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F. Bracci, M.D. Contreras, S. Díaz Madrigal [3] proved that any evaluation family of order d is described by a generalized Löwner chain. G. Ivanov and A. Vasil'ev considered randomized version of the chain and found a substitution which transforms the chain to an Itô diffusion. We generalize their result to vector randomized Löwner chain and prove there are no other possibilities to transform such Löwner chains to Itô diffusions. [ABSTRACT FROM AUTHOR]

One common negative side effect of orthodontic treatment with fixed appliances is the development of white spot lesions (WSLs) around brackets. This study aimed to compare the efficacy of various oral hygiene practices in preventing enamel demineralization around orthodontic brackets under similar in-vitro conditions. The study included 90 extracted bovine incisors, which were randomized into 6 groups. The changes in the demineralization degree were evaluated by measuring the Ca+2 concentration (mg/dL) in the demineralization solution at days 5, 10, 15, 19. The procedures were carried out at the Medical Biochemistry Laboratory at Near East University Hospital. Calcium content of each beaker was measured with the Abbott Architect c8000 biochemistry autoanalyzer system using the Arsenazo III method. [ABSTRACT FROM AUTHOR]

This study investigates the cointegration and causality relationships between business confidence and financial stress for the PIGS countries (Portugal, Italy, Greece, and Spain) based on monthly data covering between January 2008 and December 2019. Panel ARDL methodology and Pooled Mean Group estimation techniques are used to test the short-run and long-run relationships between the variables. The findings indicate that financial stress is significantly and negatively affected by business confidence in the examined countries in both the long run and short run. Furthermore, the current month's financial stress level is negatively affected by the last month's business confidence and financial stress levels. Finally, a univariate causality relationship running from business confidence towards financial stress is revealed. [ABSTRACT FROM AUTHOR]

In the present paper, the initial value problem for the first order ordinary differential equation with involution is studied. We obtain equivalent initial value problem for the second order ordinary differential equations to the initial value problem for first order linear differential equations with involution. Theorem on stability estimates for the solution of the initial value problem for the first order ordinary linear differential equation with involution is proved. Theorem on existence and uniqueness of bounded solution of initial value problem for first order ordinary nonlinear differential equation with involution is proved. [ABSTRACT FROM AUTHOR]

In this paper, we study an initial boundary value problem for a two-dimensional differential equation with a fractional time derivative in the sense of Caputo. This equation is of great applied importance in modeling flow processes and anomalous dispersion. The uniqueness and continuous dependence of the solution on the input data in differential form is proved. A computationally effective implicit scheme with weights is proposed. A priori estimates are obtained for the solution of the problem under the assumption that a solution exists in the class of sufficiently smooth functions. These estimates imply the uniqueness of the solution and the stability of the scheme with respect to the initial data and the right-hand side of the equation. The convergence of the approximate solution to the solution of the differential problem with the second order both in time and space variables is proved. The results of computational experiments confirming the reliability of theoretical analysis are presented. [ABSTRACT FROM AUTHOR]

In the present study, first and second order of accuracy difference schemes for the numerical solution of the boundary value problem with nonlocal conditions for a one-dimensional third order partial differential equation are presented. Results of numerical experiments are provided. [ABSTRACT FROM AUTHOR]

Covid-19 is the most recently discovered infectious disease affecting the countries all around the world. SARS-CoV-2, which is a member of coronavirus family, is the virus that makes the infection. Until the 28th of September 2020, almost 34 million people infected by the virus and more than 1 million people died all around the world. One of the most discussed ideas about the disease to die out is vaccination. In our study, we tried to analyze this idea and show the effect of vaccine for Covid-19. Our work starts with constructing an SVI mathematical model. Afterwards, we made the analyze of our model. Then, by taking into consideration of incoming passengers and precautions that should be taken, we used the vaccination idea with changing the percentage of vaccinated people in a population. In last section, we used numerical simulations to support our idea. In our work, we conclude that vaccination is substantially effective if we consider the other things that affect the disease which is incoming passengers and precautions like wearing mask, maintaining social distance, etc. [ABSTRACT FROM AUTHOR]

Mathematical modeling of the nonlinear problem biological population nondivergent form with absorption, variable density are considered. Qualitative properties of considered problem which include the critical and double critical cases are discussed. Results of the numerical experiments are analyzed. [ABSTRACT FROM AUTHOR]

In this paper, we study numerical methods for solving the Navier-Stokes equations in doubly connected domains. Two methods for solving the problem are considered. The first method is based on constructing a difference problem in variables of the stream function and the vortex of velocity using the uniqueness condition for pressure. The numerical solution of the elliptic equation for stream functions is found as the sum of the solutions of two simple problems of an elliptic type. One problem is with homogeneous boundary conditions, and the other is with a homogeneous equation. An alternative approach to solving the problem is the fictitious domain method with the continuation of the least coefficient. This method does not require satisfying the pressure uniqueness condition, and is simple to implement. An important direction in the development of numerical simulation methods is the study of approximate methods for solving problems of mathematical physics in complex multidimensional areas. To solve many applied problems in irregular areas, the fictitious domain method is widely used, which is characterized by a high degree of automation of programming. The main idea of the fictitious domain method is that the problem is solved not in the original complex domain, but in some other, simpler domain. This allows to create software immediately for a fairly wide class of problems with arbitrary computational domains. The possibilities of applying the fictitious domain method to the problems of hydrodynamics in the variables "stream function, vortex of velocity" are considered in many works. In this paper, we study a numerical method for solving the Navier-Stokes equations in doubly connected domains. A computational finite difference algorithm for solving an auxiliary problem of the fictitious domain method has been developed. The results of numerical modeling of the two-dimensional Navier-Stokes equations by the fictitious domain method with continuation by the lowest coefficient are presented. For this problem, a parallel algorithm was developed using the CUDA architecture, which was tested on various grid dimensions. [ABSTRACT FROM AUTHOR]

Firstly, a perturbation based correction of an admissible open-loop control in an unperturbed problem is constructed in the form of linear feedback. The constructed control transfers the perturbed system to a neighborhood of a given point. Secondly, then the resulting feedback is refined to reach the end point. The proposed algorithm is illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

We consider the problem of interpolation of scattered data in ℝ3 and propose a solution based on Nielson's minimum norm network and triangular Bézier patches. Our algorithm applies splitting to all triangles of an associated triangulation and constructs G1-continuous bivariate interpolant consisting of quartic triangular Bézier patches. The algorithm is computationally simple and produces visually pleasant smooth surfaces. We have created a software package for implementation, 3D visualization and comparison of our algorithm and the known Shirman and Séquin's method which is also based on splitting and quartic triangular Bézier patches. The results of our numerical experiments are presented and analysed. [ABSTRACT FROM AUTHOR]

As we know the Lindelöfness play an important role in the General Topology. Therefore, the finding of uniform analogues of Lindelöfness is an important and interesting problem in the theory of Uniform Topology. For example, uniform B- Lindelöfness in the sense of A. A. Borubaev [1], uniform A-Lindelöfness in the sense of L.V. Aparina [2], uniform I- Lindelöfness in the sense of D. R. Isbell [3]. In this article we show a new approach to the definition of a uniform analog of Lindelöfness. We introduce and study uniform R-Lindelöf and uniform Lindelöf spaces. [ABSTRACT FROM AUTHOR]

In this paper, difference schemes of the high-order finite element method for the Sobolev type equation are constructed and investigated. In particular, boundary value problems for the two-temperature plasma equation are considered. A high order of accuracy of the scheme is achieved by special sampling of time and space variables. The stability and convergence of the constructed algorithms are proved. A priori estimates are obtained in various norms, which are used later to obtain estimates of the accuracy of the scheme under weak assumptions about the smoothness of solutions to differential problems. [ABSTRACT FROM AUTHOR]

In this study, we developed a mathematical model to study the transmission dynamics of HIV infection and analyzed the effect of horizontal and vertical transmission in Turkey. We fit the model by using confirmed HIV cases of both vertical and horizontal transmission between 2011 and 2018. By using the next generation operator, we obtained the basic reproduction number of the model which shows whether the disease persists or dies out in time. Further, the most sensitive parameters, that are efficient for the control of the infection, obtained by using forward normalized sensitivity index. The results obtained with the aid of mesh and contour plots. [ABSTRACT FROM AUTHOR]

In the present paper, source identification problem for the elliptic-telegraph equation is investigated. The second order of accuracy absolute stable difference scheme for the numerical solution of the one-dimensional identification problem for the elliptic-telegraph equation with the Dirichlet condition is presented. Some numerical results are provided. [ABSTRACT FROM AUTHOR]

In this study, the solutions of a radial Schrödinger equation which has got the potential V (r) = 0 are found by using symmetries. These solutions are compared with the classical solution of the equation. [ABSTRACT FROM AUTHOR]

In this paper, we shall establish the existence and uniqueness of fixed point of a Chatterjea - type contraction in Cone rectangular metric spaces over Banach algebras. We shall further give an example to illustrate our main results. Our results extend and generalize some results in the literature. [ABSTRACT FROM AUTHOR]

Let Γ(x) denotes the gamma function of a real number x ∉ {0,−1,−2,...}. Then the backward difference matrix ΔBq of fractional order q is defined as (Δ B q v) i = ∫ l = 0 ∞ (− 1) l Γ (q + 1) l ! Γ (q − l + 1) v i − l. In this paper we introduce paranormed Riesz difference sequence space rt (ΔBq) of fractional order q obtained by the domain of generalized difference operator Rt ΔBq in Maddox's space ℓ(p). We investigate certain topological properties and obtain the Schauder basis of the space rt (ΔBq). We also obtain the α–, β– and γ–duals and characterize certain matrix classes related to the space rt (ΔBq). [ABSTRACT FROM AUTHOR]

The generators of the quasi-regular representation of the group SO(3,2) are obtained for parabolic coordinates. By the generators, the expression of the quadratic Casimir operator is presented. From the relation between the Casimir operator and Hamiltonian, the corresponding physical system is expressed, and its exact solution is given. [ABSTRACT FROM AUTHOR]

In this study, it was aimed to determine the course of COVID-19 infection in Libya with a new modified mathematical modeling and to show the possible number of cases and deaths in the upcoming period. We performed detailed analyzes with the help of the analytical solution of the time-dependent logistics model that we obtained. The results obtained separately on a total and daily basis were shown graphically. In the last part, it is emphasized how important individual and public precautions in order to decrease the spread rate of the disease and to be better controlled. [ABSTRACT FROM AUTHOR]

Coronavirus disease 2019, also known as Covid-19, is an infectious disease that has infected more than nineteen million people all around the world. This virus is a member of coronavirus family but it is the most mortal one. It has named as 2019-nCoV by World Health Organization(WHO) after Chinese Center for Disease Control and Prevention(CDC) discovered a new coronavirus from a swab sample of a patient. As we know this pandemic started December 2019 in China, and it is still spreading and causing deaths all around the world. In this paper, we aimed to estimate the right size of epidemic. For that purpose, we chose 10 countries, which are affected by, and still fighting with this disease, to forecast the upcoming death rates by using the previous week deaths. These 10 countries are Argentina, Austria, Brazil, France, Iran, Italy, Sweden, Turkey, United Kingdom, and United States of America. We used the death data of WHO with assumption that data is accurate. For this estimation, firstly, we used the assumption that the reported death delay distributed according to a gamma distribution. Then, we used a binomial distribution for assumption of deaths. This binomial formula led us to find a posterior distribution which is an extension of Bayes' theorem for death ratio. Lastly, we compared our estimations with real data. [ABSTRACT FROM AUTHOR]

A uniform estimation of order O(h4), for the convergence of the finite difference solution for the general second order elliptic equation with nonlocal integral boundary condition is obtained where h is the mesh step. [ABSTRACT FROM AUTHOR]

In the present article the Analytic Hierarchy Process (AHP) method, which has an important place among multi-criteria decision making methods, will be used in the solution. In addition, the group decision making will be applied as it will be beneficial to the result that there will be more than one decision maker. The method will be handled with the Interval Type-2 Fuzzy Sets (IT2FSs) that have high success in handling uncertainties. [ABSTRACT FROM AUTHOR]

Employee satisfaction plays an important role in the effective operation of any type of organization. The study aimed to investigate the explanatory factors influencing job satisfaction and model the satisfaction of employees (teachers) using logistic regression. Analysis results indicated that current workplace experience had a positive influence on teacher job satisfaction. However, as the teachers' education level and their overall years of experience in teaching increased their satisfaction levels decreased. [ABSTRACT FROM AUTHOR]

This study used two quantitative methods to investigate the efficacy of different methods in preventing enamel deminer- alization around orthodontic brackets under similar in vitro conditions. The study included 90 extracted bovine incisors randomized into six groups: fluoride toothpaste(FT), non-fluoride toothpaste(NFT), fluoride varnish plus fluoride toothpaste(FV+FT), casein phosphopeptide–amorphous calcium phosphate(CPP-ACP) varnish plus fluoride toothpaste(CPP-ACP+FT), medical mineral gel plus non-fluoride toothpaste(MMG+NFT), and no intervention(control). All groups were subjected to a pH cycle. The buccal surfaces were assessed with a DIAGNOdent pen(DD) at baseline(T0) and the 19th day(T1). For each group, the mean Ca2+ loss was also measured by the colorimetric method. The current study focused on the assessment of total mineral loss using DD and colorimetric methods. [ABSTRACT FROM AUTHOR]

In this research paper, we extended an existing SIR epidemic integer model containing two strains and two vaccinations by using a system of fractional ordinary differential equations in the sense of Caputo derivative of order σ ∈ (0, 1]. Four equilibrium points were established which are disease free equilibrium, strain1 disease free equilibrium, strain2 disease free equilibrium and endemic equilibrium. Explicit analysis of the equilibrium points of the model was given by applying fractional calculus and Routh-Hurwitz criterion. Stability analysis of the equilibrium points was carried out by employing the Jacobian matrix. Numerical simulations were iterated to support the analytic results. It was shown that when both of the reproduction numbers R1 and R2 are less than one, the disease die out over time and while it persist in relation to the thriving strain when either of them is greater than one. We also studied the effect of vaccine. With the fractional order technique, the memory effect of the system is made visible and hence easier to predict. [ABSTRACT FROM AUTHOR]

In this article the solvability of the problem of optimal control of oscillatory processes described by the integro- differential equation with the Fredholm operator, with given control limitation is investigated. It is established that the desired control is among the solutions of the nonlinear Fredholm integral equation of the first kind. Sufficient conditions for the existence of a solution of nonlinear optimization problem are found. [ABSTRACT FROM AUTHOR]

Some factors related to students maths anxiety are perceived to be important for academic failure. Such of these factors and some other factors contribute immensely to the problem of mathematics achievement that is spreading among students of Economics and Administrative Sciences. Considering such a problem as a maths anxiety, we propose a mathematical model to study how this problem is spread in the Faculty. We have discussed about basic properties of the system. Basic reproduction numbers are calculated. Our numerical findings are illustrated through computer simultaneous using MATLAB, which show the reliability of our model from the practical point of view. Students' math-anxiety implications of our analytical findings are addressed critically. The model analysis reveals that all of the students start to show better maths achievement on the positive way during the semester (approximately 3,5 months). The sensitivity analysis of the parameters of the model shows that reducing maths anxiety by focusing positive change of behaviour in relation to the teaching of maths and the teachers' way of teaching is an effective on students' achievement of maths. [ABSTRACT FROM AUTHOR]

In this paper, we consider a variant of the fictitious domain method associated with the modification of nonlinear terms in a fictitious subdomain. The model problem shows the effectiveness of using this modification. The proposed version of the method is used to solve the problem of an arbitrary region and to set a boundary condition for pressure. A numerical solution is implemented and the results of numerical results are given. [ABSTRACT FROM AUTHOR]

A three stage (9-point, 5-point and 5-point) difference method for solving the Dirichlet problem for Laplace's equation on a rectangle is proposed and justified. It is proved that the proposed difference solution converges uniformly to the exact solution of order O(h8 |ln h|), h is the mesh size, when the boundary functions are from C9,1. Numerical experiment is illustrated to support the analysis made. [ABSTRACT FROM AUTHOR]

In this paper, a fractional order mathematical model is constructed to study the dynamics of coronavirus. The model consists of a system of eight non-linear fractional order differential equations in Caputo sense. Existence and uniqueness of the solution of the model are studied. [ABSTRACT FROM AUTHOR]

The necessity of e-signature has been accepting by all organizations like finance, education, business. With the effect of this, the popularity has been increasing day by day especially uncertainty times such as the Covid-19 pandemic. However, there is a missing gap in the literature about e-signature studies. The literature review showed that the studies on e-signature awareness and the benefits of e-signature usage in any organization or/and the person are not enough. For this reason, the purpose of the study is to develop a valid and reliable scale to use in scientific studies to understand the awareness of users towards e-signature. Therefore, both validity and reliability of scale have been investigated. Through the exploratory factor analysis, the AoE-sign scale has 16 items and 2 subfactors which are "Awareness" and "Benefits". The factor analysis results indicated that Cronbach Alpha for Awareness was.888, for Benefits was.790 and for the overall scale was.889. Consequently, the study results demonstrated that the AoE-sign scale is reliable and valid tool and the developed scale could be used by top-level managers, in developing countries such as Cyprus, to be able to understand the awareness level of users. Moreover, they can organize staff training on e-signature to make it possible to use e-signature efficiently in the organizations. [ABSTRACT FROM AUTHOR]

The initial value problem for the parabolic type involutory partial differential equation is studied. Applying Green's function of space operator generated by the differential problem, we get formula for solution of this problem. The theorem on stability estimates for the solution of this problem with involution is established. [ABSTRACT FROM AUTHOR]

Heart failure is a condition that affects a great part of the world population. A heart transplant is one of the alternatives to survive heart failure. Since the organ donors are very limited and the wait list for the organ is very long it is difficult to find the organ. A viable alternative until the organ becomes available is the total artificial heart (TAH) and ventricle assisting devices. The total artificial heart is used to bridge the time to heart transplants. There are different types of artificial hearts. In this paper, we compared the various TAH devices by creating a database, and by using a simulation we determined which device is the best out in the market. We used Fuzzy Promethee as the methodology. It is observed that with pneumatic (SynCardia) TAHs as a bridge to transplant, promising results have been achieved, but still, they are not free of problems. Nevertheless, implantable total artificial hearts have a long way to go if they are to replace the natural heart permanently, made for destination therapy. So far, the only device that is commercially approved is SynCardia TAH, it's the only one in the market for patient use. [ABSTRACT FROM AUTHOR]

Stochastic differential equations (SDEs) have been intensively used to analyze data from physics, finance, engineering, medicine, biology, and forestry. This study proposes general mixed effect parameters (fixed and random) multivariate SDE model of a population growth which includes random forces governing the dynamic of multivariate distribution of tree size variables. The dynamic of the multivariate probability density function of the size variables in a population is described by mixed effect parameters Gompertz type SDE. The advantages of the multivariate SDE model are that it does not need to choose many different equations to be tried, it relates the size variables dynamic against the time dimension, and considers the underlying covariance structure driving changes in the size variables. SDE model allows us a better understanding of processes driving the dynamic of natural phenomena. The new derived multivariate probability density function and its marginal univariate, bivariate, trivariate, conditional univariate, bivariate, trivariate, and much more distributions can be applied for the modeling of population attributes such as the mean value, quantiles and much more. This study introduces general multivariate mutual information measures based on the differential entropy to capture multivariate interactions between size variables. The purpose of the present study is therefore to experimentally confirm the effectiveness of using multivariate information measures to reconstruct multivariate interactions in size variables. The study of information sharing amongst size variables is illustrated using a dataset of the Scots pine (Pinus Sylvestris L.) stands measurements in Lithuania. [ABSTRACT FROM AUTHOR]

In this paper, the source identification problem for the telegraph equation is studied. We propose the first order of accuracy absolute stable difference scheme for the numerical solution of the one-dimensional identification problem for the telegraph equation with the Neumann condition. The obtained numerical results have been compared with the exact solution to verify the accurate nature of our method. [ABSTRACT FROM AUTHOR]

A linear boundary value problem for a system of integro-differential equations with involution is studied by the parameterization method. Sufficient conditions for the existence of a unique solution to the problem are established in terms of coefficients. An algorithm for finding the solution to the problem under consideration is proposed. [ABSTRACT FROM AUTHOR]

In this study, second order of accuracy difference scheme for approximate solution of initial-boundary value problem for time delay telegraph equation with Dirichlet condition is presented. The main theorem on stability of the difference scheme is established. Numerical results are provided. [ABSTRACT FROM AUTHOR]

The aim of this paper is to show how North Cyprus fights Covid-19 by using the basic reproduction number R0 and effective reproduction number Rt. According to the Wikipedia page with title Covid-19 pandemic in Northern Cyprus, North Cyprus is the first country in Europe to free from Covid-19. One of the important reasons of this is that the government decided for tackling Covid-19 pandemic by using R0 and Rt daily. For R0, we constructed a new SEIR model by using the real data for North Cyprus. From March 11, 2020 to May 15, 2020 R0, varies from 0.65 to 2.38. [ABSTRACT FROM AUTHOR]

In this article we study strongly uniformly R-paracompact space and strongly uniformly R-paracompact mappings. In particular, the characterizations of strongly uniformly R-paracompact spaces by using Hausdorff compact extensions and finite additive coverings are obtained. [ABSTRACT FROM AUTHOR]

In a rectangular domain, we discuss about an approximation of the first order derivatives for the solution of the mixed boundary value problem. The boundary values on the sides of the rectangle are supposed to have the second order derivatives satisfying the Hölder condition. Under these conditions for the approximate values of the first derivatives of the solution of mixed boundary problem on a square grid, as the solution of the constructed difference scheme a uniform error estimation of order O(h) (h is the grid size) is obtained. Numerical experiments are illustrated to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this work, He's semi-inverse variation method and the ansatz method with the modified Riemann-Liouville derivative are used to construct the exact solutions for time fractional Korteweg-de Vries (KdV) equation. The fractional KdV equation is transformed to another non-linear differential equation by travelling wave transformations and then these two methods are applied to find the solution. [ABSTRACT FROM AUTHOR]

Every day the number of attacks increases to break the encryption algorithms. Therefore, it is considered necessary for designing a new algorithm with higher security. Any cryptographic system must have some fundamental features to resist any effective attack, preserve the transmitted information, and robust the statistical characteristics. This article aims to improve the RSA algorithm using a three-dimensional chaotic dynamic system with sophisticated attributes, which proposed for this purpose. It is derived from Memristive's and Sprott's chaotic systems. We call it a 3D-hyperchaotic Memristive Sprott system (3D-HMSS). This new system is adopted in generating keys for the RSA encryption algorithm. Some tests are used to show the efficiency of the proposed cryptosystem. [ABSTRACT FROM AUTHOR]

The work is devoted to the proof of the convergence of trajectory and global attractors of approximation problems to trajectory and global attractors of the Bingham model on the torus. For research, the theory of trajectory attractors of non-invariant trajectory spaces is used. Namely, the existence of attractors for the Bingham model on a torus, and the existence of attractors for the approximation problem is proved. Then it is shown that the attractors of the approximation problems converge to the attractors of the Bingham model in the sense of the Hausdorff semi-distance in corresponding metric spaces. [ABSTRACT FROM AUTHOR]

The article explores general nonlinear equations with a parameter. Sufficient conditions for the existence of a solution of nonlinear integral equations in the form of the sum of two functions for the individual values of the parameter are found. [ABSTRACT FROM AUTHOR]

In this paper, the theory of conjugate equations is used to solve the inverse problem of the continuation of potential fields in the direction of disturbing masses, in the inverse problem of magnetotelluric sounding (MTS), for problems of mathematical epidemiology. [ABSTRACT FROM AUTHOR]

In this paper, we study solvability of new classes of nonlocal boundary value problems for second-order elliptic type equation. The considered problems are multidimensional analogues (in the case of circular regions) of classical periodic boundary value problems in rectangular domains. To study the main problem, first, an auxiliary boundary value problem with inclined derivative is considered for the second order elliptic equation. The main problems are solved by reducing them to a sequential solution of the Dirichlet problem and the problem with inclined derivative. Theorems on existence and uniqueness of a solution of the problems are proved. [ABSTRACT FROM AUTHOR]