Relativistic Burgers equations on curved spacetimes. Derivation and finite volume approximation

Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler equations of relativistic compressible fluids. This model is unique up to normalization and converges to the standard inviscid Burgers equation in the limit of infinite light speed. Furthermore, from the Euler system of relativistic compressible flows on a curved background, we derive, both, the standard inviscid Burgers equation and our relativistic generalizations. The proposed models are referred to as relativistic Burgers equations on curved spacetimes and provide us with simple models on which numerical methods can be developed and analyzed. Next, we introduce a finite volume scheme for the approximation of discontinuous solutions to these relativistic Burgers equations. Our scheme is formulated geometrically and is consistent with the natural divergence form of the balance laws under consideration. It applies to weak solutions containing shock waves and, most importantly, is well-balanced in the sense that it preserves steady solutions. Numerical experiments are presented which demonstrate the convergence of the proposed finite volume scheme and its relevance for computing entropy solutions on a curved background.Comment: 19 page

The role of the dimensions of marketing social responsibility in improving the quality of institutional services: A field study on a sample of mobilis Telecom customers

تهدف هذه الورقة البحثية إلى إبراز أهمية المسؤولية الإجتماعية في المؤسسات الإقتصادية, وتحديد أبعادها (الإنسانية, الإقتصادية, القانونية و الأخلاقية) والتي قد تؤثر بشكل كبير في جودة الخدمات المقدمة للعملاء, وعليه بات من الضروري فهم العلاقة بين هذين المتغيرين من أجل إستغلالها في تطوير وتحسين أنشطة المؤسسات,  ومنه قمنا بإجراء دراسة ميدانية على عينة من عملاء مؤسسة موبيليس بإستخدام أداة الإستمارة, وقد خلصت هذه الدراسة إلى وجود علاقة إيجابية بين أبعاد المسؤولية الإجتماعية بالمؤسسة وبين جودة الخدمات .This research paper aims to highlight the importance of social responsibility in economic institutions, and to define its dimensions (human, economic, legal, and ethical) that have been greatly affected by the quality of services provided to clients, as it becomes necessary to understand the relationship between these two variables in order to exploit them in developing and improving the activities of institutions, and accordingly we conducted a field study on a sample of the mobilis telecome  institution’s clients using the questionnaire tool. The study concluded that there is a positive relationship between the dimensions of social responsibility and the quality of services

Evaluation of Polycladia myrica mediated selenium nanoparticles (PoSeNPS) cytotoxicity against PC-3 cells and antiviral activity against HAV HM175 (Hepatitis A), HSV-2 (Herpes simplex II), and Adenovirus strain 2

IntroductionThe trace element selenium is an essential micronutrient for the health of humans, animals, and microbesMany researchers have recently become interested in selenium nanoparticles (SeNPs) because of their biocompatibility, bioavailability, and low toxicity. Consequently, selenium nanoparticles are widely used in various biomedical applications and wastewater bioremediation due to their greater bioactivity. Green biosynthesis of nanoparticles is common and preferable nowadays.MethodsIn this work, the selenium nanoparticles were synthesized using the brown seaweed Polycladia myrica aqueous extract and characterized using seven parameters, SEM, TEM, UV spectra, Zeta potential, EDX, X-ray differaction and FTIR, then examined for their cytotoxicity using PC-3 cells and normal mammalian cells from the African green monkey kidney (Vero) were used to test the effectiveness of the produced Polycladia myrica mediated selenium nanoparticles as an anticancer agent and antiviral activity against HAV HM175 (Hepatitis A), HSV-2 (Herpes simplex II), and Adenovirus strain 2.ResultsThe phycosynthesized nanoparticles exhibit antiviral activity (40.25 ± 2.61, 8.64 ± 0.82, and 17.39 ± 1.45%) against HAV-10, Adenovirus, and HSV-2, respectively. The IC50 values of the two cell types human prostate PC-3 and Vero were 123.51 ± 4.07 g/mL and 220.53 ± 6.89 g/ mL, respectively. The maximum inhibitory percent was 86.15 ± 2.31 against PC-3 cells. At the same time, at a concentration of 125 g/mL.DisscusionThis work showed that PoSeNPS have good antiviral activity against HAV-10 virus with an antiviral percent of 40.25%, despite weak antiviral activity against Adenovirus and HSV-2 with antiviral percent (8.64% and 17.39%), respectively. The cytotoxicity effect of these nanoparticles was determined against PC-3 with a maximum inhibitory percent of 80.53%. These nanoparticles have no hazardous effect against normal Vero cells as the viability percent was (78.39% and 49.23%) for Vero cells and PC-3 cells, respectively, at 125 μg/mL

RELATIVISTIC BURGERS EQUATIONS ON CURVED SPACETIMES. DERIVATION AND FINITE VOLUME APPROXIMATION

Within the class of nonlinear hyperbolic balance laws posed on a curved spacetime (endowed with a volume form), we identify a hyperbolic balance law that enjoys the same Lorentz invariance property as the one satisfied by the Euler equations of relativistic compressible fluids. This model is unique up to normalization and converges to the standard inviscid Burgers equation in the limit of infinite light speed. Furthermore, from the Euler system of relativistic compressible flows on a curved background, we derive both the standard inviscid Burgers equation and our relativistic generalizations. The proposed models are referred to as relativistic Burgers equations on curved spacetimes and provide us with simple models on which numerical methods can be developed and analyzed. Next, we introduce a finite volume scheme for the approximation of discontinuous solutions to these relativistic Burgers equations. Our scheme is formulated geometrically and is consistent with the natural divergence form of the balance laws under consideration. It applies to weak solutions containing shock waves and, most importantly, is well balanced in the sense that it preserves static equilibrium solutions. Numerical experiments are presented which demonstrate the convergence of the proposed finite volume scheme and its relevance for computing entropy solutions on a curved background