Age structure, growth and mortality estimates of an endemic Ptychobarbus dipogon (Regan, 1905) (Cyprinidae: Schizothoracinae) in the Lhasa River, Tibet

Ptychobarbus dipogon is an endemic fish in the Yarlung Tsangpo River, but its biology is poorly known. We sampled 582 specimens (total length, TL, between 70.6 and 593.0 mm) from April 2004 to August 2006 in the Lhasa River, Tibet. We estimated ages based on the counts of alternating opaque and translucent zones (annuli) in thin transverse sections of lapilli otoliths. Ages ranged from 1(+) to 23(+) years for males and 1(+) to 44(+) for females. The observed 44(+) years was the oldest reported for schizothoracine fishes. Females attained a larger size than males. The TL weight relationship was W=7.12 x 10(-6)TL(3.006) for combined sexes. The growth parameters fitted von Bertalanffy growth functions were L-infinity = 598.66 mm, k=0.0898 year(-1), t(0)=-0.7261 year and W-infinity = 1585.38 g for females and L-infinity = 494.23mm, k=0.1197 year(-1), t(0)=-0.7296 year and W-infinity = 904.88g for males. The longevities of 32.7 year for females and 24.3 year for males were similar to the observed ages. Using an empirical model we estimated the instantaneous rate of total mortality (Z) at 0.28 per year in the lower reaches. Z in the upper and middle stocks was close to the M because of unexploited or lightly exploited stock. Protracted longevity, slow growth, low natural mortality and large body size were typical characteristics of P. dipogon. The current declining trend of P. dipogon could be prevented by altering fishing regulations.

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.