This paper presents the results of a recent pilot project aimed at obtaining optically stimulated luminescence (OSL) dates from a group of ancient irrigation dams in central India. The dams are all situated within an area of 750 km2 around the wellknown Buddhist site of Sanchi, the latter established in c. third century B.C. and having a continuous constructional sequence up to the twelfth century A.D. They were documented during earlier seasons of the Sanchi Survey, initiated in 1998 in order to relate the site to its wider archaeological landscape. The pilot project builds upon earlier hypotheses regarding the chronology and function of the Sanchi dams and their relationship to religious and political history in Central India. The principal suggestion is that the earliest phase of dam construction coincided with the rise of urbanization and the establishment of Buddhism in central India between c. third and second centuries B.C.; and that they were connected with wet-rice cultivation as opposed to wheat, the main agricultural staple today. Similarities with intersite patterns in Sri Lanka, where monastic landlordism is attested from c. second century B.C. onward, have also led to the working hypothesis that the Sanchi dams were central to the development of exchange systems between Buddhist monks and local agricultural communities. The pilot project focused on two out of a total of 16 dam sites in the Sanchi area and involved scraping back dam sections created by modern road cuttings. This cast new light on aspects of dam construction and allowed for the collection of sediments and ceramics for OSL dating. The results confirmed the suitability of local sediments to OSL dating methods, as well as affirming our working hypothesis that the dams were constructed—along with the earliest Buddhist monuments in Central India—in the late centuries B.C. Sediment samples were also collected from cores hand drilled in the dried-up reservoir beds, for supplementary OSL dating and pollen analysis, which shed useful insights into land use.

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0. Introduction. Asymptotic behaviour of distributions (Silva(8) and Benedetto (l)) plays a fundamental role in the analysis of singularities of generalized integral transforms. Such analysis in terms of Abelian theorems for the distributional Stieltjes transformation has been obtained by Misra (6) and Lavoine and Misra (3). To obtain his results Misra used some Abelian theorems (see Misra (6), theorems 3·1·1 and 4·1·1) for the Stieltjes transformation of functions which were essentially generalizations of the results given by Widder (9), pp. 183–185. The object of the present paper is to complete the work given by the authors in (3); Sections 2 and 3 of this paper are devoted to obtaining Abelian theorems concerning the distributional Stieltjes transformation in terms of the behaviour of this transform near the origin and at infinity.

a b s t r a c tA predator-prey model with logistic growth in prey is modified by introducing an SIS parasite infection in the prey. We have studied the combined effect of environmental toxicant and disease on prey-predator system. It is assumed in this paper that the environmental toxicant affects both prey and predator population and the infected prey is assumed to be more vulnerable to the toxicant and predation compared to the sound prey individuals. Thresholds are identified which determine when system persists and disease remains endemic.

In this paper, the effect of toxicant on the dynamics of Leslie-Gower tritrophic food chain population model is studied. Two models have been studied to visualize the dynamical behaviour of prey and predator populations under toxicant stress. All the feasible equilibria of the systems are obtained and using stability theory the conditions are derived for the survival or extinction of species. From the analysis of the models it is observed that the effect of toxicant on predator population increases the equilibrium density of prey population. Finally, we support our analytical findings with numerical simulations.

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Abstract. A mathematical model is proposed to study the simultaneous effects of toxicant and infectious disease on Lotka-Volterra prey-predator system. It is considered in the model that only the prey population is being affected by disease and toxicant both, and the susceptible and infected prey populations are being predated by predator. All the feasible equilibrium of the model are obtained and the condition for the existence of interior equilibrium point is also been determined. The criteria for both local stability and instability involving ecotoxicological and epidemiological parameters are derived. The global stability of the interior equilibrium point is discussed using Lyapunov's direct method. The results are compared with the case when environmental toxicant is absent. Moreover, threshold conditions depending upon toxicant, disease and predation related parameters for the non-linear stability of the model is determined. Finally, the numerical verifications of analytic results are carried out.