A submoduleA of amodule M is said to be strongly pure , if for each finite subset {ai} in A , (equivalently, for each a ?A) there exists ahomomorphism f : M ?A such that f(ai) = ai, ?i(f(a)=a).A module M is said to be strongly F–regular if each submodule of M is strongly pure .The main purpose of this paper is to develop the properties of strongly F–regular modules and study modules with the property that the intersection of any two strongly pure submodules is strongly pure .
To enhance interfacial bonding between carbon fibers and epoxy matrix, the carbon fibers have been modified with multiwall carbon nanotubes (MWCNTs) using the dip- coating technique. FT-IR spectrum of the MWCNTs shows a peak at 1640 cm−1 corresponding to the stretching mode of the C=C double bond which forms the framework of the carbon nanotube sidewall. The broad peak at 3430 cm−1 is due to O–H stretching vibration of hydroxyl groups and the peak at 1712 cm−1 corresponds to the carboxylic (C=O) group attached to the carbon fiber. The peaks at 2927 cm−1 and 2862 cm−1 ar
Cerium oxide (CeO2), or ceria, has gained increasing interest owing to its excellent catalytic applications. Under the framework of density functional theory (DFT), this contribution demonstrates the eect that introducing the element nickel (Ni) into the ceria lattice has on its electronic, structural, and optical characteristics. Electronic density of states (DOSs) analysis shows that Ni integration leads to a shrinkage of Ce 4f states and improvement of Ni 3d states in the bottom of the conduction band. Furthermore, the calculated optical absorption spectra of an Ni-doped CeO2 system shifts towards longer visible light and infrared regions. Results indicate that Ni-doping a CeO2 system would result in a decrease of the band gap. Finally,
... Show MoreIn this paper, three approximate methods namely the Bernoulli, the Bernstein, and the shifted Legendre polynomials operational matrices are presented to solve two important nonlinear ordinary differential equations that appeared in engineering and applied science. The Riccati and the Darcy-Brinkman-Forchheimer moment equations are solved and the approximate solutions are obtained. The methods are summarized by converting the nonlinear differential equations into a nonlinear system of algebraic equations that is solved using Mathematica®12. The efficiency of these methods was investigated by calculating the root mean square error (RMS) and the maximum error remainder (𝑀𝐸𝑅n) and it was found that the accuracy increases with increasi
... Show MoreIn the present study, ( Schiff's bases 6a - 6e) and (new amids derivatives 6f - 6j) have been synthesized . The glutaroyl chloride(2) has been prepared by the reacting of glutaric acid and thionyl chloride in presence of (DMF) . The new compound bis(4-formylphenyl) glutarate (3) has been Synthesized from reaction of one mole of glutaroyl chloride and two moles of 4-hydroxybenzaldehyde . Compound 4,4'-(glutaroylbis(oxy))dibenzoic acid (4) was Synthesized from one mole of glutaroyl chloride and two moles of 4-hydroxybenzoic acid, while compound bis(4-(chlorocarbonyl)phenyl) glutarate (5) was prepared from 4,4'-(glutaroylbis(oxy))dibenzoic acid and Thionyl chloride . Then Schiff's bases 6a - 6e that prepared
... Show MoreHighly Modified Asphalt (HiMA) binders have garnered significant attention due to their superior resistance to rutting, fatigue cracking, and thermal distress under heavy traffic loads and extreme environmental conditions. While elastomeric polymers such as Styrene- Butadiene-Styrene (SBS) have been extensively used in HiMA applications, the potential of plastomeric polymers, including Polyethylene (PE) and Ethylene Vinyl Acetate (EVA), remains largely unexplored. This study aims to evaluate the performance of reference binder (RB) modified with plastomeric HiMA asphalt in comparison to SBS-modified binders and determine the optimal polymer dosage for achieving an optimal balance between rutting resistance and fatigue durability. The experi
... Show MoreBy condensation of benzaldehyde with thiourea in absolute ethanol in the presence of glacial acetic acid as a catalyst, the Schiff base(1-benzylidenethiourea)[I] was synthesized by synthesis of 4-(3-benzylidenethioureido)-4-thioxobut-2-enoic acid compound[II] by reaction of maleic anhydride with schiff base [I] in DMF. When treating compound [II] with ammonium persulfate (NH4)2S2O8 (APS) as an ethanol initiator to obtain polymer [III], compound [III] reacted to polymer [IV] with SOCl2 in benzene. Sulfamethizole, celecoxib, salbutamol, 4-aminoantipyrine to yield polymers [V-VIII], compound [IV] reaction with different drugs. Spectral evidence established the structure of synthesized compounds: FTIR an