Volume 21 – Issue 1

This paper will use Lagrange parameter in Adomain decomposition method to suggest new method for solving nonlinear differential equation. This method will be highly order convergent. Also, this method will be compared with old existence method. At last, some numerical examples will be given to illustrate the efficiency of newly developed method.

This paper is devoted to some new applications of Laplace-Weierstrass transform (i.e., for solving two dimensional diffusion equations). Solution of Cauchy’s linear differential equation is also given. Some results are also given which are required for solving Cauchy’s linear differential equation.

The Wiener index is classic and well-known topological index for the characterization of molecular graphs. In this paper, we study interval weighted graphs such as graphs where the edge weights are interval or interval matrices. In this study firstly we define interval weighted graph. Later we define Wiener index of interval weighted graph. From this definition, we give algorithms for finding Wiener index of interval weighted directed and undirected graph.

In this paper, we define and study another interesting generalization of the Fibonacci quaternions is called k-order Fibonacci quaternions. Then we obtain for k=2 Fibonacci quaternions, for k=3 Tribonacci quaternions and for k=4 Tetranacci quaternions. We give generating function, the summation formula and some properties about k-order Fibonacci quaternions. Also, we identify and prove the matrix representation for k-order Fibonacci quaternions. The Q_k matrix given for k-order Fibonacci numbers is defined for k-order Fibonacci quaternions and after the matrices with the k-order Fibonacci quaternions is obtained with help of auxiliary matrices, important relationships and identities are established.

The paper aims to study the dynamics of a system of nonlinear difference equations x_(n+1)=x_(n-1) y_n+A,y_(n+1)=y_(n-1) x_n+A where A is real number. We especially investigate the stability of equilibrium points, convergence of equilibrium points, existence of periodic solutions, and existence of bounded solutions of related system. Moreover, we present some numerical examples to verify the theoretical results.

In this paper, bicomplex balancing quaternions and bicomplex Lucas-balancing quaternions was defined. Moreover we give some properties involving these sequences. Finally, a different way to obtained the n th terms of these sequence is stated using the determinant of tridiagonal matrix whose entries are bicomplex balancing quaternions and bicomplex Lucas-balancing quaternions.

In this study, on the semi-axis, Sturm – Liouville problem under boundary condition depending on spectral parameter is considered. In what follows scattering data is defined and its properties are given for the problem. The kernel of resolvent operator which is Green function is constructed. Using Titchmarsh method, expansion is obtained according to eigenfunctions and expansion formula is expressed with the scattering data.

In this study, the Bézier curves and surfaces, which have an important place in interactive design applications, are expressed in matrix form using a special matrix that gives the coefficients of the Bernstein base polynomial. The matrix forms of higher order derivatives of the Bézier curves and surfaces are obtained. It is demonstrated by numerical examples that the bidirectional transition between the control points and parametric equations of the Bézier curves and surfaces can be easily achieved using these matrix forms. In addition, it is demonstrated that this type of curve and surface, whose control points are known, its higher order derivatives can be calculated without it’s parametric equations. In this study, the Bézier curves and surfaces are presented in a more easily understandable and easy to use format in algebraic form for designers.

In this paper, new exact traveling wave solutions for the coupling Boiti-Leon-Pempinelli system are obtained by using two important different methods. The first is the modified extended tanh function methods which depend on the balance rule and the second is the Ricatti-Bernoulli Sub-ODE method which doesn’t depend on the balance rule. The solitary waves solutions can be derived from the exact wave solutions by give the parameters a special value. The consistent and inconsistent of the obtained solutions are studied not only between these two methods but also with that relisted by the other methods.

The aim of this paper is to give main properties of the generating function of the Bernstein polynomials of triple sequence spaces. It was proved the recurrence relations and derivative formula for Bernstein polynomials of triple sequences. Further more, some new results are obtained by using this generating function of these polynomials.

In this paper, we obtain the Fermi-Walker derivatives of x_1 , x_2 , B magnetic curves according to the type-2 Bishop frame in the space. Moreover, we obtain the energy of the Fermi-Walker derivative of magnetic curves according to the type-2 Bishop frame in space. Finally, we have energy relations of some vector fields associated with type-2 Bishop frame in the space.

In this study, we introduce a new class of generating functions of odd and even Gaussian (p,q)-Fibonacci numbers, Gaussian (p,q)-Lucas numbers, Gaussian (p,q)-Pell numbers, Gaussian (p,q)-Pell Lucas numbers, Gaussian Jacobsthal numbers and Gaussian Jacobsthal Lucas numbers and we will recover the new generating functions of some Gaussian polynomials at odd and even terms. The technique used her is based on the theory of the so called symmetric functions.

In this paper, we show that the system of difference equations x_n=(x_(n-2) z_(n-3))/(z_(n-1) (a_n+b_n x_(n-2) z_(n-3) ) ),y_n=(y_(n-2) x_(n-3))/(x_(n-1) (α_n+β_n y_(n-2) x_(n-3) ) ),z_n=(z_(n-2) y_(n-3))/(y_(n-1) (A_n+B_n z_(n-2) y_(n-3) ) ),n∈N_0, where the sequences (a_n )_(n∈N_0 ), (b_n)_(n∈N_0 ), (β_n)_(n∈N_0 ), (A_n)_(n∈N_0 ), (B_n)_(n∈N_0 ), and the initial values x_(-j),y_(-j),z_(-j), j∈{1,2,3} are non-zero real numbers, can be solved in the closed form. Also, we determine the forbidden set of the initial values by using the obtained formulas. Finally, we obtain periodic solutions of aforementioned system.

The paper produces some new modified forms of the ratio estimators using the auxiliary information. The large sample properties, that is, the bias and mean squared error up to the first order of approximation are determined. The comparison is made with other existing estimators by using an applied data. It has been observed that the proposed estimators have a fewer mean squared error and leads to the efficient results as compared to the classical ratio estimator, Sisodia and Dwivedi, Singh and Kakran, Upadhyaya and Singh estimators.

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

The research purpose represents the identification and mathematical definition of some models expressed by regression equations describing the GE per inhabitant according to the GDP per inhabitant. The study is customized at EU level and in seven states located in the Eastern-EU (RO, PL, GR, BG, SI, SK and HU) for the period 2009-2018. The research methodology is based on econometric modelling and testing of their viability. Relevant conclusions are also made regarding RO’s position in the European Union in terms of government spending. The research provides useful information to substantiate micro and macroeconomic decisions designed to ensure a dynamic of GE’s sustainable growth on education, health, general public services, defense, public order and safety. Based on the developed econometric models, values of endogenous variables (GE per capita) can be estimated depending on the variants of predictable scenarios for the size of the GDP per capita.

Carved limestone false door dating back to the late Sixth Dynasty or the First Intermediate Period in Abusir archaeological area suffers from many physiochemical and mechanical deterioration factors, which lead to various deterioration phenomena, such as distort the carvings, decorations, the disappearance of paint, cracks in different depths, and salt calcification. It was found in the fill of Shaft 5 in the tomb AS 79 at Abusir South, Excav. No. 9/AS79/2015 and located in the storeroom of Czech Excavation in Abusir area. The current work aims to study the type of limestone which the false door is made of, and to know if there were colors on the false door or not, also to know if there were deterioration mechanisms that affect the carved limestone false doors of Abusir to evaluate the deterioration ratio in stone structure and the effects of surrounding environmental factors on stone. The investigation and characterization processes of archaeological limestone samples were carried out by polarizing microscopy (PLM), optical microscopy (OM), scanning electron microscopy (SEM-EDX) micro-analysis system, X-ray diffraction (XRD), X-ray fluorescence (XRF), and Fourier transform infrared spectroscopy (FTIR). The results revealed that the limestone material of the false door belongs to micrite limestone with very fine grains and needs to be conserved.

This study aimed to evaluate the existence of muscarinic receptors in the new corneal blood vessels, experimentally induced with ketamine in rat pups. The experimental model of neovascularization was performed on 15-day-old Wistar rats, in which 5 intraperitoneal injections of ketamine were administered at a dose of 150 mg/kg body weight at 5-day intervals. Examination of the reactivity of new corneal blood vessels was performed on day 45 of life. Each eye that developed neovascularization was evaluated with a Nikon stereomicroscope, coupled to a Mshot video camera, and the total magnification of the system was 400X. The vascular diameter was measured at a chosen point, the same point /points for each recording made to that eye, and the acquisition of images was performed at set time intervals, every 60 seconds for each eye to be examined, throughout the recording period. The parameters under investigation were the variations of the vascular diameter, and the processing of the obtained data was performed with the help of Microsoft Office Excel. Our results suggest that muscarinic receptors are present in the new corneal blood vessels because the administration of conjunctival instillations of acetylcholine caused statistically significant vasodilation, while atropine, a blocker of muscarinic receptors, antagonized this effect.

Spectrometric analysis belongs to a group of measurement methods used for their simplicity and large selectivity to solve various problems of analytes. The total phenolic content of different plant extracts used for cosmetic purpose was determined by a slightly modified version of traditionally Folin-Ciocalteau method. The objective of this work was the validation of UV-Vis spectrometric method, investigation of uncertainty sources when measuring gallic acid concentration and evaluation of the calibration equation effect on measurement uncertainty of UV– Vis spectrophotometer. Validation was performed by studying analytical curve linearity (R2=0.9995) and range (37.5 – 225 mg L-1), estimated limit of detection (LOD, 0.11mg L-1) and limit of quantification (LOQ, 0.37 mg L-1), precision (%RSD, 0.14 – 1.34), recoveries (83-110%) and stability (%RSD, 0.8 – 2.83). To obtain more representative values for precision, recoveries and stability simultaneous replicates at different times, on different matrices including plant (marigold, chamomile and lavender) were performed during the study period. The validated method was successfully applied to determine TPC in marigold extracts. For chamomile and lavender extracts, the spectrometric method presented only acceptable precision, among all the performance parameters studied. The sources of the gallic acid concentration measurement uncertainty include purity, volume of flasks, mass and the calibration equation. The results indicated that the uncertainty components from purity were the smallest. An important source of the uncertainty was the mass.The volumes of the volumetric flasks had only modest effect on the uncertainty. The contribution of calibration equation is the greatest from all sources.

Methylene blue is generally used as dyeing agent in textile, printing and pharmaceutical industries, which leads to the obtaining of large amounts of wastewater. The purpose of this study is to remove methylene blue dye from aqueous solutions using fir wood sawdust waste as low cost biosorbent material. In order to evaluate the adsorption process, analyses for determination of micrometric properties, infrared spectroscopy, optical microscopy and colorimetry were performed. To increase the efficiency of the process and the adsorption surface, the fir wood sawdust was grinded and sieved. Some specific parameters were varied in the experimental part in order to study the influence of the adsorbent support dose, concentration, temperature, contact time, volume and stirring rate. The removal efficiency of methylene blue dye was further studied for evaluating the adsorption capacity of the fir wood sawdust.

Heterocyclic derivatives are unavoidable in many fields of natural disciplines. These derivatives play numerous significant roles in research, medication, and nature. Nitrogenous heterocyclic derivatives extremely are the main target of concern in synthetic chemistry to ensue active natural products with pharmaceuticals and agrochemicals interest. Benzimidazole skeleton is another example of some active heterocyclic moiety that significantly contributes in the numerous bioactive of essential compounds. Benzimidazole skeleton is studied as a prominent moiety of biologically active compounds with various activities including antimicrobial, antiprotozoal, anticancer, antiviral, acetylcholinesterase, antihistaminic, anti-inflammatory, antimalarial, analgesic, anti-HIV and antitubercular. Therefore, in this review we summarize the various antiviral activities of several benzimidazole derivatives and outline the correlation among the structures of different benzimidazoles scaffold with their therapeutic significance.

The aim of this paper is to find out – for the first time – through archaeometric analysis the provenance of the Precucuteni-type pottery from Alba Iulia-Lumea Nouă settlement and whether it has a local origin or is an imported ceramic. The presence of so-called Precucuteni-type pottery in Transylvanian sites, decorated by motifs using excision techniques, represents one of the most challenging debates related to the understanding of the material culture that belongs to Early Eneolithic human communities in the Intra-Carpathian area. A combination of non-invasive / micro-destructive analytical techniques and statistical methods were applied to provide comprehensive information about the studied fragments. In this respect, ten pottery samples were investigated to establish the elemental and molecular composition, as well as its origin. Overall, the analytical and statistical analyses show us that the local production of pottery is predominant, with a limited presence of imports. In summary, nine ceramic fragments out of all analyzed samples belong to the same group, with a strong correlation between them, confirming that they are locally made, while one sample can be considered as imported from elsewhere or obtained through mixing clay with some existing soils in the area during the pottery production stage.

High productivities and economic benefits in modern agriculture have been accomplished only by the use of pesticides. The introduction of these compounds in the food chain can be considered a risk for human health due to their toxicity. So, pesticides residues and their degradation products resulted by hydrolytic, photochemical and microbial processes in soil and cereals must be monitored and controlled. The aim of this research was to develop rapid and sensitive HPLC-DAD methods for residues detection of several pesticides, imidacloprid, amidosulfuron, bromoxynil and deltamethrin, from soil and some crops, maize, wheat and rape seeds, cultivated in Banat County-Moravita Zone. In order to perform the pesticides extraction, the samples were subjected to an ultrasonic technique, at 59 kHz and 30°C, during 30-45 min., using acetonitrile and acetonitrile-water mixture as solvents. Acetonitrile alone proved to be more appropriate for this purpose. The HPLC analyses were conducted on HPLC-DAD apparatus, Dionex Ultimate 3000 (Dionex Corp., USA), equipped with quaternary pump LPG 3400A, thermostat of columns TCC-3000 and a C-18 Acclaim® 120 Silica-reversed-phase (4.6×150 mm, 5 µm) column, using different compositions of acetonitrile-water as mobile phase. The presented HPLC – Dionex system proved to be very suitable for determination of pesticides residues in soil and crops.

In this study, the effect of different stages of ripening (i.e., unripe, semi-ripe and ripe) on quality parameters of oils extracted from the kernels of Mango (Magnifera indica) seeds was investigated. The kernels were oven-dried and oil extracted from them using soxhlet apparatus and n-hexane as solvent. The fatty acid profile, phospholipids, sterol contents and some chemical properties such as saponification value, peroxide value, iodine value and acid value of oils obtained from the seeds at different level of maturity were determined. The results show that the oils are rich in saturated fatty acid most especially stearic and palmitic acids varying from 34.36 – 37.86% and 8.84 -10.66 %, respectively. The predominant unsaturated fatty acid present in the oils is oleic acid ranging from 41.96 – 45.65 %. For the chemical parameters, the peroxide values (1.82 – 2.23 %) meq/kg, acid values (5.00 – 5.50) mg/KOH/g decreased with fruit maturity. For phospholipids, phosphatidyl choline (380 – 451 mg/100 g) and phosphatidyl ethanolamine (217.42 – 342.63 mg/100 g) having the highest quantities, they all increased with fruit maturity except sphingomyelin and phosphatidic acid. Stigmasterol, sitosterol and cholesterol contents of the oils decreased with fruit maturity while Δ-5-avenasterol, campesterol and the cholestanol contents increased with fruit maturity. Sitosterol and stigmasterol and had the highest values at 345.81 – 386.96 mg/100 g and 83.70 – 137.09 mg/100 g, respectively. Conclusively, the kernel oils have potential for use as domestic and industrially as a non-conventional source of vegetable oil in chocolate and confectionery products.