We have investigated theoretically the formation of a coherent population trapping resonance in a finite-size vapour cell without a buffer gas. We have demonstrated the novel mechanisms of the resonance narrowing: an analogue of the Dicke effect and light-induced narrowing. In the light-induced narrowing regime the parameters of the coherent population trapping resonance weakly depend on the ce...

In the optimal nonlinear income taxation problem of Mirrlees and Stiglitz, the government's tax schedules guarantee consumption-income bundles for each type of consumer regardless of others’ actions. Piketty (Journal of Economic Theory, 1993) allows tax schedules to depend on other consumers' actions. When the government knows the exact distribution of abilities, it can construct more complicat...

In this article we present a model for analyzing patterns of genetic diversity in a continuous, finite, linear habitat with restricted gene flow. The distribution of coalescent times and locations is derived for a pair of sequences sampled from arbitrary locations along the habitat. The results for mean time to coalescence are compared to simulated data. As expected, mean time to common ancestr...

In this paper, we study the classical problem of estimating the proportion of a finite population. First, we consider a fixed sample size method and derive an explicit sample size formula which ensures a mixed criterion of absolute and relative errors. Second, we consider an inverse sampling scheme such that the sampling is continue until the number of units having a certain attribute reaches a...

One crucial feature of zygotic linkage disequilibrium (LD) analysis is its direct use of diploid genotyping data, irrespective of the type of mating system. Previous theories from an evolutionary perspective mainly focus on gametic LD, but the equivalent development for zygotic LD is not available. Here I study the evolution of zygotic LD and the covariances between gametic and zygotic LDs or b...

systems in which reaction terms are coupled to diffusion and advection transports arise in awide range of chemical engineering applications, physics, biology and environmental. in these cases, thecomponents of the unknown can denote concentrations or population sizes which represent quantities andthey need to remain positive. classical finite difference schemes may produce numerical drawbacks s...