How One can Repair Non-integrable Kahan Discretizations. II. A Planar System with Invariant Curves of Degree 6

We find a novel one-parameter family of integrable quadratic Cremona maps of the plane preserving a pencil of curves of degree 6 and of genus 1. They turn out to serve as Kahan-type discretizations of a novel family of quadratic vector fields possessing a polynomial integral of degree 6 whose level curves are of genus 1, as well. These vector fields are non-homogeneous generalizations of reduced Nahm systems for magnetic monopoles with icosahedral symmetry, introduced by Hitchin, Manton and Murray. The straightforward Kahan discretization of these novel non-homogeneous systems is non-integrable. However, this drawback is repaired by introducing adjustments of order $$O(\epsilon ^2)$$ O ( ϵ 2 ) in the coefficients of the discretization, where $$\epsilon $$ ϵ is the stepsize.

Improved Associated Task Scheduling in Different Heterogeneous systems: تحسين جدولة المهام المترابطة في الأنظمة مختلفة التجانس

Scheduling of associated tasks in heterogeneous systems is very important to reduce the total completion time as heterogeneity and coherence introduce more complexity. Several studies have focused on studying task scheduling in homogeneous systems and some studies have been limited to scheduling in heterogeneous systems. In this paper, a new algorithm was created and a simulation of the proposed algorithm was designed and tested using a random schema generator. This algorithm showed better results than its predecessors in terms of schedule length ratio relative to heterogeneity factor and Communication to Computation Ratio factor.

Quercetin Induces Lipid Domain-Dependent Permeability

In this work, we present our results on quercetin interaction with distinct model membranes exploring the importance of lipid phases, ld, ld/lo and ld+lo+so, to the action of this flavonoid in bilayers and possibly contributing to clarifying some controversial aspects related to quercetin multiple activities. We found out that quercetin is able to increase membrane permeability in a manner dependent on the presence and characteristics of lipid domains. In the presence of sphingomyelin, we found the greatest increase in mean membrane permeability (at least 10 times higher than the other lipid compositions). We also observed the presence of micrometric domains whose shape and size were disturbed by the action of quercetin. The presence of cholesterol increased membrane rigidity. This effect was enhanced with the presence of quercetin, but for chol-sphingomyelin combination, the bilayers became more flaccid at low quercetin/lipid proportions (< 1/5) and moderately rigid at proportions of the 1/1 order. The affinity parameters were higher for the most homogeneous systems and with larger areas and extensions of disordered liquid phase than for those systems of higher heterogeneity.

Quercetin Induces Lipid Domain-Dependent Permeability

In this work, we present our results on quercetin interaction with distinct model membranes exploring the importance of lipid phases, ld, ld/lo and ld+lo+so, to the action of this flavonoid in bilayers and possibly contributing to clarifying some controversial aspects related to quercetin multiple activities. We found out that quercetin is able to increase membrane permeability in a manner dependent on the presence and characteristics of lipid domains. In the presence of sphingomyelin, we found the greatest increase in mean membrane permeability (at least 10 times higher than the other lipid compositions). We also observed the presence of micrometric domains whose shape and size were disturbed by the action of quercetin. The presence of cholesterol increased membrane rigidity. This effect was enhanced with the presence of quercetin, but for chol-sphingomyelin combination, the bilayers became more flaccid at low quercetin/lipid proportions (< 1/5) and moderately rigid at proportions of the 1/1 order. The affinity parameters were higher for the most homogeneous systems and with larger areas and extensions of disordered liquid phase than for those systems of higher heterogeneity.

Quercetin Induces Lipid Domain-Dependent Permeability

In this work, we present our results on quercetin interaction with distinct model membranes exploring the importance of lipid phases, ld, ld/lo and ld+lo+so, to the action of this flavonoid in bilayers and possibly contributing to clarifying some controversial aspects related to quercetin multiple activities. We found out that quercetin is able to increase membrane permeability in a manner dependent on the presence and characteristics of lipid domains. In the presence of sphingomyelin, we found the greatest increase in mean membrane permeability (at least 10 times higher than the other lipid compositions). We also observed the presence of micrometric domains whose shape and size were disturbed by the action of quercetin. The presence of cholesterol increased membrane rigidity. This effect was enhanced with the presence of quercetin, but for chol-sphingomyelin combination, the bilayers became more flaccid at low quercetin/lipid proportions (< 1/5) and moderately rigid at proportions of the 1/1 order. The affinity parameters were higher for the most homogeneous systems and with larger areas and extensions of disordered liquid phase than for those systems of higher heterogeneity.