Different palaeoenvironmental features that pose natural geological, environmental, and engineering hazards to human operations occur frequently around the Nile Valley. Moreover, where these features were initially created, their relevance focuses on how the urban communities responded to the processes. So, a ground penetrating radar (GPR) field survey was carried out on different paleoenvironments of Pre-Quaternary and Quaternary sediment around Assiut. Deep and critical analyses of georadar facies were made to obtain clear images of these features with unprecedented resolution. The main objective of this study is to find some reasonable geological interpretations for these features. From this study, it is possible to identify and differentiate these features originating from different geological environments and climatological conditions in arid regions such as those around Assiut. In addition, the study serves as guidelines for environmental management and climatic changes for enhancing knowledge of urban development. Also, the study demonstrates how georadar can be used to create precise images of intricate shallow subsurface anatomy with possible palaeoenvironmental and palaeoclimatic indicators.

This paper introduces a generalization of the Hasse derivative in the sense of the complex conformable derivative. The definition coincides with the classical version of the Hasse derivative of order i$$ i $$. Accordingly, a new base, named complex conformable Hasse derivative bases (CCHDBs), is defined. We investigate the existence of expansions of analytic functions in a series of CCHDBs in Fréchet space on closed and open disks, open regions surrounding closed disks, for all entire functions and at the origin. Moreover, an upper bound for the order and type of the CCHDBs is obtained and proved to be attainable. The ‐property of CCHDBs is also discussed. Our results improve and extend the analog results in the complex analysis related to the classical complex derivative of a base of polynomials (BPs). The obtained results clarify several implications for the CCHDBs of special functions such as Euler …

The present paper investigates the approximation of special monogenic functions (SMFs) in infinite series of hypercomplex Hasse derivative bases (HHDBs) in Fréchet modules (F-modules). The obtained results ensure the existence of such representation in closed hyperballs, open hyperballs, closed regions surrounding closed hyperballs, at the origin, and for all entire SMFs (ESMFs). Furthermore, we discuss the mode of increase (order and type) and the Tρ-property. This study enlightens several implications for some associated HHDBs, such as hypercomplex Bernoulli polynomials, hypercomplex Euler polynomials, and hypercomplex Bessel polynomials. Based on considering a more general class of bases in F-modules, our results enhance and generalize several known results concerning approximating functions in terms of bases in the complex and Clifford settings.

This paper presented a new Ruscheweyh fractional derivative of fractional order in the complex conformable calculus sense. We applied the constructed complex conformable Ruscheweyh derivative (CCRD) on a certain base of polynomials (BPs) in different regions of convergence in Fréchet spaces (F-spaces). Accordingly, we investigated the relation between the approximation properties of the resulting base and the original one. Moreover, we deduced the mode of increase (the order and type) and the Tρ-property of the polynomial bases defined by the CCRD. Some bases of special polynomials, such as Bessel, Chebyshev, Bernoulli, and Euler polynomials, have been discussed to ensure the validity of the obtained results.

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.