Zeros of Systems of p{\mathfrak p}-adic Quadratic Forms

It is shown that a system of $r$ quadratic forms over a ${\mathfrak p}$-adic field has a non-trivial common zero as soon as the number of variables exceeds $4r$, providing that the residue class field has cardinality at least $(2r)^r$.Comment: Revised version, with better treatment and results for characteristic

The largest prime factor of X3+2X^3+2

The largest prime factor of $X^3+2$ has been investigated by Hooley, who gave a conditional proof that it is infinitely often at least as large as $X^{1+\delta}$, with a certain positive constant $\delta$. It is trivial to obtain such a result with $\delta=0$. One may think of Hooley's result as an approximation to the conjecture that $X^3+2$ is infinitely often prime. The condition required by Hooley, his R$^{*}$ conjecture, gives a non-trivial bound for short Ramanujan-Kloosterman sums. The present paper gives an unconditional proof that the largest prime factor of $X^3+2$ is infinitely often at least as large as $X^{1+\delta}$, though with a much smaller constant than that obtained by Hooley. In order to do this we prove a non-trivial bound for short Ramanujan-Kloosterman sums with smooth modulus. It is also necessary to modify the Chebychev method, as used by Hooley, so as to ensure that the sums that occur do indeed have a sufficiently smooth modulus

Seeding materials: Health and safety considerations

The choice of a proper seeding material for laser velocimeters must include health and safety considerations. Failure to do so can lead to catastrophic results. All materials are toxic, and laser velocimeter seeding materials are no exception. Toxicity may be considered an inherent property of a given material. The manifestation of that property or the physiological response to the material is dependent on dose and exposure conditions. An approximate physiological classification of toxicity is given in tablular form. Toxicity in some situations is not necessarily the most restrictive factor in selection of materials. It is also very important to consider how the material is used so that actual exposure to the material in a damaging form can result. For example, nickel and cadmium are both extremely toxic as systemic poisons and in the case of nickel as a carcinogen. Seeding materials are dispersed in air under conditions that favor personnel exposure. Dispersal equipment is frequently if not normally manned, and personnel are often required to make frequent adjustments to assure proper operations