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
This paper studies the behavior of reinforced Reactive Powder Concrete (RPC) two-way slabs under static and repeated load. The experimental program included testing six simply supported RPC two-way slabs of 1000 mm length, 1000 mm width, and 70 mm thickness. All the tested specimens were identical in their material properties, and reinforcement details except their steel fibers content. They were cast in three pairs, each one had a different steel fibers ratio (0.5 %, 1 %, and 1.5 %) respectively. In each pair, one specimen was tested under static load and the other under five cycles of repeated load (loading-unloading). Static test results revealed that increasing steel fibres volume fraction from 0.5 % to 1 % and from 1% to 1.5%,
... Show MoreOff-nucleus isotropic magnetic shielding (σiso(r)) and multi-points nucleus independent chemical shift (NICS(0-2 Å)) index were utilized to find the impacts of the isomerization of gas-phase furfuraldehyde (FD) on bonding and aromaticity of FD. Multidimensional (1D to 3D) grids of ghost atoms (bqs) were used as local magnetic probes to evaluate σiso(r) through gauge-including atomic orbitals (GIAO) at density functional theory (DFT) and B3LYP functional/6-311+G(d,p) basis set level of theory. 1D σiso(r) responses along each bond of FD were examined. Also, a σiso(r) 2D-scan was performed to obtain σiso(r) behavior at vertical heights of 0–1 Å above the FD plane in its cis, transition state (TS) and trans forms. New techniques fo
... Show MoreThe purpose of this experiment was to determine the relationship between the path coefficient and seed rate for four different barley cultivars (Amal, Ibaa 265, Ibaa 99, and Buhooth 244) during the 2019-2020 winter season. The experiment was carried out using a split plot design with three replications according to a randomized complete block design (RCBD). The highest positive thru effect on grain yield was found for flag leaf area and harvest index at aseeding rate of 130 kg.h-1; the highest positive direct effect on grain yield was found for flag leaf area and plant height at aseeding rate of 160 kg.h-1; and the highest positive direct effe
Heterogeneous organic compounds play an important role in our daily life as they contribute in many medical and industrial fields and are in continuous development as a result of the preparation of new derivatives with different properties. From this premise, the goal of this work appears, which is preparation of (four, five, six, and seven) membered ring systems derived from furfural, by its reaction with different aromatic aldehydes, and record their antioxidant activity by using free radical scavenging method of DPPH radicals. The new ring systems are synthesized by reacting the prepared Schiff-bases with different ring closure agents (chloroacetyl chloride, mercaptoaceticacid, anthranilic acid, and phthalic anhydride), the prep
... Show MoreBased on the results of standard penetration tests (SPTs) conducted in Al-Basrah governorate, this research aims to present thematic maps and equations for estimating the bearing capacity of driven piles having several lengths. The work includes drilling 135 boreholes to a depth of 10 m below the existing ground level and three standard penetration tests (SPT) at depths of 1.5, 6, and 9.5 m were conducted in each borehole. MATLAB software and corrected SPT values were used to determine the bearing capacity of driven piles in Al-Basrah. Several-order interpolation polynomials are suggested to estimate the bearing capacity of driven piles, but the first-order polynomial is considered the most straightforward. Furthermore, the root means squar
... Show MoreBecause of Cadmium selenide quantum dots (CdSe quantum dots) has a tuning energy gap in the visible light range, therefore; it is provided a simple theoretical model for the absorption coefficient of CdSe quantum dots, where the absorption coefficient determines the extent to which the light of a material can penetrate a specific wavelength before it is absorbed. CdSe quantum dots have an energy gap can be controlled through two effects: the temperature and the dot size of them. It is found that; there is an absorption threshold for each directed wavelength, where CdSe quantum dots begin to absorb the visible spectrum at a size of 1.4 nm at room temperature for a directed wavelength 3
Rutting has a significant impact on the pavements' performance. Rutting depth is often used as a parameter to assess the quality of pavements. The Asphalt Institute (AI) design method prescribes a maximum allowable rutting depth of 13mm, whereas the AASHTO design method stipulates a critical serviceability index of 2.5 which is equivalent to an average rutting depth of 15mm. In this research, static and repeated compression tests were performed to evaluate the permanent strain based on (1) the relationship between mix properties (asphalt content and type), and (2) testing temperature. The results indicated that the accumulated plastic strain was higher during the repeated load test than that during the static load tests. Notably, temperatur
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