Legendre-Gauss-Lobatto collocation method for solving multi-dimensional systems of mixed Volterra-Fredholm integral equations

Integral equations play a crucial role in many scientific and engineering problems, though solving them is often challenging. This paper addresses the solution of multi-dimensional systems of mixed Volterra-Fredholm integral equations (SMVF-IEs) by means of a Legendre-Gauss-Lobatto collocation method. The one-dimensional case is addressed first. Afterwards, the method is extended to two-dimensional linear and nonlinear SMVF-IEs. Several numerical examples reveal the effectiveness of the approach and show its superiority in comparison to other alternative techniques for treating SMVF-IEs

A Novel Triazole Schiff Base Derivatives for Remediation of Chromium Contamination from Tannery Waste Water

Tannery industries are one of the extensive industrial activities which are the major source of chromium contamination in the environment. Chromium contamination has been an increasing threat to the environment and human health. Therefore, the removal of chromium ions is necessary to save human society. This study is oriented toward the preparation of a new triazole Schiff base derivatives for the remediation of chromium ions. 4,4′-((1E)-1,2-bis ((1H-1,2,4-triazol-3-yl) imino)ethane-1,2-diyl) diphenol was prepared by the interaction between 3-Amino-1H-1,2,4-triazole and 4,4′-Dihydroxybenzil. Then, the produced Schiff base underwent a phosphorylation reaction to produce the adsorbent (TIHP), which confirmed its structure via the different tools FTIR, TGA, 1HNMR, 13CNMR, GC-MS, and Phosphorus-31 nuclear magnetic resonance (31P-NMR). The newly synthesized adsorbent (TIHP) was used to remove chromium oxyanions (Cr(VI)) from an aqueous solution. The batch technique was used to test many controlling factors, including the pH of the working aqueous solution, the amount of adsorbent dose, the initial concentration of Cr(VI), the interaction time, and the temperature. The desorption behaviour of Cr(VI) changes when it is exposed to the suggested foreign ions. The maximum adsorption capacity for Cr(VI) adsorption on the new adsorbent was 307.07 mg/g at room temperature. Freundlich’s isotherm model fits the adsorption isotherms perfectly. The kinetic results were well-constrained by the pseudo-second-order equation. The thermodynamic studies establish that the adsorption type was exothermic and naturally spontaneous. © 2022 by the authors.The APC was funded by “Dunarea de Jos” University of Galati, Romania. The researcher H.A.A is funded by a scholarship under the Joint (Executive Program between Egypt and Russia)

A Novel Triazole Schiff Base Derivatives for Remediation of Chromium Contamination from Tannery Waste Water

Tannery industries are one of the extensive industrial activities which are the major source of chromium contamination in the environment. Chromium contamination has been an increasing threat to the environment and human health. Therefore, the removal of chromium ions is necessary to save human society. This study is oriented toward the preparation of a new triazole Schiff base derivatives for the remediation of chromium ions. 4,4′-((1E)-1,2-bis ((1H-1,2,4-triazol-3-yl) imino)ethane-1,2-diyl) diphenol was prepared by the interaction between 3-Amino-1H-1,2,4-triazole and 4,4′-Dihydroxybenzil. Then, the produced Schiff base underwent a phosphorylation reaction to produce the adsorbent (TIHP), which confirmed its structure via the different tools FTIR, TGA, 1HNMR, 13CNMR, GC-MS, and Phosphorus-31 nuclear magnetic resonance (31P-NMR). The newly synthesized adsorbent (TIHP) was used to remove chromium oxyanions (Cr(VI)) from an aqueous solution. The batch technique was used to test many controlling factors, including the pH of the working aqueous solution, the amount of adsorbent dose, the initial concentration of Cr(VI), the interaction time, and the temperature. The desorption behaviour of Cr(VI) changes when it is exposed to the suggested foreign ions. The maximum adsorption capacity for Cr(VI) adsorption on the new adsorbent was 307.07 mg/g at room temperature. Freundlich’s isotherm model fits the adsorption isotherms perfectly. The kinetic results were well-constrained by the pseudo-second-order equation. The thermodynamic studies establish that the adsorption type was exothermic and naturally spontaneous

Spectral technique with convergence analysis for solving one and two-dimensional mixed Volterra-Fredholm integral equation.

A numerical approach based on shifted Jacobi-Gauss collocation method for solving mixed Volterra-Fredholm integral equations is introduced. The novel technique with shifted Jacobi-Gauss nodes is applied to reduce the mixed Volterra-Fredholm integral equations to a system of algebraic equations that has an easy solved. The present algorithm is extended to solve the one and two-dimensional mixed Volterra-Fredholm integral equations. Convergence analysis for the present method is discussed and confirmed the exponential convergence of the spectral algorithm. Various numerical examples are approached to demonstrate the powerful and accuracy of the technique

Pulsed laser ablation in liquid assisted growth of gold nanoparticles: evaluation of structural and optical features

High purity gold (Au) nanoparticles (NPs) with desired morphology are demanding for various applications. Being simple, versatile, and cost-effective technique, PLAL is promising for the production of impurities free nanoparticles (NPs) of diverse materials. This paper reports the preparation and characterization of colloidal Au-NPs. Such Au-NPs were produced via PLAL route, wherein the Au target was immersed inside deionized water and ablated using a Q-switched Nd:YAG laser (wavelength 1064 nm and pulse width 8 ns). The structural, morphological, and optical characteristics of the as-synthesized Au-NPs were evaluated as a function of varied laser energies and repetition rates. Optical traits of Au-NPs were analyzed by ultraviolet–visible (UV–Vis) absorption, photoluminescence, and Raman spectroscopy. Surface plasmon resonance (SPR) absorbance at the excitation wavelength of 633 nm was recorded to find the shape of the Au-NPs. Attenuated total reflection infrared (ATR-IR) spectra was obtained to verify the achieved Au-NPs purity. High-resolution transmission electron micrographs approved the nucleation of spherical colloidal Au-NPs (mean diameter of 7 to 30 nm) in deionized water. The UV–Vis spectra of Au-NPs disclosed the occurrences of SPR peaks in the range of 521 to 524 nm accompanied by blue-shift. The UV absorption edge of the UV–Vis spectra was used to determine the optical band gap energies of the produced Au-NPs which were further confirmed by the photoluminescence spectral analyses. Present findings based on PLAL-assisted synthesis of pure Au-NPs may be beneficial for the development photocatalysis and solar cells

Electronic and optical correlation effects in bulk gold: role of spine-orbit coupling

The modified Becke-Johnson exchange potential proposed by Tran and Blaha (TB-mBJ) is useful for accurate calculations of electronic band structures of solids. In this view, we used such potential together with spin–orbit coupling to calculate the electronic and optical correlation effects in bulk gold (Au) via first principle DFT. Inclusion of the relativistic effects in the simulation were found to play vital role on the optical properties of bulk Au. Furthermore, the imaginary part of the dielectric function of Au disclosed good agreement with the experimental results. Disclosure of good agreement between simulation and experimental results (up to Fermi level) was due to the improvement in the band structure of bulk Au achieved by incorporating spin–orbit coupling

A New Partially Phosphorylated Polyvinyl Phosphate-PPVP Composite: Synthesis and Its Potentiality for Zr (IV) Extraction from an Acidic Medium

A newly synthesized partially phosphorylated polyvinyl phosphate derivative (PPVP) was functionalized to extract Zirconium (IV) from Egyptian zircon sand. The specifications for the PPVP composite were approved effectively via different techniques, namely, FT-IR, XPS, BET, EDX, TGA, 1H-NMR, 13C-NMR, GC-MS, XRD and ICP-OES analyses, which demonstrated a satisfactory synthesis of PPVP and zircon dissolution from Egyptian zircon sand. Factors controlling parameters, such as pH values, shaking time, initial zirconium concentration, PPVP dose, nitrate ions concentration, co-ions, temperature and eluting agents, have been optimized. At 25 °C, pH 0, 20 min shaking, 0.05 mol/L zirconium ions and 0.5 mol/L nitrate ions, PPVP has an exciting preservation potential of 195 mg/g, equivalent to 390 mg/L zirconium ions. From the extraction–distribution isotherm, the practical outcomes of Langmuir’s modeling are better than the Freundlich model. With a theoretical value of 196.07 mg/g, which is more in line with the experimental results of 195 mg/g. The zirconium ions adsorption onto the PPVP composite follows the pseudo-second-order kinetics with a theoretical capacity value of 204.08 mg/g. According to thermodynamic potential, the extraction process was expected to be an exothermic, spontaneous and beneficial extraction at low temperatures. The thermodynamic parameters ΔS (−0.03 kJ/mol), ΔH (−12.22 kJ/mol) and ΔG were also considered. As the temperature grows, ∆G values increase from −2.948 kJ/mol at 298 K to −1.941 kJ/mol at 338 K. Zirconium ions may be eluted from the working loaded PPVP by 0.025M HNO3, with a 99% efficiency rate. It was found that zirconium ions revealed good separation factors towards some co-ions such as Hf4+ (28.82), Fe3+ (10.64), Ti4+ (28.82), V5+ (86.46) and U6+ (68.17). A successful alkali fusion technique with NaOH flux followed by the extraction with PPVP is used to obtain a high-purity zirconia concentrate with a zircon content of 72.77 % and a purity of 98.29%. As a result of this, the improved factors could finally be used

Prevalence of Low Back Pain and Associated Risk Factors among Saudi Arabian Adolescents: A Cross-Sectional Study

Low back pain is the most prevalent musculoskeletal condition. Studies on adolescent low back pain are scarce, with no research to determine its prevalence in Saudi Arabia. This study aimed to assess the prevalence and associated risk factors of low back pain in Saudi Arabian adolescents. This cross-sectional study was conducted among Saudi Arabian high school students, which included demographic data, medical and low back pain history. The completed survey by 2000 participants showcased 57.9% of students experiencing low back pain in the last 12 months. This included 31.2% men and 26.7% women. This study found a link between low back pain and age, clinical symptoms of diabetes, heart disease, lung disease, thyroid disease, arthritis, and back surgery, a family history of low back pain, as well as smoking. There is substantial prevalence of low back pain in Saudi Arabian adolescents. This study identified several modifiable and non-modifiable risk factors stemming from adolescent low back pain