Scattering of a Baseball by a Bat

A ball can be hit faster if it is projected without spin but it can be hit farther if it is projected with backspin. Measurements are presented in this paper of the tradeoff between speed and spin for a baseball impacting a baseball bat. The results are inconsistent with a collision model in which the ball rolls off the bat and instead imply tangential compliance in the ball, the bat, or both. If the results are extrapolated to the higher speeds that are typical of the game of baseball, they suggest that a curveball can be hit with greater backspin than a fastball, but by an amount that is less than would be the case in the absence of tangential compliance.Comment: Accepted for publication in American Journal of Physic

Photoproduction of K^+ Mesons in Hydrogen

The photoproduction of K^+ mesons in hydrogen has been measured with the purpose of extending the previous CalTech measurements to smaller angles, and obtaining better absolute values for the cross sections. The technique of Donoho and Walker, using a magnetic spectrometer and a time-of-flight measurement to detect the K^+ mesons, was modified so as to achieve a better discrimination against pions and scattered protons. The results obtained are in fairly good agreement with the more extensive measurements made at Cornell by a somewhat different method

SPECIAL PROJECT: LABOR-MANAGEMENT COOPERATION

Much of the current debate concerning labor-management cooperative efforts centers on section 8(a)(2) of the National Labor Relations Act (the Act), which makes dominating, interfering with, or contributing to the formation or administration of any labor organization an unfair labor practice. On its face, this section may inhibit cooperative efforts through a prohibition of management support for employee organizations. The effect of section 8(a)(2), however, need not be so restrictive because of the Act\u27s underlying concern for the effectuation of employee freedom of choice. A concern for employee free choice provides a means for permitting positive cooperative efforts, consistent with trends in labor-management relations, while preventing the abuses feared by the drafters of the Act. An examination of the legislative history surrounding the passage of the Act in 19354 is crucial to understanding section 8(a)(2) because much of the debate on the original Act 5 centered on what eventually became section 8(a)(2) . Although the stated purpose of the 1935 Act was [t]o promote equality of bargaining power between employers and employees [and] to diminish the causes of labor disputes, \u27 the discussion surrounding the formation of this Act reveals that the controlling intent of the Act\u27s drafters was to eliminate the company-dominated union. To effectuate their goals, the drafters structured the Act in a way that forces labor and management into adversarial positions. Contrary to the contentions of later cases, the Act\u27s drafters did not intend to promote cooperation between labor and management. The legislative history indicates that the drafters were more concerned with cooperation among labor itself,\u27 with the belief that if employees could in-crease their power through cooperation with each other, then labor could bargain as an equal with management

Statistical Geometry in Quantum Mechanics

A statistical model M is a family of probability distributions, characterised by a set of continuous parameters known as the parameter space. This possesses natural geometrical properties induced by the embedding of the family of probability distributions into the Hilbert space H. By consideration of the square-root density function we can regard M as a submanifold of the unit sphere in H. Therefore, H embodies the `state space' of the probability distributions, and the geometry of M can be described in terms of the embedding of in H. The geometry in question is characterised by a natural Riemannian metric (the Fisher-Rao metric), thus allowing us to formulate the principles of classical statistical inference in a natural geometric setting. In particular, we focus attention on the variance lower bounds for statistical estimation, and establish generalisations of the classical Cramer-Rao and Bhattacharyya inequalities. The statistical model M is then specialised to the case of a submanifold of the state space of a quantum mechanical system. This is pursued by introducing a compatible complex structure on the underlying real Hilbert space, which allows the operations of ordinary quantum mechanics to be reinterpreted in the language of real Hilbert space geometry. The application of generalised variance bounds in the case of quantum statistical estimation leads to a set of higher order corrections to the Heisenberg uncertainty relations for canonically conjugate observables.Comment: 32 pages, LaTex file, Extended version to include quantum measurement theor

The Information Geometry of the Ising Model on Planar Random Graphs

It has been suggested that an information geometric view of statistical mechanics in which a metric is introduced onto the space of parameters provides an interesting alternative characterisation of the phase structure, particularly in the case where there are two such parameters -- such as the Ising model with inverse temperature $\beta$ and external field $h$. In various two parameter calculable models the scalar curvature ${\cal R}$ of the information metric has been found to diverge at the phase transition point $\beta_c$ and a plausible scaling relation postulated: ${\cal R} \sim |\beta- \beta_c|^{\alpha - 2}$. For spin models the necessity of calculating in non-zero field has limited analytic consideration to 1D, mean-field and Bethe lattice Ising models. In this letter we use the solution in field of the Ising model on an ensemble of planar random graphs (where $\alpha=-1, \beta=1/2, \gamma=2$) to evaluate the scaling behaviour of the scalar curvature, and find ${\cal R} \sim | \beta- \beta_c |^{-2}$. The apparent discrepancy is traced back to the effect of a negative $\alpha$.Comment: Version accepted for publication in PRE, revtex

Resting energy metabolism and pulmonary ventilation in growing swine.

Publication authorized February 9, 1944."Animal Husbandry Department and Dairy Department, Missouri Agricultural Experiment Station, and the Bureau of Animal Industry, Agricultural Research Administration, United States Department of Agriculture, cooperating."Includes bibliographical references