Stickstoffbestimmung

Ohne Zusammenfassung     

Implications of population change on social insurance systems providing old-age benefits

General agreement, although not completely universal, exists in North America that cost analysis of programs providing old-age retirement benefits should be conducted over the long range, and not merely over the next few years. The actuarial cost estimates for what is now the U.S. Old-Age, Survivors, and Disability Insurance program have always been made over a long period of future years. Initially, for the 1935 Act, this period was 44 years (up through 1980), but most subsequent valuations of the program have used a 75-year period. The justification for this length of time is that it covers essentially the entire lifetime of every person in covered employment on the valuation date.It must be recognized that outside of North America — but with the exception of the United Kingdom — long-range social insurance programs providing retirement benefits are not generally considered over long future periods. The argument made in support of this short-sighted approach is that it is impossible to predict with any precision such long-range future operations. Countering this is the point that an estimate prepared by well-qualified persons is far better for policy planning and analysis than nothing at all.     

Efficient synthesis and intramolecular cyclopropanation of unsaturated diazoacetic esters

New and efficient procedures are described for the conversion of homoallylic alcohols to esters of diazoacetic acid and for the further intramolecular cyclopropanation of those esters.     

The intramolecular mode in isotopically substituted NO+ β- and β″-alumina

Single crystals of ¹⁵N-substituted NO⁺ β- and β″-alumina were prepared and Raman scattering spectra of the nitrosonium intramolecular stretching mode were measured. The harmonic frequency and the cubic anharmonic force constant were calculated using these and similar data from the naturally abundant nitrosonium aluminas. Differences in the calculated values between the β and β″ system were attributed to structural differences in the conduction planes.     

Detection by low temperature photoluminescence of oxygen recoils in “through-oxide” arsenic implanted silicon

The technique of low-temperature photoluminescence is used to study the damage induced by arsenic implantations through SiO₂ layers. The presence of an oxygen dependent damage center in only the “through-oxide” implanted samples and in none of the samples implanted into bare surfaces is interpreted as indicating the presence of oxygen recoils from the oxide. It is also seen that the in-diffusion of oxygen during thermal growth of the SiO₂ is insufficient to produce detectable oxygen-dependent luminescence after irradiation.     

Properties of the conjugate-gradient and Davidon methods

Two quadratically convergent gradient methods for minimizing an unconstrained function of several variables are examined. The heart of the Fletcher and Powell reformulation of Davidon's method is a variableH-matrix. The eigenvalues and eigenvectors of this matrix for a quadratic function are explored, leading to a proof that the gradient vectors at each step are mutually orthogonal. From this, a geometric interpretation of theH-matrix in terms of the projection of the gradient into a solution subspace is derived. These properties are then used to arrive at the main result, which states that, for a quadratic function, the direction vectors generated by the Davidon algorithm and the conjugate-gradient algorithm of Hestenes and Stiefel are scalar multiples of each other, provided the initial step each takes is in the direction of steepest descent. If one assumes no round-off error and a perfect one-dimensional search, the methods generate identical steps leading to the minimum.It is also shown that, for a quadratic function, the Davidon algorithm has a simplified version which searches in the same directions. However, the unique advantage of the original scheme, that it yields the curvature of the function at the minimum, is sacrificed for simplicity.Although these results apply to the case of a quadratic function, a comparative study of the same algorithms for a general function can be found in a companion paper.This research was carried out under Contract No. NAS 9-4036, NASA-Manned Spacecraft Center, Houston, Texas. The author is indebted to Dr. H. J. Kelley, whose suggestions and encouragement provided the inspiration for this paper.     

Plutonium-244 dating VI. Initial ratios of plutonium to uranium in achondrites

Re-examination of all known xenon isotopic data for achondrites reveals that²⁴⁴Pu fission xenon can be resolved in about three-fourths of the meteorites of this class. The amounts of²⁴⁴Pu fission xenon found in these meteorites range from ca. 1–2 up to 20–40·10^–12 ccSTP/g. These meteorites started to retain their xenon some 200–500 million years later than did the carbonaceous chondrites Allende, Groznaya, Mokoia, Murchison, Murray, and Renazzo, which began to retain their xenon over 4800 million years ago.     

A computational study of the chromatographic separation of racemic mixtures

Summary A model is devised using molecular mechanics to simulate chromatographic separations of enantiomers. Theoretical results derived from this model are compared with experimental findings obtained using supercritical fluid chromatography. The model is then developed to incorporate the effects of binding the stationary phase to a matrix. Computed results show that addition of the matrix into the model has significant effects on the ability of the stationary phase to separate racemic mixtures.     

Adjustability as a requirement of ideal clocks

A coordinate frame is considered as an arrangement of clocks that meet certain criteria of synchronization. Einstein's ideal clock is compared with the behavior required for clocks to maintain synchrony in the group of coordinate frames that leaves Maxwell's equations invariant. The required clock rates differ from the rate of Einstein's clock. An ideal adjustable clock is defined as an Einstein clock augmented by variable “gearing” that can offset its rate. Ongoing adjustment of these clocks enables them to meet all synchronization criteria in the group of coordinate frames. The need for adjustment is due to the well known invariance of Maxwell's equations under a group of coordinate transformations larger than the Lorentz group, and has nothing to do with imperfections in clocks. It is shown that the adjustments needed by ideal adjustable clocks to maintain synchrony can be measurably separated from additional adjustments that may be needed to compensate for random imperfections. The necessity for adjustment brings with it the necessity for ongoing measurement of the light signals whose exchange defines synchronization. Implications are discussed, both for the interpretation of Maxwell's equations and for the role of measuring instruments.