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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]

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]

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]

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]

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]

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 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]

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]

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 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]

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 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]

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]

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]

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]

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]

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 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]

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]