On gevrey asymptotics for some nonlinear integro-differential equations

We construct formal power series solutions of nonlinear integro-differential equations for given initial conditions which are holomorphic functions on a strip in the complex plane C. We give sufficient conditions on the shape of the equations and on the initial conditions under which there exist actual holomorphic solutions which are Gevrey asymptotic to the given formal series solutions with respect to the time variable on sectors in C. We get 1−Gevrey asymptotic expansions on sectors of opening less than π but not 1−summability as it is the case for linear partial differential equations. Moreover, our approach yields global analytic solutions of these equations in both time and space variables.     

Technological and safety properties display biodiversity among enterococci isolated from two Egyptian cheeses, "Ras" and "Domiati"

The technological and safety properties of 35 indigenous strains of Enterococcus faecium isolated from two Egyptian cheeses were characterised in order to determine their ability for rational manufacture of diversified and typical dairy products in the Middle East. A great diversity was observed within the 35 strains on the basis of their technological properties. A statistical analysis made it possible to distribute the 35 strains of E. faecium into different groups. Three groups were identified in terms of their acidification activity, measured by the Cinac system: a group of strains that quickly acidified milk, a second that moderately acidified milk, and a last cluster that revealed weak acidification activity. On the basis of texturing properties that were evaluated using a texturometer and a viscometer, a cluster of strains produced viscous and firm gels, a second cluster included fairly viscous, firm and cohesive gels, and a last group generated slightly viscous, but firm and very cohesive gels. By considering the aroma profiles that were determined by gas chromatography coupled with mass spectrometry, four clusters were identified. One cluster displayed a high dimethyl disulfide level, a second group of strains was highly aromatic, a third cluster led to typical “lactic” products, and the last cluster made it possible to obtain low aromatic products. None of the 35 strains proved to be β-haemolytic on the basis of the characterisation of their safety properties. The resistance to 20 antibiotics was assessed by the disc diffusion method. The 35 isolates were sensitive to 12 antibiotics, and among them, one isolate was resistant to only two antibiotics (nalixidic acid and streptomycin). The resistance to eight antibiotics was strain-dependant. Finally, this study demonstrates that some indigenous strains of E. faecium displayed interesting technological properties for cheese manufacture, together with good safety characteristics. They could be useful for the manufacture of typical products in Egypt.     

Analysis of Linear Scaling Method in Downscaling Precipitation and Temperature

Climate change is one of the greatest challenges in the 21^st century that may influence the long haul and the momentary changeability of water resources. The vacillations of precipitation and temperature will influence the runoff and water accessibility where it tends to be a major issue when the interest for consumable water will increase. Statistical downscaling model (SDSM) was utilized in the weather parameters forecasting process in every 30 years range (2011-2040, 2041-2070, and 2071-2100) by considering Representative Concentration Pathways (RCP2.6, RCP4.5, and RCP8.5). The Linear Scaling (LS) method was carried out to treat the gaps between ground/ observed data and raw/ simulated results after SDSM. After the LS method was executed to raw/ simulated data after SDSM, the error decrease reaches over 13% for rainfall data. The Concordance Correlation Coefficient (CCC) value clarifies the correlation of rainfall amount among observed and corrected data for all three (3) RCPs categories. There are very enormous contrasts in rainfall amount during the wet season where CCC-values recorded are 0.22 and beneath (low correlation). The findings demonstrated that the rainfall amount during the dry season will contrast for all RCPs with the CCC-values are between 0.44-0.53 (moderate correlation). RCP8.5 is the pathway with the the most elevated ozone-depleting substance emanations and demonstrated that the climate change impact is going on and turn out to be more awful step by step.

     

On the Summability of Formal Solutions of Nonlinear Partial Differential Equations with Shrinkings

We investigate the existence and Borel summability of formal power series in one variable with holomorphic coefficients, solutions of nonlinear partial differential equations with shrinkings having non-Kowalewski type in the complex domain. Sufficient conditions are given in terms of the shape of the functional partial differential equations and initial conditions. The existence and asymptotic behavior of local sectorial holomorphic solutions of these nonlinear functional partial differential equations are obtained as a by-product. We apply the results to the study of asymptotic the behavior of solutions of some advanced-argument partial differential equations in a neighborhood of infinity.