Probable usefulness of induced gynogenesis followed by diploidization has been discussed as a part of breeding technologies for genetic improvement of aquacultural organisms.The present study examined sets of conditions of treating spermatozoa by ultraviolet ray irradiation for effective induction of gynogenesis in the pacific abalone Haliotis discus hannai on the basis of observations on fertilization rate of the eggs, survival rate and chromosome constitutions of the zygotes.An aliquot of sperm suspension, placed in a plastic petri dish ion-sputtered in advance, was exposed to irradiation of ultraviolet ray of 42 erg per mm2 per s for varying durations.Immediate after the irradiation, the treated spermatozoa suspension was added to egg suspension at room temperature for fertilization. Irradiation of spermatozoa by ultraviolet ray of the above intensity for 30 to 60 s successfully induced gynogenesis, indicating the high frequency occurrence of the haploid zygotes consonant with the recovery in survival rate of zygotes, called Hertwig effect.

Let F = Q( √ m) be a real quadratic field over Q with m a square-free positive rational integer and O be the integer ring in F . A totally positive definite integral n-ary quadratic formis called universal if f represents all totally positive integers in O. Chan, Kim and Raghavan proved that ternary universal forms over F exist if and only if m = 2, 3, 5 and determined all such forms. There exists no ternary universal form over real quadratic fields whose discriminants are greater than 12.In this paper we prove that there are only two quaternary universal forms (up to equivalence) over Q( √ 13). For the proof of universality we apply the theory of quadratic lattices.

In this paper we prove that every positive definite n-ary integral quadratic form with 12 < n < 13 (respectively 14 < n < 20) that can be represented by a sum of squares of integral linear forms is represented by a sum of 2 • 3" + n + 6 (respectively 3 • 4" + n + 3) squares. We also prove that every positive definite 7-ary integral quadratic form that can be represented by a sum of squares is represented by a sum of 25 squares.

No abstract