Lie symmetries analysis for SIR model of epidemiology

Abstract In this paper a system of nonlinear ordinary differential equations arising from SIR model of epidemiology is transformed into a system of one equation of second order and one of first order. We use the property of the Lie generators algebras for any two dimensional Lie algebra to solve the first equation of the system. Then, the Lie point symmetry method is applied and differential invariants are used to obtain some exact solutions of the model. Mathematics Subject Classification: 35Bxx, 35Dxx, 92Bx

Semiclassical Strings Probing NS5 Brane Wrapped on S^5

We study little string theory on R^1 x S^5, defined by a theory which lives on type IIA N NS5 branes wrapped on S^5, using its supergravity dual. In particular we study semiclassical rotating closed strings in this background. We also consider Penrose limit of this background that leads to a plane wave on which string theory is exactly solvable.Comment: 14 pages, Latex, v2: typos corrected, Refs. added, v3: typos correcte

Semi-classical Probe Strings on Giant Gravitons Backgrounds

In the first part of this paper we study two $Z_2$ symmetries of the LLM metric, both of which exchange black and white regions. One of them which can be interpreted as the particle-hole symmetry is the symmetry of the whole supergravity solution while the second one is just the symmetry of the metric and changes the sign of the fivefrom flux. In the second part of the paper we use closed string probes and their semi-classical analysis to compare the two 1/2 BPS deformations of $AdS_5\times S^5$, the smooth LLM geometry which contains localized giant gravitons and the superstar case which is a solution with naked singularity corresponding to smeared giants. We discuss the realization of the $Z_2$ symmetry in the semi-classical closed string probes point of view.Comment: 29 pages, 6 .eps figures; v2: References adde

Stakeholders’ Perspective on Groundwater Management in Four Water-Stressed Mediterranean Areas: Priorities and Challenges

Recent studies highlight the fragility of the Mediterranean basin against climate stresses and the difficulties of managing the sustainable development of groundwater resources. In this work, the main issues related to groundwater management have been identified from the stake-holder’s perspective in the following four representative water-stressed Mediterranean areas: the coastal aquifer of Comacchio (Italy), the Alto Guadalentín aquifer (Spain), the alluvial aquifer of the Gediz River basin (Turkey), and the Azraq aquifer (Azraq Wetland Reserve, Jordan). This has been achieved by designing a methodology to involve and engage a representative set of stakeholders, including a questionnaire to learn their point of view concerning the current management of aquifer systems and their experience with the already available tools for groundwater resource manage-ment, such as monitoring networks and numerical models. The outcome of the survey has allowed us to identify both particular and common challenges among the four study sites and among the various groups of stakeholders. This information provides valuable insights to improve the transfer of scientific knowledge from the research centers to the authorities managing the groundwater resources and it will help to plan more effective research activities on aquifer management. The proposed methodology could be applied in other aquifers facing similar problems

Concentration-dependent supramolecular patterns of C3 and C2 symmetric molecules at the solid/liquid interface

Here we report on a scanning tunnelling microscopy (STM) investigation on the self-assembly of C3- and C2-symmetric molecules at the solution/graphite interface. 1,3,5-tris((E)-2-(pyridin-4-yl)vinyl)benzene and 1,1,2,2-tetrakis(4-(pyridin-4-yl)phenyl)ethane are used as model systems. These molecules displayed a concentration dependent self-assembly behaviour on graphite, resulting in highly ordered supramolecular structures, which are stabilized jointly by van der Waals substrate-adsorbate interactions and in-plane intermolecular H-bonding. Denser packing is obtained when applying a relatively high concentration solution to the basal plane of the surface whereas a less dense porous network is observed upon lowering the concentration. We show that the molecular conformation does not influence the stability of the self-assembly and a twisted molecule can pack into dense and porous architectures under the concentration effect

Does Extract of Pleurotus sajor-caju affect Liver Enzymes and Histological Integrity?

Pleurotus sajor-caju (PSC) was believed to have both antihyperlipidemic and hepatoprotective activities. The present study aimed to investigate the effect of PSC on liver enzymes and histological integrity. This study used five groups of rats fed with ghee in the ratio 32g ghee per 68g pellet to induce hypercholesterolemia and one group was fed on cholesterol free basal diet. Rats treated with 100 mg/kg of PSC for a month was found to have an effect on the liver enzymes activities since plasma alkaline phosphatase (ALP) concentration in this group showed a significant reduction (P<0.05) and a higher percentage reduction (66.01%) as compared to 20 mg/kg-PSC and 200 mg/kg- PSC treatment groups. The plasma aspartate aminotransferase (AST) and alanine aminotransferase (ALT) only showed a mild increased by 35.04% and 15.00% respectively in 100 mg/kg-PSC treatment group and there was no significant increased (P>0.05) found in these both AST and ALT concentrations. Atorvastatin treatment also showed reduction in ALP enzymes but no significant reduction (P>0.05) as compared to 100 mg/kg-PSC treatment group. On the other hand, plasma AST and ALT in 20 mg/kg of atorvastatin treatment were increased in percentage by 275.97% and 112.50% respectively indicated the adverse effects of statin in term of elevation of plasma enzymes activities. On the histological part, there was no significant finding in the micrograph study between treatment and hypercholesterolemic (HPC) liver rat. The micrograph of rat liver treated with 100 mg/kg PSC showed smooth and clear surface of hepatocytes compared to HPC group