How powerful is demography ? The Serendipity Theorem revisited

Introduced by Samuelson (1975), the Serendipity Theorem states that the competitive economy will converge towards the optimum steady-state provided the optimum population growth rate is imposed. This paper aims at exploring whether the Serendipity Theorem still holds in an economy with risky lifetime. We show that, under general conditions, including a perfect annuity market with actuarially fair return, imposing the optimum fertility rate and the optimum survival rate leads the competitive economy to the optimum steady-state. That Extended Serendipity Theorem is also shown to hold in economies where old adults work some fraction of the old-age, whatever the retirement age is fixed or chosen by the agentsSerendipity Theorem, fertility, mortality, overlapping generations, retirement

SDSS J080434.20+510349.2: Eclipsing WZ Sge-Type Dwarf Nova with Multiple Rebrightenings

We observed the 2006 superoutburst of SDSS J080434.20+510349.2 during its plateau phase, rebrightening phase, and post-superoutburst final decline. We found that this object is a grazing eclipsing system with a period of 0.0590048(2) d. Well-defined eclipses were only observed during the late stage of the superoutburst plateau and the depth decreased during the subsequent stages. We determined the superhump period during the superoutburst plateau to be 0.059539(11) d, giving a fractional superhump excess of 0.90(2)%. During the rebrightening and post-superoutburst phases, persisting superhumps with periods longer than those of superhumps during the plateau phase: 0.059632(6) during the rebrightening phase and 0.05969(4) d during the final fading. This phenomenon is very well in line with the previously known long-period "late superhumps" in GW Lib, V455 And and WZ Sge. The amplitudes of orbital humps between different states of rebrightenings suggest that these humps do not arise from the classical hot spot, but are more likely a result of projection effect in a high-inclination system. There was no clear evidence for the enhanced hot spot during the rebrightening phase. We also studied previously reported "mini-outbursts" in the quiescent state and found evidence that superhumps were transiently excited during these mini-outbursts. The presence of grazing eclipses and distinct multiple rebrightenings in SDSS J080434.20+510349.2 would provide a unique opportunity to understanding the mechanism of rebrightenings in WZ Sge-type dwarf novae.Comment: 14 pages, 12 figures, PASJ accepte