Theoretical approach to study the formation of C2H4O2 isomers in interstellar medium through reaction between interstellar formaldehyde molecules

The three isomers of C2H4O2,viz.,glycolaldehyde(HCOCH2 OH),acetic acid(CH3 COOH)and methyl formate(HCOOCH3),have been detected in copious amounts in the interstellar medium(ISM).The possibility for formation of these molecules through interstellar formaldehyde(HCHO)has been explored by using the quantum chemical approach described by density functional theory(DFT)and second order Moller-Plesset perturbation(MP2)theory with a 6–311 G(d,p)basis set in the gas phase as well as in icy grains.The associated molecule-molecule interactions have been discussed to study the formation of isomers of C2H4O2 in ISM.The reactions of two formaldehyde molecules exhibit a considerable potential barrier but due to quantum tunneling,these reactions could be possible in ISM.The chemical pathway is exothermic,which gives rise to a high probability for the formation of all three isomers,viz.glycolaldehyde,methyl formate and acetic acid,in interstellar space.Anharmonic rotational vibration,centrifugal distortion constants and coupling constants are also calculated and results suggest that the vibrations are harmonic in nature.

A stage structured model of malaria transmission and efficacy of mosquito larvicides in its control

In this paper,we analyze a stage structured mathematical model for the transmission of malaria and its control by killing mosquitoes in larvae(immature)stage.Both the Mosquito and human populations are divided into susceptible and infective class.Sus-ceptible class of mosquito population is further divided into mature and immature.The model is analyzed by using stability theory of nonlinear ordinary differential equations.Basic reproduction ratio is derived which is found to be the decreasing function of maturation delay and larvicidal activity.In addition,it is observed that biting rate of mosquito,transmission efficiency of parasitic infection from infective human to mosquito and critical value of maturation delay are the key parameters determining the stability switch in the system.Numerical simulation is also carried out to confirm the analytical results obtained in the paper.

A RESOURCE-DEPENDENT COMPETITION MODEL:EFFECTS OF POPULATION PRESSURE AUGMENTED INDUSTRIALIZATION

In this paper,a nonlinear mathematical model is proposed and analyzed to study the effects of population pressure augmented industrialization on the survival of competing species dependent on resource.It is assumed that the growths of competing species are logistic and carrying capacities increase with increase in the density of resource biomass.Further,it is assumed that the resource biomass too is growing logistically in the envi-ronment and its carrying capacity decreases with the increase in densities of competing species and industrialization.The growth rate of population pressure is assumed to be proportional to the densities of competing species.Stabilities of all equilibria and con-ditions which influence the permanence of the system are carried out using theory of differential equations.Numerical simulations are performed to accomplish our analytical findings.It is shown that the equilibrium density of resource biomass decreases as(i)the growth rate coefficient of population pressure increases(ii)the growth rate coeffi-cient of industrialization due to population pressure increases and(iii)the growth rate coefficient of industrialization due to resource biomass increases.It is found that the competitive outcome alters with increase in the growth rate coefficient of population pressure.Decrease in the equilibrium densities of competing species is also noted with increase in the growth rate coefficient of industrialization due to resource biomass.