ASYMPTOTIC EQUIVALENCE OF ALTERNATELY ADVANCED AND DELAYED DIFFERENTIAL SYSTEMS WITH PIECEWISE CONSTANT GENERALIZED ARGUMENTS

In this paper, we investigate the existence, uniqueness and the asymptotic equiv- alence of a linear system and a perturbed system of differential equations with piecewise alternately advanced and retarded argument of generalized type （DEPCAG）. This is based in the study of an equivalent integral equation with Cauchy and Green matrices type and in a solution of a DEPCAG integral inequality of Gronwall type. Several examples are also given to show the feasibility of results.

Antifungal activity against Fusarium oxysporum of quinolizidines isolated from three controlled-growth Genisteae plants:structure-activity relationship implications

The Genisteae tribe belongs to the Fabaceae family.The wide occurrence of secondary metabolites,explicitly high-lighting the quinolizidine alkaloids(QAs),characterizes this tribe.In the present study,twenty QAs(1-20),including lupanine(1-7),sparteine(8-10),lupanine(11),cytisine and tetrahydrocytisine(12-17),and matrine(18-20)-type QAs were extracted and isolated from leaves of three species(i.e.,Lupinus polyphyllus(’rusell’hybrid),Lupinus muta-bilis,and Genista monspessulana)belonging to the Genisteae tribe.These plant sources were propagated under greenhouse conditions.The isolated compounds were elucidated by analyzing their spectroscopical data(MS,NMR).The antifungal effect on the mycelial growth of Fusarium oxysporum(Fox)of each isolated QA was then evaluated through the amended medium assay.The best antifungal activity was found to be for compounds 8(IC_(50)=16.5μM),9(IC_(50)=7.2μM),12(IC_(50)=11.3μM),and 18(IC_(50)=12.3μM).The inhibitory data suggest that some QAs could effi-ciently inhibit Fox mycelium growth depending on particular structural requirements deduced from structure-activity relationship scrutinies.The identified quinolizidine-related moieties can be involved in lead structures to develop further antifungal bioactives against Fox.

Durgapal IV model considering the minimal geometric deformation approach

The present article reports the study of local anisotropic effects on Durgapal's fourth model in the context of gravitational decoupling via the minimal geometric deformation approach.To achieve this,the most general equation of state relating the components of the−θsector is imposed to obtain the decoupler function f(r).In addition,certain properties of the obtained solution,such as the behavior of the salient material content threading the stellar interior;causality and energy conditions;hydrostatic balance through the modified Tolman−Oppenheimer−Volkoff conservation equation and stability mechanism against local anisotropies using the adiabatic index;sound velocity of the pressure waves;convection factor;and the Harrison−Zeldovich−Novikov procedure,are investigated to check whether the model is physically admissible or not.Regarding the stability analysis,it is found that the model presents unstable regions when the sound speed of the pressure waves and convection factor are used in distinction with the adiabatic index and Harrison−Zeldovich−Novikov case.To produce a more realistic picture,the numerical data for some known compact objects were determined and different values of the parameterαwere considered to compare with the GR case,i.e.,α=0.