Intensive research efforts have been dedicated to the extension and development of essential aspects that resulted in the theory of one complex variable for higher-dimensional spaces. Clifford analysis was created several decades ago to provide an elegant and powerful generalization of complex analyses. In this paper, first, we derive a new base of special monogenic polynomials (SMPs) in Fréchet–Cliffordian modules, named the equivalent base, and examine its convergence properties for several cases according to certain conditions applied to related constituent bases. Subsequently, we characterize its effectiveness in various convergence regions, such as closed balls, open balls, at the origin, and for all entire special monogenic functions (SMFs). Moreover, the upper and lower bounds of the order of the equivalent base are determined and proved to be attainable. This work improves and generalizes several existing results in the complex and Clifford context involving the convergence properties of the product and similar bases.

We implement the fractional Hirota bilinear technique to compute analytical solution for hyperbolic generalized space–time fractional Burgers model. We construct double soliton wave for the desired fractional differential model under study. These calculations are performed by the symbolic computation such as maple, which has been used more recently by researchers which proves that the Hirota bilinear method is a promising and straightforward procedure for treatment nonlinear differential models of integer and fractional orders. We checked whether the results demonstrate that the process is easy to calculate, effective, and direct to address a wide range of engineering and physics models. The arbitrary and random selection of the fractional orders enables us and allow to build richer structures. The changes in the soliton based on the changes of fractional order allows more applications in applied sciences. The dynamical behavior of the obtained solutions have been depicted and underlined in 3D and 2D graphical drawings with different chooses of the fractional order. 

In the present study, the structural properties, as well as the photodegradation performance of methylene blue (MB) and rhodamine B (Rh B) using hydrothermal synthesized Ag_xSn_1–xO₂ (0 ≤ x ≤ 1) nanocomposites were studied. The study was investigated using various techniques including EDS, XRD, FE-SEM, HR-TEM, photoluminescence spectroscopy, N₂ adsorption-desorption, GC-MS, and a double-beam spectrophotometer. The tetragonal SnO₂ phase dominates, while the cubic Ag₂O phase appears at larger x ratios (x ≥ 0.5). The crystallite and particle sizes were slightly raised for a low Ag ratio but dramatically increased for higher x ratios. Different morphologies emerge depending on the composition, such as spherical and irregular particles for x = 0 and 1, sheet-like morphology for x = 0.05, 0.2, and 0.4, and worm-like morphology for x = 0.5. The maximum surface area was calculated using the BET …

Glasses with varying compositions were prepared using the melt-quenching process within the 40B₂O₃-20PbO-xZnO-(40-x)CaO system, where x=20, 25, 30 and 35 mol%. ZnO's influence on the prepared glasses' radiation shielding properties was studied in the 0.015–15 MeV energy range. The results demonstrated that ZnO has a significant shielding effect at low energies, where there is an increased in the linear attenuation coefficient from 279.96 to 319.17 cm^-1 at 0.015 MeV due to the 20-to-35 mol% increase in ZnO. The values of the mean free path (MFP) for the prepared glasses are very small when the energy is less than 0.1 MeV, in the order of 0.013-0.015 cm at 0.03 MeV, 0.051-0.055 cm at 0.05 MeV and 3.051-3.248 cm at 1 MeV, which revealed an enhanced attenuation efficiency with increasing ZnO content. According to the MFP results, the Zn35Ca5 sample (which contains 35 mol% ZnO) offers the …

A method of forming metal nanostructures is a low temperature closed space vacuum deposition method. The method includes disposing a source material in an enclosed space at low evaporation temperatures to controllably form nanostructures of different dimensionalities on a substrate. The nanostructures have dimensionalities determined by a chosen evaporation temperature. An apparatus is also provided for performing the method.

In this study, we present a novel definition for hyperbolic Theta operator bases (HTOBs) and hyperbolic integral operator bases (HIOBs) within the context of complex calculus. We employ the constructed HTOBs and HIOBs on a specific base of polynomials (BPs) across diverse convergence regions within Fréchet spaces. Consequently, we explore the correlation between the approximation properties of the resulting base and the original one. Furthermore, we derive insights into the -property and the mode of increase of the polynomial bases as defined by HTOBs and HIOBs. The investigation extends to various bases of special polynomials, including Chebyshev, Bessel, Gontcharaff, Euler and Bernoulli, polynomials, ensuring the robustness and applicability of the obtained results.

This study investigates non-rhizobial endophytic bacteria in the root nodules of chickpea (Cicer arietinum L), faba bean (Vicia faba), and cowpea (Vigna unguiculata L. Walp), as well as arbuscular mycorrhizal fungi in the rhizospheric soil of chickpea and faba bean. Out of the 34 endophytic bacterial populations examined, 31 strains were identified as non-rhizobial based on nodulation tests. All strains were assessed for their plant growth-promoting (PGP) activities in vitro. The results revealed that most isolates exhibited multiple PGP activities, such as nitrogen fixation, indole-3-acetic acid (IAA) and ammonia (NH₃) production, phosphate solubilization, and exopolysaccharide production. The most effective PGP bacteria were selected for 16S rRNA analysis

High-load reactors face a significant challenge with fatty acid accumulation. Although injecting acidogenic gas (H2 and CO2) into methanogenic reactors improves biogas production, its mechanisms and stability enhancement remain unclear. Therefore, this study investigated the potential of using acidogenic gas to enhance methane production and system stability in a high substrate-loading co-digestion system with decreasing hydraulic retention time (HRT) and its regulatory role by considering biological pathways. Acidogenic gas injection effectively managed volatile fatty acid accumulation, with a concomitant increase in methane production from 0.042 to 0.066 L/L h as HRT decreased (16–8 days). However, the methane yield decreased from 611 to 460 mL/g volatile solids. Microbial community analysis revealed an increased abundance of hydrogenotrophic methanogens, along with several acidogenic and syntrophic fatty acid oxidizing consortia with decreasing HRT. The HRT10.67 sample exhibited the highest microbial species diversity and richness in the methanogenic reactor. Metabolomics analysis showed acidogenic gas reduced energy synthesis related to the tri-carboxylic acid cycle and oxidative phosphorylation while profoundly regulating the metabolism of amino acids, lipids, fatty acids, membrane transporters and inhibitory substances, thereby strengthening methane metabolism pathways. This study provides valuable insights into the roles of acidogenic gas in regulating energy metabolism to enhance methane production and offers potential opportunities for improving lipid and protein degradation.

Two-stage anaerobic digestion (AD) system is an efficient technology; however, organic loading rate (OLR), a critical design and process parameter, influences the performance and capacity of digesters. This study investigates the impact of various OLRs on biogas production during co-digestion of food waste, chicken manure and corn straw in an innovatively designed two-stage reactor system, including variations in the enzyme and electron transfer system (ETS) activities and microbial community. The production of hydrogen and methane increased gradually with increasing OLR, with maximum production at 8 g VS/L d (690 mLH₂/L d and 690 mLCH₄/L d), which is 30–97 % higher than OLR of 1.5 to 6 g VS/L d. However, the maximum methane yield of 535 mL/g VS_added was attained at OLR of 4 g VS/L d consistent with the highest coenzyme F420 activity. Although no substantial ETS activity was seen during the acidogenic stage, the ETS activity decreased with increasing OLR in the methanogenesis stage, indicating that high substrate loading results in low syntrophic methanogenesis. Microbial analysis revealed a more diverse enrichment of acidogens and acetogens at high OLR with a wider range of substrate consumption, resulting in balanced acetoclastic and hydrogenotrophic methanogens (Methanosarcina and Methanothermobacter) in the biomethane process. These findings suggest the strengthening of syntrophic methanogenesis in high substrate-loading AD systems.