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Groundrules, advantages, and disadvantages to using systems modeling to address stress management questions are discussed. A systems model designed to explore the effects of multiple climatic stresses on potential site productivity is presented as an example of systems modeling applied to stress management research. Predictions from this model are used to examine the effect of multiple versus single climatic stresses on seasonal stand productivity. The model is also used to explore the possible effect of changing climates on future loblolly pine plantation productivity.

All significant experimental results on the 3 H-3 He mass difference are reviewed. The weighted average of mass doublet measurements is 18596.7±3.6 eV, of tritium β measurements in magnetic spectrometers is 18610±7 eV and in implanted Si(Li) detectors is 18578±6 eV. The data within each group are consistent but there are discrepancies among the groups; possible explanations are proposed. Our best estimate for the 3 H-3 He atomic mass difference is 18599.4 ± 3.0 eV.

The Chalk River π ≫2 iron‐free beta spectrometer is being recommissioned and upgraded for a precise meaurement of the shape of the tritium spectrum near the end point. With a multiple strip source and 60—element detector array an overall energy resolution of σ 19 eV FWHM is expected. Computer simulation of the expected experimental Kurie plots are presented for various and anti‐neutrino mass assumptions.

WE have recently made a detailed study of the beta disintegration of 127-day thulium-170, and have obtained results which are in general agreement with those of Saxon and Richards1, but which do not agree with those recently reported by Grant and Richmond2.

In [2] it was shown that A(k, 4)= oo for k? 1048909 and it was conjectured that A(k, 4) = cfor all k. In this paper we establish this conjecture with the following THEOREM. A(k, 4)-= co. PROOF. It suffices to prove the theorem for values of k which are prime. The proof makes use of the following proposition which is a special case of a result of Kummer [1 ] (see also [3]). PROPOSITION. Let k be a prime and let y', * * *, ye be an arbitrary sequence of kth roots of unity. Then there exist infinitely many primes p with corresponding kth power character X modulo p such that x (Pi) = -Y , 1< i _ n, where pi denotes the ith prime. Thus, for any n and prime k, there exists a prime p with corresponding kth power character X modulo p such that X(2) 5 1, x(pi) = 1, 2 < i? n. Now consider any four consecutive positive integers all less than pn. It is clear that exactly one of these integers must equal 2(2d+1) for some integer d. But we have %(2(2d + 1)) = X(2)X(2d + 1) = x(2) * 1 = 1 since 2d +1 is the product of odd primes less than pn. Therefore

The authors wish to acknowledge the observation of J. Zaks concerning an assertion appearing in On isometric embeddings of graphs, this Journal 288, No. 2 (April 1985), 527-536. In particular, a factor of v2 was inadvertently omitted from the conclusion of Theorem 4, where V denotes the n-dimensional volume of the parallelepiped spanned by the vectors ak aO, 1 < k < n. Of course, this factor should also be included in the related conclusions of Theorems 5 and 6. When the set {ao,. . . ,an} is generated by a tree then V = 1, and Theorem 4 reduces to (2), as asserted.

Studies using Xe125 tracers were conducted to determine the mobile species in anodic oxidation of Al and Ta. Specimens of Al and Ta were bombarded with 5-kev Xe125 ions to form layers of Xe125 below the surfaces, and the energy distribution of the conversion electrons coming from the surfaces was used as an indication of the depth of the Xe125 layers. The bombarded specimens were then anodized at constant current in aqueous 3% ammonium citrate. The Xe125 layer in Al was found to remain at the same depth near the surface, indicating that the film grows mainly by oxygen migration, although metal migration probably also occurs. In Ta, the Xe125 layer moves to deeper depths but remains at the middle of the oxide film, indicating that both oxygen and metal migrations contribute to the oxide film growth.