Finite Volume Method for the Relativistic Burgers Model on a (1+1)-Dimensional de Sitter Spacetime

Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure Euler equations of relativistic compressible fluids on a (1+1)-dimensional background and construct a second order Godunov type finite volume scheme to examine numerical experiments within an analysis of the cosmological constant. Numerical results demonstrate the efficiency of the method for solutions containing shock and rarefaction waves

İlköğretim Matematik Öğretmenlerinin GeoGebra Yazılımının Derslerde Uygulanabilirliği Hakkındaki Görüşleri

Computer becomes an essential tool for teachers at schools, especially in teaching and learning processes. Therefore, teachers need to be informed about computer assisted instruction and develop various skills through both pre and in-service training courses they enrolled during their professional developments. Knowing how they could utilize this knowledge and skills they gained, and which and how software would be helpful in courses are among the questions that should be answered at the end of any pre-service course. Thus, this study aimed to examine the views of primary school mathematics teachers on the applicability of GeoGebra, as a dynamic mathematics software program for teaching mathematics. In this study, as it allows a deep investigation of a certain group and the data obtained from the data collection tools were investigated without making any generalizations case study method was preferred

In vitro biological activities of potassium metaborate; antioxidative, antimicrobial and antibiofilm properties

Antioxidant, antimicrobial and antibiofilm activities of potassium metaborate (KBO2) was investigated within the present study. Antioxidant capacity of potassium metaborate was determined by β-carotene bleaching (BCB) assay and hydroxyl radical scavenging activity. Potassium metaborate was evaluated for its antimicrobial effects against selected Gram-positive bacteria, Gram-negative bacteria and a yeast via broth dilution method. The inhibition capability of potassium metaborate on the microbial biofilm formation of tested microorganisms was measured by microplate biofilm method using MTT (3- [4, 5- dimethyl-2-thiazolyl]-2, 5-diphenyl-2H-tetrazolium-bromide). Biofilm inhibition capacity of potassium metaborate was also observed by Scanning Electron Microscope (SEM). Potassium metaborate was found to have the ability to scavenge hydroxyl radicals with an inhibition rate of 71.13% at 100 mM concentration. Antioxidant activity of potassium metaborate as determined by BCB assay gave higher result with an inhibition rate of 86.96% at the same concentration. According to the MIC (minimum inhibition concentration) values, the potassium metaborate inhibited the growth of C. albicans, S. aureus and E. coli at 62.5 mM concentrations while it was 31.25 mM for B. subtilis and 125 mM for P. aeruginosa. The highest antibiofilm activity was determined at the MIC of potassium metaborate with the reduction rate of 90.18% against C. albicans. It was concluded that, potassium metaborate have strong biological activities and can be effectively used for biomedical and environmental solutions

Finite Volume Method for the Relativistic Burgers Model on a (1+1)-Dimensional de Sitter Spacetime

Several generalizations of the relativistic models of Burgers equations have recently been established and developed on different spacetime geometries. In this work, we take into account the de Sitter spacetime geometry, introduce our relativistic model by a technique based on the vanishing pressure Euler equations of relativistic compressible fluids on a (1+1)-dimensional background and construct a second order Godunov type finite volume scheme to examine numerical experiments within an analysis of the cosmological constant. Numerical results demonstrate the efficiency of the method for solutions containing shock and rarefaction waves

Friedmann–Lemaitre–Robertson–Walker (FLWR) uzayzamanında rölativistik Burgers denklemi ve sonlu hacim metodları.

In this thesis, applications of generalized integral inequalities especially on biomathematics and physics are studied. Application on Biomathematics is about the predatorprey dynamic systems with Beddington DeAngelis type functional response and application on physics is about water percolation equation. This thesis consists 6 chapters. Chapter 1 is introductory and contains the thesis structure. Chapter 2 is about under which conditions the two dimensional predator-prey dynamic system with Beddington DeAngelis type functional response is permenent and globally attractive. Chapter 3 is about the same type dynamic system but with impulses. In that chapter under which conditions the dynamic system has at least one periodic solution is investigated. To get the result we use Continuation Theorem. Using impulse on this type of dynamic system is also important. Because we can model the real life much better by this way. In Chapter 4, the predator-prey dynamic system with Beddington DeAngelis type functional response on periodic time scales in shifts is studied. In this chapter, first we prove which kind of periodic time scales in shifts should be used to find there is at least one δ±-periodic solution for the given system. Then again by using Continuation Theorem we get the desired result. In Chapter 5, first we generalize the Constantin’s Inequality on Nabla and Diamond-α calculus on time scales. Then by using a topological transversality theorem and using the generalization of Constantin’s Inequality on Nabla Calculus, we have showed that the vwater percolation equation on nabla time scales calculus has solution. This solution is unique and bounded. The last chapter is the summary of what we have done in this thesis. As a result, since this study is on time scales, the findings are also important on the discrete and continuous case.Ph.D. - Doctoral Progra

Finite volume approximation of the relativistic Burgers equation on a Schwarzschild--(anti-)de Sitter spacetime

The relativistic versions of Burgers equations on the Schwarzschild, FLRW, and de Sitter backgrounds have recently been derived and analyzed numerically via finite volume approximation based on the concerned models. In this work, we derive there lativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime and introduce a second-order Godunov-type finite volume scheme for the approximation of discontinuous solutions to the model of interest. The effect of the cosmological constantis also taken into account both theoretically and numerically. The efficiency of the method for solutions containing shock and rarefaction waves are presented by several numerical experiments

Derivation of the relativistic burgers equation on a de sitter background

Recently several versions of relativistic Burgers equations have been derived on different spacetime geometries by the help of Lorentz invariance property and the Euler system of relativistic compressible flows on the related backgrounds. The concerning equations on Minkowski (flat) and Schwarzshild spacetimes are obtained in the article [6] where the finite volume approximations and numerical calculations of the given models are presented in detail. On the other hand a similar work on the Friedmann–Lemaˆıtre–Robertson–Walker (FLRW) geometry is described in [3]. In this paper, we consider a family member of FLRW spacetime so-called de Sitter background, introduce some important features of this spacetime with its metric and derive the relativistic Burgers equation on it. The Euler system of equations on de Sitter spacetime can be found by a known process by the help of Christoffel symbols and tensors for perfect fluids. We applied the usual techniques used in [3, 6] to derive relativistic Burgers equations from the Euler system on de Sitter background. By the help of finite volume method on curved spacetimes, we examined the numerical illustrations of the given model in the last part

Finite volume approximation of the relativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime

The relativistic versions of Burgers equations on the Schwarzschild, FLRW, and de Sitter backgrounds have recently been derived and analyzed numerically via finite volume approximation based on the concerned models. In this work, we derive there lativistic Burgers equation on a Schwarzschild-(anti-)de Sitter spacetime and introduce a second-order Godunov-type finite volume scheme for the approximation of discontinuous solutions to the model of interest. The effect of the cosmological constantis also taken into account both theoretically and numerically. The efficiency of the method for solutions containing shock and rarefaction waves are presented by several numerical experiments