Volume 22 – Issue 3

In this paper, we characterize the directional derivatives in accordance with the asymptotic orthonormal frame {x,α,y} in Q^2. Also, we express the extended Serret-Frenet relations by using cone Frenet formulas and we explain the geometrical understanding of energy on each asymptotic orthonormal vector fields in null cone. Furthermore, we express the bending elastic energy function for the same particle according to curve x(s,ξ,η) and we finalize our results by providing energy variation sketches according to directional derivatives for different cases. Additionally, we explain a geometrical interpretation of the energy for unit vector fields and we express Maxwell’s equations for the electric and magnetic field vectors in null cone 3-space.

In this study, we examine timelike helices in !_4^2 and some integral characterizations of these curves in terms of Frenet frame. In addition, we study timelike B_2 slant helices in !_4^2 and present the differential equations for vector positions.

In this study, the dynamics of a discrete-time plant-herbivore model obtained using the forward Euler method are discussed. The existence of fixed points is investigated. A topological classification is made to examine the behavior of the positive fixed point where the plant and the herbivore coexist. In addition, the existence conditions and direction of Neimark-Sacker bifurcation of the model are investigated using bifurcation theory. Hybrid control method is applied to control the chaos caused by Neimark-Sacker bifurcation. Examples including time series figures, bifurcation figures, phase portraits and maximum Lyapunov exponent are provided to support our theoretical results.

In this paper, inspiring Hosoya’s triangle, we define a new Narayana triangle. Then, we represent this Narayana triangle geometrically on the plane. In addition, we give some identities and properties of the new Narayana triangle

The purpose of this paper, first, is to give a definition of the focal surfaces of the inverse of a given regular surface in E^3. Second, some new characteristic properties of the focal surfaces are to express depending on the algebraic invariants of the inverse surface of a given regular surface. In the last part of the study, we gave examples supporting our claims and plotted their graphics with the help of Maple software.

This work is an extension to the work of [1] on ratio estimators of variance, by modification using dual to ratio method. The consistency conditions, bias, mean square error, optimum mean square error and efficiency have been derived and its performance is illustrated using natural populations. It is observed that the proposed class of estimators is most efficient at its optimum value, due to highest percent relative efficiency generated by it, when compared to the usual unbiased estimator for variance

In this article, we have extended the results of Y. U. Gaba by taking multiplicative G-metric space instead of G-metric space. In this way, we proved contraction mapping theorems on multiplicative, G-metric spaces using rational type contraction conditions for a single map. Later on, we extended our results in the settings of triplet maps. We have also given examples to support our results.

In science and technology, the phenomena of transportation are crucial. Advection and diffusion can occur in a wide range of applications. Distinct types of decay rates are feasible for different non-equilibrium systems over lengthy periods of time when it comes to diffusion. In engineering, biology, and ecology, the problems under study are used to represent spatial impacts. The fast Adomian decomposition method (FADM) is used to solve time fractional reaction diffusion equations, which are models of physical phenomena, in the current study. Caputo fractional derivative meaning applies to the specified time derivative. The results are in series form and correspond to the proposed fractional order problem. These models have a strong physical foundation, and their numerical treatments have significant theoretical and practical applications. The leaning of the rapid convergence of method-formulated sequences towards the appropriate solution is also graphically depicted. With less computational cost, this solution quickly converged to the exact solution.

In this paper, we study the spherical indicatrices of involutes of a spacelike curve with spacelike binormal. Then we give some important relationships between arc lengths and geodesic curvatures of the spherical indicatrices of involute-evolute curve couple in Minkowski 3-space. Also, we give some important results about curve couple.

This article deals with the asymptotic behavior of non oscillatory solutions
of third order differentiel equation.
x^”’+x^”+a(t)f(x) x^’+b(t)g(x)=0.
The behavior of non-oscillatory solutions are shown to be bounded and L^p [0,∞)┤ under the specified conditions, the derivative are shown to be in〖 L〗^2 [0,∞)┤ and the solutions as well as their derivatives shown to approach 0 as t⟶∞ implying stability.
We obtain results which extend and complement those known in [1]. Finally, several examples illustrating the usefulness of the procedure are given.

In this paper some new Radon type inequalities for some seminorms on pseudo-Hilbert spaces and norms in Hilbert spaces are presented. Then several consequences and applications are given.

In this paper, the analytical solution of integral equations is presented by using various advance analytical techniques. The comparison between the prososed methods: variational iteration method (VIM), and series solution method (SSM) with the Adomian decomposition equations is given to show the effeficency of these methods. From the Mathematical point of view, the variational iteration method (VIM) is effective, appropriate and easily using to solve the problems. Particularly, the langrange multiplier in variational iteration method plays very importnant role to reduce the computational work of integration. At the end, numerical and graphical results are obtained by using Maple programing.

In this study, a new distribution is introduced. The Burr-Hatke distribution is considered the baseline distribution. Since the baseline distribution has one parameter, the new unit distribution also has one parameter. Some distributional properties such as moments, coefficients of skewness and kurtosis, stochastic ordering, etc. of the new distribution are studied. Five estimators such as maximum likelihood, least squares, weighted least squares, Anderson-Darling, and Cramer-von Mises are examined to estimate the unknown parameter of the new model. The performances of the estimators are analyzed according to the bias and mean square error criteria calculated by Monte Carlo simulation. Two numerical data analyses are performed. A new quantile regression model is also introduced based on the new distribution as an alternative to beta and Kumaraswamy regression. A Monte Carlo simulation is also conducted for the new regression model.

The rising number of out-of-school children (OOSC) constitutes a major obstacle to growth and development in Nigeria. Despite various institutional frameworks and policy initiatives, Nigeria accounts for the highest number of OOSC worldwide with one out of every five OOSC globally residing in Nigeria. In an attempt to characterize dynamics of OOSC and how it could be tackled to fount sustainable development in Nigeria, a new mathematical model was formulated. The validity of the model was examined using some mathematical theorems and the model equilibria were derived. The inclusive schooling ratio, an analytic parameter that quantified the extent to which the rising OOSC was being tackled to fount development, was computed. The stability properties of the model were studied via stability theory of differential equations based on the derived inclusive schooling ratio. Sensitivity analysis was conducted for some major parameters following the normalized forward sensitivity index approach to examine the relative importance of the model parameters to OOSC expansion and contraction. Numerical simulation was later conducted to justify the theoretical results and the results of the simulation showed that efforts to fount development through minimization of OOSC were fruitful if the inclusive schooling ratio was greater than one otherwise the menace of OOSC persisted. The policy implication of the result is that tackling the menace of OOSC to fount sustainable development in Nigeria is a long-term process and any policies designed to pursue the course must be sustained.

The wastewater treatment process significantly decreases the negative impact of the effluent on human health compared to the influent. This probabilistic study, based on mathematical formulas, which does not involve clinical studies, investigates the impact of polluting chemical elements on health, which may be higher or lower, depending on other direct or indirect factors. The conclusions from this study were (1) wastewater (the effluent, which falls within legal limits) cannot be used for domestic consumption, much less as drinking water; (2) regarding dermal absorption, this can only be possible if people use the wastewater (influent/effluent) for recreational purposes (bathing, fishing, etc.). If this were theoretically possible, the risks related to the respective water matrices can be much higher because in this study only five heavy metals (Cd, Pb, Cu, Ni, and Zn) found in the international legislation in the categories of substances with carcinogenic risk, were investigated in the wastewater, and it may also contain other substances with different risk degrees. In the future studies will be investigated the health risk assessment gradient related to the effluent from the point of discharge of the wastewater on the flow of the natural receiver.

To identify the pattern of myoglobin compared to hemoglobin blockade by the combustion products contained in the fire smoke using computational chemistry tools. The myoglobin unavailability can be a determining factor of the severity and consequences of smoke poisoning, generating the inability of patients to attempt evacuate themselves, compromising myocardial function, leading to crush syndrome-like effects and increasing of multi-organ failure to the victims of mass burn casualties event. In this study, it was used quantum chemical calculations performed with the Gaussian program suite using DFT/B3LYP/6-311G level of theory to optimize molecular geometries, calculate the molecular electrostatic potential, and obtain the vibrational spectrum. These calculations were applied to the myoglobin and hemoglobin model, thus studying their binding to the essential components of toxic fire smoke. Comparing the structural descriptors – frontier molecular orbitals, energy difference, electric dipole moment (μ), was obtained the highest values as belonging to hydrogen cyanide (2.9), which may explain its increased reactivity, meaning strong interaction with both myoglobin and hemoglobin, followed by hydrochloric acid (1.03) and carbon monoxide (0.122). Within the framework of complex intoxication generated by the inhalation of fire smoke, myoglobin is blocked in a temporal manner and according to a very similar pattern to hemoglobin. It follows that the significant rhabdomyolysis found in these patients is due not only to hypoxemia but also to the primary unavailability of myoglobin, and myocardial damage is also multifactorial. Although slightly discussed, the calculation of different structural and geometric descriptors for hydrochloric acid reveals for hydrochloric acid high values, suggesting binding affinities comparable to those of carbon monoxide. Molecular modeling programs allow for new approaches and can identify parameters or areas of their reference that influence the management of patients intoxicated with fire smoke components.

The current work describes the different methods used to investigate various potsherds. The potsherds were discovered at the Abusir archaeological site, dating back to the Old Kingdom period. This research aims to study the chemical and mineralogical composition of the potsherds and salt crystallization. For this purpose, the analytical study was carried out using different techniques such as a digital and polarizing microscopy, scanning electron microscopy coupled with X-ray energy dispersion (SEM/EDX), and X-ray diffraction. Microscopic examination shows that potsherds suffer, from different deterioration aspects, such as salt crystallization, accumulation of dust, and black spots. The results of the polarized microscope proved that sand, grog powder, and calcite were used as additive materials to improve clay’s properties. The EDX and XRD methods used in the current work provide an essential chemical view of the structure of the samples. The results of EDX confirmed the presence of a high percentage of chloride salts, iron, and aluminium oxides. XRD results revealed that the firing temperature of the potsherds is high, around 850-950 °C. Therefore, the hardness of these sherds is high. There is little doubt that this will aid in conserving this valuable pottery.

The objective of this research work was to formulate, develop and evaluate immediate release tablet of paracetamol and orphenadrine citrate by direct compression method. Paracetamol which is antipyretic and orphenadrine citrate is skeletal muscle relaxant. The drug paracetamol and orphenadrine citrate was taken and formulated with different concentration of cross-povidone, mannitol, micro-crystalline cellulose, magnesium stearate and talc. Where cross-povidone as a superdisintegrant, mannitol as diluent, micro-crystalline cellulose as binder, magnesium stearate as lubricant and talc as a glidant used. the preformulation parameters such as bulk density, tapped density, compressibility index and hausner’s ratio were analysed. The thickness, hardness, friability, weight variation, disintegration time & drug content uniformity was evaluated. the in-vitro drug release studied were performed in the usp type (ii) paddle using 0.1N HCl as a dissolution media at 75 rpm speed and temperature of 37±0.5ºC. The % drug release at different time interval was estimated using UV method. Based on the evaluation result f9 trial was selected as the best formulation. The in-vitro drug release profile of the drugs was compared with marketed reference product. All the evaluated result was found to be satisfied with the reference products.

Rapid industrialization, urbanization and technological advancement in this century have drastically changed the biogeochemical cycles and balance of some of the heavy metals, thereby leading to environmental pollution in alarming proportions. Lead (i.e., Pb2+) is toxic to most organisms for concentrations higher than 0.05 mg/L, moreover, it is carcinogenic to animals. In the present study, batch biosorption of Pb2+ from wastewaters was studied using the nonliving biomass of Aspergillus sp. and Fusarium sp. isolated from soil. The specific metal removal increased with increase in initial lead ion concentration upto 500 mg/L observed with both the biomasses. A complete removal of the metal was observed at an initial metal ion concentration 50 mg/L and at pH 5.0. A maximum removal of 42.5 mg/g with Fusarium sp. and 37.3 mg/g with Aspergillus sp. was observed at pH 5.0 at 500 mg/L initial lead ion concentration. The adsorption equilibrium was obtained within 1h for all the concentration used. The adsorption equilibrium constants were obtained using both Freundlich and Langmuir adsorption isotherms. The desorption studies disclose the effective recovery of lead from the metal concentrated biomass using 0.1N Nitric acid solution within 0.5 h of time period increasing its effectiveness of reuse.

The increasing number of IoT (Internet of Things) based embedded systems, used nowadays in every aspects of our lives, inherently generates new challenges that require specific technical attention regarding: the increasing power demand directly proportional with the rising oftheir computational power and wireless communication functions, a more complex and flexible UPS (Uninterruptible Power Supply) design with load sharing function, a correctly balanced BMS (Battery Management System) consistent with the battery technology used and the manufacturer technical specifications, a more stable DC to DC converter output, a smarter system fail-safe algorithm, all concentrated in a more compact form factor. Taking all that into consideration, this article addresses all the previously mentioned issues in order to design, evaluate and present a fully functional UPS prototype for most IoT embedded systems. Although the proposed UPS prototype design can also be successfully used on non-OS (Operating System) IoT embedded platforms, with minor adaptations, the focus experimentation in this article will be on the every student’s favorite, but power demanding, Raspberry Pi 4 Model B. Basically, being acomplete and miniaturized OS computer, the popular Raspberry Pi 4 is a very adamant candidate for tightinput DC power parameters, that work in direct correlation with the system’s stability and performance. The final goal of the proposed UPS prototype is to provide Raspberry Pi 4 with enough independent runtime, until it safely shuts down the OS, in case of an external power blackout, and start back on at anexternal power restore event, all in order to protect the file system stability, or the data acquisition and storage processes from corruption.

The present study reveals the analysis of steady mixed convection MHD stagnation point flow of Casson fluid of non-Newtonian nature and Heat transfer over an exponentially stretching surface where the consequence of uniform heat source and sink are taken in to consideration. The presiding Non-linear Partial differential equations and the corresponding boundary conditions are formulated and thus transformed into pair of non-linear ordinary differential equations. The equations thus obtained are deciphered using Runge-Kutta fourth – order method with the help of MATLAB software. The results obtained for Skin friction coefficient and heat transfer rate for the case of Newtonian fluid are determined, which are in good harmony with the previously proclaimed results of other researchers.The impact of physical quantities such as Casson parameter, buoyancy parameter, Hartmann number, Prandtl number, heat source and sink, Suction parameter, on the fluid velocity and temperature are discussed through graphs for both assisting and opposing flow. The variation in Skin friction coefficient and Nusselt number are tabulated for various values of Hartmann number. Divergence in the velocity profile is observed for increase in Suction for two different values of Velocity ratio parameter. As Skin friction coefficient escalates with suction parameter indicating the exertion of drag force by the surface on the fluid flow. Also, the study reveals that the impact of Hartmann number is to minimize the boundary layer separation.