Volume 21 – Issue 4

In this article, we construct the plastic number in the three-dimensional space. We examine the nested radicals and continued fraction expansions of the plastic ratio. In addition, we give some properties and geometric interpretations of the plastic constant.

This article is concerned with designing numerical schemes for the generalised Oskolkov equation using the quintic B-spline collocation finite element method. Applying the von-Neumann theory, it is shown that the proposed method is marginally unconditionally stable. It was obtained the theoretical bound of the error in the full discrete scheme for the first time in the literature. The accuracy and effectiveness of the method checked with three model problems, consisting of a single solitary wave, Gaussian initial condition and growth of an undular bore. The performance of the new method is demonstrated by calculating invariant I and error L_2 norms and L_¥ . Results are displayed both numerically and graphically. Numerical experiments support the correctness and robustness of the method which can be further used for solving such problems.

The modified Kudryashov approach along with the conformable derivative is used to find a variety of askew wave solutions, with some free parameters, of the space-time fractional modified KdV equations. We study the wave solutions of the aforesaid mKdV equations that are obliquely propagated to consider the behaviour of physical issues in water waves and other fluids. The graphical depiction of these solutions is given via Mathematica for better understanding. Moreover, apart from the physical implication, these solutions may be helpful for an upgraded understanding of numerical solvers to compare the accuracy of their results and performances of wave dynamics as observed in science and engineering.

In this paper, the hyperbolic tangent function method is applied for constructing exact solutions for space-time conformal fractional Burgers’ equation. Furthermore, the space-time conformal fractional Burgers’ equation is tested for the Painlevé property, and consequently, new numerous exact solutions are generated via Bäcklund transform.

In this paper we present a fixed point theorem for order-preserving Prešić type operators on ordered vector metric spaces. This result extends many results in the literature obtained for Prešić type operators both on metric spaces and partially ordered metric spaces. We also emphasize the relationships between our work and the previous ones in the literature. Finally we give an example showing the fact that neither results for Prešić type contractions on metric spaces nor the results for ordered Prešić type contractions on ordered metric space is applicable to it.

In this paper, we investigated some basic properties of rough I-convergence of a triple sequence spaces of fuzzy in three dimensional matrix spaces which are not earlier. In addition, it was studied the set of all rough I-limits of a triple sequence spaces and also the relation between analytic ness and rough I-core of a triple sequence spaces.

This study introduces a new lifetime distribution as an alternative to power function distribution and modified ones. This model is generated by using a method based on the distributions of lower records. We discuss some statistical inferences and mathematical properties of the suggested distribution. We consider five estimation methods for the point estimation of the proposed distribution. Then, a comprehensive Monte Carlo simulation study is carried out to assess the risk behavior of examined estimators.

In this paper our aim is to get the general structure equation which covers previously acquired structures. In this context this paper consists of three main sections. In the first section, we define the general F_(a,λ) (K,T)-structure satisfying aF^K+λ^g F^T=0,(F≠0,K≥3,T≥1 and (K≥T),a and λ are non zero complex numbers, g some finite integer) on manifold M^n and studied to give some special examples. The second part, we find the integrability conditions by calculating Nijenhuis tensors of the horizontal lifts of the general F_(a,λ) (K,T)-structure satisfying aF^K+λ^g F^T=0. Later, we get the results of Tachibana operators applied to vector and covector fields according to the horizontal lifts of the general F_(a,λ) (K,T)-structure in cotangent bundle T^* (M^n). In addition, we have studied to show the purity conditions of Sasakian metric with respect to the horizontal lifts of the structure. In the final section, all results obtained in the second section were investigated according to the complete and horizontal lifts of the general F_(a,λ) (K,T)-structure on tangent bundle T(M^n).

In this study, the relation between Frenet Frame of the natural lift curve` g of the curve g and Bishop Frame vectors of g is given in IR^3 and IR_1^3 .

In this paper, a technique called Tanh method is applied to obtain some traveling wave solutions for Boussinesq’s equation, and by using new transform iterative method (NTIM) which is a combination of the new iterative method (NIM) and Laplace transform, we obtain an approximate solution to Boussinesq’s equation. A comparison between the traveling wave solution (exact solution) and the approximate one of equation under study, indicate that new transform iterative method (NTIM) is highly accurate and can be considered a very useful and valuable method.

In this study we introduce q-deformed split quaternions, that is, this deformation reduces to classical split quaternions as q®1 where q is a real parameter. It is also shown that there is a quantum group associated with q-deformed split quaternions, which is isomorphic to SU_q(1,1).

In this paper, we introduce some new generalizations of the Vieta-Pell polynomial, which is called the Vieta-Pell-Like polynomial. We also give the generating function, the Binet’s formula, the sum formula, and some well-known identities for this Vieta polynomial. Furthermore, the relations between the Vieta-Pell-Like polynomial and the previously well-known identities are presented.

In this paper, we define Gaussian Mersenne numbers and we give some properties of them. Moreover we present some relations among Gaussian Mersenne numbers, Gaussian Jacobsthal numbers and Gaussian Jacobsthal-Lucas numbers. We also present some results with matrices involving Gaussian Mersenne numbers.

In this paper, numerical solutions of generalized Huxley are obtained by using a new scheme: Crank-Nicolson logarithmic finite difference method (CN-LFDM). The efficiency of the presented method is illustrated by a numerical example for different cases of parameters which confirm that obtained results are in good agreement with the exact solutions and numerical solutions obtained by some other methods in literature. The method is analyzed by von-Neumann stability analysis method and it is displayed that the method is unconditionally stable.

In this study, we consider the existence of multiple weak solutions to a class of Dirichlet type problem involving p(.)-triharmonic {(-∆_p(.)^3 u=λ|u|^(q(.)-2) u in Ω, @u=Δu=Δ^2 u=0 on ∂Ω,) under some suitable conditions.

The main purpose of this paper is to investigate unit speed curve with constant geodesic, normal curvature and geodesic torsion of curve on a surface in the Euclidean 3-space. In accordance with this scope, the position vector of a curve is stated by a linear combination of its Darboux Frame with differentiable functions. Some special results have been obtained within the scope of this position curve and differentiable functions. As a physical application of obtained results, differential geometric properties of a surface with binormal motion of a given curve are given with the obtained characterization of the curve.

This research demonstrates the application of methylcellulose (MC) as a gelator for cleaning acrylic painted surfaces. Highly thickened methylcellulose gels were predominantly tested to investigate the residue left after cleaning. The function of methylcellulose as a molecular trap was also assessed to minimize the clearance issue. The presence of residue, the efficacy of the methylcellulose as a cleaning agent and its physical impact on the paint surfaces were investigated using a digital microscope in normal, raking, and ultraviolet lights. Scanning electron microscopy (SEM), coupled with energy-dispersive X-ray spectroscopy (EDS) was used to study the compositional and topographical changes on the paint surface. Fourier transform infrared spectroscopy (FTIR) was performed in attenuated total reflectance (ATR) mode to observe the presence of residues after complete removal of the gelling agent. The experimental results indicated a minimum interaction of methylcellulose on the paint surface as the concentration increases in the gel formulation. The super-thickened hydrogels also worked like molecular traps useful for removal of soiling from the painted surfaces.

Osteomyelitis continues to be a major concern when orthopedic surgery is performed. Orthopedic infections have an incidence of 5% to 10% but their management proves to be quite difficult due to both biofilm formation and limited access of the drug to the infected area when systemic treatment is employed. The aim of the study was to optimize the synthesis process of a gentamicin loaded poly(-lactic-co-glycolic) acid (PLGA) based biodegradable composite by varying parameters that affect both efficiency encapsulation and nanoparticle size. Furthermore, a kinetic study was conducted to study the biodegradation process of the polymer. Gentamicin loaded PLGA nanoparticles were obtained using the double emulsion technique which allows the variation of several factors such as gentamycin concentration, PLGA concentration, buffer concentration and stirring speed. Out of the four factors evaluated, gentamicin concentration had the highest impact on both encapsulation efficiency and nanoparticle size. A few relevant interactions between factors were also registered.

A range of nanostructured oxides with excellent properties is used in technology and science for applications in several fields: catalysis, gas detection, biomedical applications. The most studied forms of oxides are hematite, maghemite and magnetite. In this study, microwave-assisted hydrolytic synthesis and microwave-assisted coprecipitation synthesis are described for the preparation of undoped and doped iron oxide powders using iron (III) chloride (FeCl3), potassium chloride (KCl) as precursors and sodium hydroxide (NaOH) solution as a hydrolysis agent. Microwave-assisted hydrolysis was performed at different concentrations of FeCl3 precursor: 0.1 M, 0.4 M, 0.7 M to which a constant concentration of hydrolysis agent was added, and the synthesis to obtain potassium-doped powders consisted of co-precipitation of 0.1M FeCl3 and 0.025M KCl precursor solutions in the presence of 2M NaOH hydrolysis agent. The developed powders were characterized by X-ray diffraction (XRD), scanning electron microscopy (SEM), and Fourier transform infrared spectroscopy (FTIR). The novelty is the use of potassium as a doping element for iron oxide, for potential application as catalyst. Hematite doped with 5% K was obtained by microwave-assisted coprecipitation synthesis. The presence of K was evidenced by EDS, while XRD spectra indicate successful doping of iron oxide with potassium, either interstitially or by substitution. By microwave synthesis, an increase in particle size was observed with increasing calcination temperature. The formation of the crystalline hematite phase was not obtained in the microwave heating process but following calcination of the powders.

This study aims to determine the levels of caffeine in beverages commonly consumed in Saudi Arabia.10 samples collected from Riyadh market. Caffeine level was determined using high-efficiency liquid chromatography (HPLC). Three types of samples were analyzed. The caffeine concentration ranged from 0.446 to 6.374 mg / 1000 mL in coffee samples, and from 0.053 to 8.897 mg/1000 mL in tea samples. In soft drinks the caffeine amount was in the range of 1.466 – 4.698 mg / 1000 mL. Green tea (Alwazah tea) had the highest caffeine content among all the studied drinks (i.e., 8.897 mg/1000 mL). This study is the first in terms of caffeine levels, applied for a variety of beverages in Saudi Arabia. On the other hand, this investigation highlights the useful results for controlling caffeine intake or setting safe limits for it in drinks consumed in the Kingdom, and for nutritional education as well.

Bee products are essential natural resources in promoting a healthy diet with very important therapeutic properties, therefore they are used in medicine and cosmetics. That is why we set out to determine the degree of contamination with organic and inorganic pollutants in various bee products. For this purpose, different samples of honey were investigated, as follows: linden honey from Romanian accredited beekeepers (1); linden honey from H Company (2); linden honey from A Company (3) and acacia honey from accredited beekeepers (4). The concentrations of eight pesticides and five heavy metals were analyzed in the four honey samples taken. According to experimental data, there have been identified honey varieties in which the maximum permissible limits for pesticides (A Company) and heavy metals (H Company) were exceeded. As a result, a more rigorous control is required regarding the honey assortments sold on the market for consumer safety.

Chlorophyll-a is the pigment whose concentration is an important indicator for the development of microalgae biomass. This study aims at evaluating the concentration of chlorophylls in the biomass of granular activated algae, using acetone and 90% ethanol for the extraction procedures applied. Concentrations of chlorophyll a, b and c were determined by applying three calculation types: methods proposed by Jeffrey and Humphrey for the extracts in acetone, Ritchie method for ethanolic extracts, and monochromatic method with acidification for ethanolic extracts. Experimental findings show that the solvent 90% ethanol is more efficient than acetone for extracting chlorophyll from biomass of granular activated algae. Also, by comparing results obtained by the two methods proposed for ethanolic extracts, it was found that the values obtained through the acidification method are influenced by the volume of hydrochloric acid added to the organic chlorophylls extract

In this paper was studied eight bivalve shells (with pigments traces) collected from Cheia archaeological site (Eneolitihic site, dated between the end of the 6th millennium and the beginning of the 5th millennium cal BC, Romania), in order to established correlations related to morphology, composition, longevity and belonging to the archaeological site of these shells. The samples (pigments and shells) were investigated, from morphological and chemical composition point of view, by optical microscopy, scanning electron microscopy coupled with energy dispersive spectroscopy (SEM-EDS), and attenuated total reflectance – Fourier transform infrared (ATR-FTIR) spectroscopy, respectively. Principal component analysis (PCA) and cluster analysis (CA) were carry out using IBM SPSS Statistics software to assess the similarities between the investigated samples.

On Romania’s territory, after the major floods that took place during the 70s, the hydrotechnical setup of the large rivers that drain the peri-Carpathian areas was made. The purpose of building these anthropogenic dam lakes is complex, given that extreme hydrological phenomena occurred in late spring and early summer, caused by a significant rainwater supply (about 70%), the difference being made up by the underground supply. Such a hydrotechnical setup was made in the Subcarpathian areas, on large rivers, to mitigate flood waves, but also to create water resources to supply local communities. The main problem facing these lakes is the massive silting due on the one hand to the geological and geomorphological characteristics of the Subcarpathians and, on the other hand, to the high degree of anthropization. The Subcarpathians are, from a geological point of view, made up of friable deposits (marls, clays, marl-clays, gypsums, conglomerates), which trigger a series of geomorphological processes of slope erosion (areal streaming, ravine creation, runoffs, torrential rainfall, and landslides), all of which are involved in the hydrological drainage regime. The Subcarpathians also make up a geographical area with a high density of population and, implicitly, of anthropogenic activities, which under certain conditions favour the erosion and degradation of land. These factors ensure that the solid flow recorded on the Subcarpathian Rivers is between 5-25 million tons/ha per annum. All this leads to the intense silting of anthropogenic lakes, which causes the volume of water stored in the tank to sometimes decrease to 1/3 of its initial volume. Under these conditions, in the extremity of basins, lacustrine plains were formed, and within the dam area, the pelitic sedimentary deposits exceeded 7-10 m in thickness. The aim of this study is to perform a multitemporal analysis of lake silting in the Subcarpathian area by using GIS and integrating the suite of bathymetric elevations and the series of satellite images existing from the time of the lake’s construction to present-day.

The Korteweg-de Vries Burgers (KdVB) is significant in applied mathematics and physical sciences. Particularly, it is a fundamental equation in the study of shallow water waves. The traditional techniques which have been suggested to solve the Korteweg-de Vries Burgers (KdVB) are labor-intensive and time-consuming. The primary goal of this study is to introduce various analytical techniques i.e., Exp-Function Method, Modified Exp-Function Method, Variational Iteration Method, and the Decomposition Method to solve the Korteweg-de Vries Burgers (KdVB) equation. These methods are quickly implemented and give very accurate results of the KdVB equation. Among them, the Variational Iteration Method is particularly user-friendly and simple to implement for the aforementioned problem. The involvement of Lagrange Multiplier is a powerful tool to reduce the cumbersome integration. At the end, Maple18 is used to find the analytical and graphic outcomes. These results show that the proposed methods are effective and applicable to other nonlinear equations of physical interest as well.

In the present problem Heat and Mass transfer of a MHD flow in the effect of radiation, viscous dissipation and Joule heating is considered. The temperature at the wall is taken as power law with variable exponent. The problem is solved analytically using concept of confluent hypergeometric function. The effects of various parameters entering into the problem are discussed and presented in graphical form. Variable power of temperature parameter provides unique and very useful results for the effects over temperature.