoma). Results: MPSE extract significantly inhibited α-glucosidase, thymidine phosphorylase, and carbonic anhydrase with half-maximal i
... Show MoreIn 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
... Show MorePolymer films of PEG and PVA and their blend with different
concentrations of MnCl2 (0, 2, 4, 6 and 10 %.wt) were study using
casting technique. The X-ray spectra of pure PEG, PVA and
PVA:PEG films and with addition of 2% concentrations from
(MnCl2) show amorphous structures. The results for FTIR show the
interaction between the filler and polymer blend results in
decreasing crystallinity with rich amorphous phase. This
amorphous nature confirms the complexation between the filler and
the polymer blend. The optical properties of (PVA:PEG/MnCl2)
contain the recording of absorbance (A) and explain that the
absorption coefficient (α), refractive index (n), extinction coefficient
(ko) and the dielectric cons
In this paper, A.C conductivity of micro and nano grain size- TiO2 filled epoxy composites is measured. The dielectric material used is epoxy resin, while micro and nano-sized titanium dioxide (TiO2) of grain size (1.5μm, and 50nm) was used as filler at low filler concentrations by weight (3%, and 5%). Additionally the effect of annealing temperature range (293-373)º K and at a frequency range of 102-106 Hz on the A.C conductivity of the various specimens was studied.
The result of real permittivity for micro and nanocomposite show that the real permittivity increases with decreasing frequency at range of 102-106Hz. The micron-filled material has a higher real relative permittivity than the nano-filled this is true at all the temper
The synthesis of conducting polyaniline (PANI) nanocomposites containing various concentrations of functionalized single-walled carbon nanotubes (f-SWCNT) were synthesized by in situ polymerization of aniline monomer. The morphological and electrical properties of pure PANI and PANI/SWCNT nanocomposites were examined by using Fourier transform- infrared spectroscopy (FTIR), and Atomic Force Microscopy (AFM) respectively. The FTIR shows the aniline monomers were polymerized on the surface of SWCNTs, depending on the -* electron interaction between aniline monomers and SWCNTs. AFM analysis showed increasing in the roughness with increasing SWCNT content. The AC, DC electrical conductivities of pure PANI and PANI/SWCNT nanocomposite h
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