The third great crisis in mathematics

Topology and measure theory, along with other branches of mathemtics, are founded upon the theory of sets. The beginnings of the theory were steeped in paradoxes. One concerns the very concept of a set itself, such as proving that ``0 is ordinary if and only if it is not.' The concepts have been debated for more than a century and from them have evolved the axiom of choice, axiom of selection, infinite set theory, well-ordering theorem, and the Banach-Tarski paradox, among others.     

Leadership and the spatial factor in small groups.

The present study extends the hypothesis that "persons tend to interact more in group discussion with persons sitting opposite them than they do with their neighbors." This effect seems to be manifested most strongly in groups with no designated leader. "It will tend to disappear in groups where group direction is shared about equally by the members and the designated leader, and it will be reversed in situations where the designated leader gives very strong direction." (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Power, pollution, and the imperiled environment II. East, Midwest, and West Coast: pollution-control plans of some major utilities; role of government in environmental matters; other proposed systems for reducing stack emissions

A number of the largest utility companies are embarking upon large-scale nuclear generating plant construction programs that may phase out up to 50 percent of their fossil-fuel stations by the end of the present decade. This move is being encouraged by the electrical suppliers, who, with the utilities and the AEC, are striving to convince a skeptical public that nuclear stations are completely safe and provide the best means for air-pollution abatement. Nevertheless, many fossil-fuel plants are still being planned and built, and more efficient methods of reducing stack gas emissions will have to be incorporated at these facilities if a general reduction in air-pollution levels is to be achieved while simultaneously meeting the accelerating demand for more electric energy. Government, too, has a role to play and a responsibility to fulfill in the public interest by enacting fair and practicable pollution-control legislation, and ensuring the enforcement of such statutes.     

Plastic deformation in Fe-Si alloys

A detailed study has been made of the compressive stress-strain behavior of polycrystal-line Fe-Si alloys containing from 0 to 25 at. pct Si. It is shown that the alloys containing less than 10 at. pct Si possess only short range atomic order and deform by slip or by twinning, depending upon temperature. At concentrations greater than 10 at. pct Si, the alloys possess long range atomic order. Deformation twinning is suppressed in this region, and the deformation occurs entirely by slip. Deformation by slip may occur either by the motion of perfect superlattice dislocations, or else by the movement of imperfect superlattice dislocations, with the subsequent generation of antiphase boundaries. The type of superlattice dislocation that prevails depends upon a critical combination of both composition and temperature.     

Shear modulus in closely packed gel suspensions

Rheological properties and swelling were examined in a series of concentrations of particles of crosslinked polyacrylate gels in water or salt solutions. The modulus during steady shear G_s = 2τ²/P₁₁-P₂₂ was determined from shear stress τ and primary normal force difference P₁₁-P₂₂ in a cone-and-plate rheometer. G_s was nearly constant with shear rate for the gel particles in the closely packed condition. The dynamic storage modulus G′ determined by ecentric rotating disc rheometry increased with increasing frequency for all concentrations. The apparent equilibrium shear modulus G_e determined by stress relaxation agreed closely at all concentrations and ionic strengths with the corresponding values of G_s, and hence G_s is considered a good estimate of equilibrium shear modulus for this gel material.     

Mobility tensor of negative ions in superfluid 3He-A

The mobility tensor of negative ions in the A phase of superfluid ³He is calculated for temperatures close to T _c . In this regime the scattering of superfluid quasiparticles from an electron bubble is practically elastic and the mobility tensor is expressed in terms of momentum transfer cross sections for an ion at rest. These generalized transport cross sections are obtained from the quasiparticle-ion scattering T-matrix, which we evaluate in terms of the normal state scattering amplitude. The p-wave pairing correlations in the intermediate states result in important interference effects among all partial waves in the scattering process, and, in addition, for the low-energy quasiparticles they lead to resonant states below the gap edge. These phenomena modify the scattering amplitude in the superfluid in an essential way and the differential quasiparticle-ion cross section is found to display strongly anisotropic, energy-dependent variations on the scale of the superfluid energy gap. We find that, in contrast to simple approximations, for low quasiparticle energies the parallel and perpendicular momentum transfer cross sections are very different from one another. Close to T _c , the calculated mobility remains rather isotropic, but at lower temperatures the anisotropy is considerably larger than predicted by simple approximations for the cross section. The computed results are compared with the available measurements.Supported in part by U.S. National Science Foundation Grants DMR78-21068 and DMR78-21069.     

Contextual cues and release from proactive inhibition in young and old people.

Three experiments examined whether elderly people perform similarly to Korsakoff amnesics on tests of release from proactive inhibition (PI). In Exp I, with 20 18–36 yr old undergraduates, 20 64–77 yr old university alumni, 20 employed 21–43 yr olds, and 21 institutionalized but healthy 71–92 yr olds, only the latter Ss failed to release from PI, like Korsakoff amnesics, whereas all the other groups of Ss showed the normal release from PI. Exp II, with 12 institutionalized 64–90 yr olds and 12 25–47 yr old controls, showed that release from PI could be induced in institutionalized elderly, as in Korsakoff amnesics, by salient environmental cues that coincided with the category shift. Exp III, with 13 67–89 yr old institutionalized Ss and 12 22–42 yr old controls, demonstrated that even in the absence of a category shift, salient environmental cues could lead to smaller, but noticeable, release from PI in institutionalized elderly, but not in young controls. The similarity in performance between the institutionalized elderly and Korsakoff amnesics suggested that it results from a common neurological deficit. (French abstract) (37 ref) (PsycINFO Database Record (c) 2010 APA, all rights reserved)