Mathematics
Chemistry
Physics
Mathematics
The extended adjacency matrix A_e(G) of a graph G is determined by graph degrees. Some inequalities are found for the extended adjacency matrix including its vertices, its edges and its degrees in this paper. Also, some bounds are established for this matrix involving its energy and its laplacian energy.
It is known that a Bishop frame of a curve is one of the effective alternative approach in the differential geometry. Recently, several important works have been done about the Bishop frames. The aim of our paper is to investigate the N-Bishop frame for timelike curves in Minkowski space. We define the N-Bishop frame for the timelike curve in Minkowski space. Then, we consider some properties of the frame. Moreover, we describe the N-Bishop Darboux frame for the first time. Additionally, we compute some geometrical characterizations for the N-Bishop Darboux axis and momentum rotation vector.
In the present article, third order differential equation and corresponding boundary value problems considered for the numerical solution. An improved finite difference method developed for the approximate numerical solution. The proposed method converges and O(h^2), the order of convergence under appropriate condition established. In the numerical experiment, model problems were considered for the purpose of testing the performance of the proposed method. The numerical results generated in numerical experiment are in good agreement with the theoretical discussion and development of the proposed method.
Singularly perturbed differential equations are encountered in mathematical modelling of processes in physics and engineering. Aim of this study is to give a collocation approach for solutions of singularly perturbed two-point boundary value problems. The method provides obtaining the approximate solutions in the form of Müntz-Legendre polynomials by using collocation points and matrix relations. Singularly perturbed problem is transformed into a system of linear algebraic equations. By solving this system, the approximate solution is computed. Also, an error estimation is done using the residual function and the approximate solutions are improved by means of the estimated error function. Two numerical examples are given to show the applicability of the method.
The subject of this paper is the current state of art in theory of continued fractions, intermediate fractions and their relation to the best rational approximations of the first and second kind. The paper provides an overview of the some well known and even some new properties of continued fractions, and the various terms associated with them. In addition to intermediate fractions, paper considers the fine intermediate fractions and gave some statements to position these fractions in the continued fraction representation of numbers.
This article is pedestal for the (p,q)-calculus connecting two concepts of (p,q)-derivatives and (p,q)-integrals. The purpose of this paper is to establish different type of identities for (p,q)-calculus. Some special cases of the (p,q)-midpoint, Simpson, Averaged midpoint trapezoid, and trapezoid type integral identities are also derived.
In this article, firstly, the isomorphism between the subset of the tangent bundle of Lorentzian unit sphere, TM̃, and Lorentzian unit sphere, S^2_1 is represented. Secondly, the isomorphism between the subset of hyperbolic unit sphere, TM̂, and hyperbolic unit sphere, H^2 is given. According to E. Study mapping, any curve on S^2_1 or H^2 corresponds to a ruled surface in R^3_1. By constructing these isomorphisms, we correspond to any natural lift curve on TM̃ or TM̂ a unique ruled surface in R^3_1. Then we calculate striction curve, shape operator, Gaussian curvature and mean curvature of these ruled surfaces. We give
developability condition of these ruled surfaces. Finally, we give examples to support the main results.
In this article, the differential equation of lorentzian spherical timelike curves is obtained in E^1_4 . It is seen that the differential equation characterizing Lorentzian spherical timelike curves is equivalent to a linear, third order, differential equation with variable coefficients. It is impossible to solve these equations analytically. In this article, a new numerical technique based on hermite polynomials is presented using the initial
conditions for the approximate solution. This method is called the modified hermite matrixcollocation method. With this technique, the solution of the problem is reduced to the solution of an algebraic equation system and the approximate solution is obtained. In addition, the validity and applicability of the technique is explained by a sample application.
In this study, a Boole polynomial based method is presented for solving the linear Fredholm integro-differential equation approximately. In this method, the given problem is reduced to a matrix equation. The solution of the obtained matrix equation is found by using Boole polynomial, its derivatives and collocation points. This solution is obtained as the truncated Boole series which are defined in the interval [a, b]. In order to demonstrate the validity and applicability of the method, numerical examples are included. Also, the error analysis related with residual function is performed and the found approximate solutions are calculated.
The present paper presents evolution of spherical indicatrix of a space curve according to the quasi frame in Minkowski 3-space. Some geometric properties such as fundamental forms and curvatures of the surfaces constructed by evolutions are obtained.
In this paper, we introduce a operator in order to derive some new symmetric properties of (p,q)-modified Pell numbers and we give some new generating functions of the products of (p,q)-modified Pell numbers with k-Fibonacci and k-Lucas numbers, k-Pell and k-Pell Lucas numbers, k-Jacobsthal and k-Jacobsthal Lucas numbers at positive and negative indices. By making use of the operator defined in this paper, we give some new generating functions of the products of (p,q)-modified Pell numbers with kbalancing and k-Lucas-balancing numbers.
This study, develops a way for representation of canal surfaces in 4-dimensional Euclidean space E^4. It examines the fundamental forms, Gaussian and mean curvature for a special type canal surface. Moreover, the conditions of both Weingarten and linear Weingarten canal surfaces are given for this new special type. Finally, the graphs of the projections of the canal surfaces using different radius functions in E^4 are presented.
In this work, a new emerging analytical techniques variational iteration method combine with Aboodh transform has been applied to find out the significant important analytical and convergent solution of some mathematical models of fractional order. These mathematical models are of great interest in engineering and physics. The derivative is in Caputo’s sense. These analytical solutions are continuous that can be used to understand the physical phenomena without taking interpolation concept. The obtained solutions indicate the validity and great potential of Aboodh transform with the variational iteration method and
show that the proposed method is a good scheme. Graphically, the movements of some solutions are presented at different values of fractional order.
In this paper, we shall give some structure equations for RB-almost solitons which generalize previous results for Ricci almost solitons. As a consequence of these equations we also derive an integral formula for the compact gradient RB h-almost solitons which enables us to show that a compact nontrivial almost Ricci soliton is isometric to a sphere provided either it has constant scalar curvature or its associated vector field is
conformal.
The mathematical analysis presented in this study identifies models of the dynamics of total tax collections and social contributions per inhabitant according to the gross domestic product per inhabitant from 2009 to 2018 for seven states in Eastern Europe by linear regression equations. The models are statistically confirmed as viable models because the required conditions for formulating this assessment are met. This study has the value and usefulness of preventive information for the correction and substantiation of individual governmental and community decisions, in order to homogenize both from the point of view of the fiscal behavior of each state and the point of view of economic development, in correlation with a financial and budgetary policy to maintain macroeconomic balances and economic stability
Chemistry
Studies of materials used for works of art and cultural monuments throughout the history contribute to the comprehensive understanding of particular cultures, their technological achievements and customs over time. Investigations of the authenticity of objects and the interventions they may have endured over time keep an important role for their successful restoration and preservation. A three-layer sample of the colored wall decoration from Ottoman Ćejvan Ćehaja mosque from Mostar, Bosnia and Herzegovina was investigated by FTIR spectroscopy. The plaster was identified as gypsum-lime binder. Inorganic pigments were found in two layers, reddish-brown mixture of Fe2O3 and MnO2 and green pigment recognized as viridian, Cr2O3 ∙ 2H2O. The upper layer of “golden color” is found to be a physically compact piece of gold foil or leaf whose fixation method meets both the Ottoman and “west” mode of binding. The mode of adhesion by animal glue could be the result of decoration immanent to Islamic culture, but also to reconstruction from the late 19th
century during the Austro-Hungarian rule in Bosnia.
Herbal extracts with antimicrobial potential represent an important research directive, in the current medical world, aiming to isolate active components, to develop new chemotherapeutic agents with applicability in the treatment or use as adjuvant therapy in infectious states. Antimicrobial properties of plants are conferred by their ability to synthesize certain secondary metabolites with relatively complex structures. The last century has been marked by sustained efforts to search for new natural compounds with antibacterial therapeutic properties, due to the gradual reduction in the number of effective allopathic antibiotics and the toxic effects of antibiotic residues. Numerous in vitro studies have shown that plants have antibacterial efficacy, discovering the importance of little-studied natural resources in this regard, as being effective in fighting against bacterial resistance and destroying bacterial agents. In this study, the antibacterial effect of the fresh onion and garlic juice was compared to the antibiotics of choice, using the diffusimetric agar method. Both
plant products tested have antibacterial effect, the bacterial species being classified as sensitive to their action. The molecular docking method helps us to see the type of interaction between ligands and targets, allicin having no common binding site with antibiotics of choice.
This paper aims with the preparation of Sr^2+ and Zn^2+ double substituted carbonated hydroxyapatite (Sr-Zn-CHAp) by the nanoemulsion method and to evaluate its consolidation capacity on artificial stone samples. The changes in CHAp lattice parameters were observed by a synergy between the shrinkage and dilatation induced by the two metallic ions, with different ionic radii by comparison with calcium. The changed morphology obtained by calcination was evidenced by SEM analysis. Also, the tendency to agglomerate of the double substituted CHAp as micron- and sub-micron-sized particles with spherical and irregular form was observed. The FTIR, XRD and EDS results confirmed that the CHAp was successfully substituted with Sr^2+ and Zn^2+ by replacing Ca^2+ resulting a AB-type CHAp. The efficacity of Sr-Zn-CHAp as inorganic consolidant for the stone was tested by mechanical strength, resistance at freeze–thaw artificial aging test, thermal shock weathering, colorimetric changes of the artificial stone sample, all the results being correlated with the
water absorption test, water repellency, and pore structure changes. By treating the stone with 0.5 g/L Sr-Zn-CHAp led to an improvement of the above-mentioned characteristics, without significant chromatic changes.
Implant infections are the result of bacterial adhesion to the implant surface and subsequent biofilm formation at the implant site. A sustained and high antibiotic concentration over minimal inhibitory concentration (MIC) of pathogenic bacteria at the implant site is expected to inhibit bacterial adhesion, colonization, and biofilm formation. In the present study we performed implants based on hydroxyapatite (HAp), HAp reinforced
with titanium particles (HAp/Ti) and Hap/Ti with added calcium fructoborate (CaFb) by chemisorption deposition method (HAp/Ti/CaFb). The implants were immersed in ciprofloxacin (CP) solution for 24 hours, then was determined the release profile of antibiotic for 14 days and the antibacterial effect of the three types of composite. The period of antibiotic release may be considered as sufficient to support osteointegration under antibacterial protection.
One of the most common problems encountered in everyday life is the pollution of the environment. Therefore, regardless of the nature of the daily activities of the population, this destructive effect of the natural balance finds its origin perhaps in the lack of capacity over time to treat the problem of waste (industrial and domestic) as it should. Although important steps have been taken in this regard, and prevention and control rules have been imposed in most countries of the world, these steps must be supported by all socioeconomic / political components through clear measures, anchored to global developments. There are among these generic sources of pollution, which are referred to above, processes that requires high power equipment (generators, transformers, etc.) or hydraulic who which also requires thermal insulation fluids. The aim of this study is to investigate the polychlorinated biphenyls (PCBs) presence in the dielectric oil of power transformers. In this matter, fifteen samples were collected from transformer oils, in the summer of the year 2017,
and analyzed from a physicochemical point of view. A more specific aim was to corroborate the findings regarding the amount of chlorine in oil samples with the age of the power transformer using statistical methods. The cluster’s analysis indicated that the investigated samples are clustered into four major groups, providing useful information for further studies on PCBs mobility in the environment.
Physics
The importance and present needs of proton cross-section data of nitrogen needed by the Ion Beam Analysis (IBA) community are briefly reviewed. Previous experimental data presently used for the theoretical determination of the proton cross-sections are discussed. The Azure code based on the R-matrix formalism was then used to evaluate the data and to determine the nitrogen cross-section in the previous and presently desired angular domain and energy region of interest. The experimental elastic backscattering cross-section data, as spectra, for back-scattering analysis determined at angles in the laboratory frame of reference, θ_i,lab, of 165°, 170°, and 176° are presented.
Water treeing phenomenon has an important and effective role in the service life of polymeric insulators used in the transmission and distribution of electricity. Water trees can be described as permanently localized degradations or damages that can occur in the presence of electric field and humidity. XLPE is widely used as a polymeric insulator material in medium and high voltage cable applications. An experimental setup was prepared to initiate and grow water trees artificially in a laboratory environment and the tests were performed in accordance with the actual values. The electrical and dielectric values of the test material were used for a detailed analysis with high accuracy. The magnitude of the electric field, which was defined by varying the distance between the water needles formed in the XLPE material and the aluminium plate electrode, has been analyzed for various conditions. After laboratory experiments, electric field and potential distribution were simulated and analyzed by FEM (Finite Element Method) using FEMM (Finite Element Method Magnetics) software package. Experiments revealed clearly, that even small changes in the shape of water needle can dramatically affect the electric field and hence the lifetime of the insulator. By using FEMM, both of these parameters (electric field and potential distribution) can be calculated rapidly with high accuracy. HVDC power cables play a significant role in electric power transmission, hence by using the previously described
experimental setup, electric field and potential distribution were simulated and analyzed under DC voltage.
The guides of the machine tools, brakes, clutches there is the possibility of the intermittent movement of stick-slip. This opens in the case of frictional couples with sliding motion, due to the low sliding speeds. Intermittent slip introduces vibrational phenomena and influences the uniformity of movement and the state of the surface of the couples due to their use. In this respect, the concerns related to the study of this phenomenon represent an interest in the machine building industry. The paper aims to achieve an original theoretical model for calculating the static and kinetic friction coefficients and its experimental verification on a stick-slip stand. The proposed theoretical model establishes the calculation relations of the static and kinetic friction coefficient and the connection between them taking into account the surface processing method. The originality of the approach is that the model is considered friction between the conical penetrator (steel material) and a polymer material. In the literature, the stick-slip phenomenon is approached only in terms of the analysis of flat surfaces. The torques of said materials is frequently used on the parts of sliding machines where this phenomenon is possible. The paper highlights the influence of exploitation factors (load, speed), the processing of surfaces, and the quality of the lubricating liquid on the stick-slip phenomenon, for a friction coupling of polymeric material / metallic material.
Counterfeited electronic components and devices raise multiple problems both for the electronics manufacturing industry and for the end-user as well. It is already a known fact that most of the Asian electronics market is flooding the world with cheap electronic components and devices, that have low-quality standards and that pose, sometimes, a threat to the end user’s experience or health, when using them. In this article it is assessed, to some degree, the electrical and physical performances of both a genuine power BJT (Bipolar Junction Transistor) and a counterfeited one, in order to observe and compare the uses and the limits of their potential, and what conclusions should be drawn from this comparative experimentation.