The u-invariant of the function fields of p-adic curves

The u-invariant of a field is the maximum dimension of ansiotropic quadratic forms over the field. It is an open question whether the u-invariant of function fields of p-aidc curves is 8. In this paper, we answer this question in the affirmative for function fields of non-dyadic p-adic curves.Comment: 20 page

Global and Partial Phase Synchronizations in Arrays of Piecewise Linear Time-Delay Systems

In this paper, we report the identification of global and partial phase synchronizations in linear arrays of unidirectionally coupled piecewise linear time-delay systems with two different coupling configurations. In particular, in a linear array with open end boundary conditions, global phase synchronization (GPS) is achieved by a sequential synchronization as a function of the coupling strength (a second order transition). Further, the asynchronous ones in the array with respect to the main sequentially synchronized cluster organize themselves to form clusters before they achieve synchronization with the main cluster. On the other hand, in a linear array with closed end boundary conditions (ring topology), partial phase synchronization (PPS) is achieved by forming different groups of phase synchronized clusters above some threshold value of the coupling strength (a first order transition) where they continue to be in a stable PPS state. We confirm the occurrence of both global and partial phase synchronizations in two different piecewise linear time-delay systems using various numerical methods.Comment: 26 pages, 25 figures, To Appear in International Journal of Bifurcation and Chaos, Vol. 22, No. 7 pp. 1250178 (1-25). arXiv admin note: substantial text overlap with arXiv:1007.280

Economic feasibility of composite fish culture in leased-in village tanks of Kanyakumari district: an invesment analysis

Kanyakumari district belonging to the high rainfall zone has resource advantages for composite fish culture in the leased-in village tanks. There are more than 400 fish farmers operating in leased-in tanks following composite fish culture under the FFDA programme. To estimate the economic feasibility and financial viability of the enterprise, the present study was taken up. 38 fish farmers selected from the district provided the necessary information like capital investment, costs and return and constraints. The data collected were analysed and a farm nearest to the average farm situation was taken as the representative farm. Investment criteria like PayBack Period (PBP), Simple Rate of Returns (SRR), Net Present Value (NPV) and Benefit Cost Ratio (BCR) were estimated taking into account a period of 10 years, the period for which the village tanks are leased-out to fish farmers under the FFDA programme. The analysis indicated the profitability of composite fish culture in village tanks in the district and the results are discussed with recommendations