On the Homology of Elementary Abelian Groups as Modules over the Steenrod Algebra

We examine the dual of the so-called "hit problem", the latter being the problem of determining a minimal generating set for the cohomology of products of infinite projective spaces as module over the Steenrod Algebra $\mathcal{A}$ at the prime 2. The dual problem is to determine the set of $\mathcal {A}$-annihilated elements in homology. The set of $\mathcal{A}$-annihilateds has been shown by David Anick to be a free associative algebra. In this note we prove that, for each $k \geq 0$, the set of {\it $k$ partially $\mathcal{A}$-annihilateds}, the set of elements that are annihilated by $Sq^i$ for each $i\leq 2^k$, itself forms a free associative algebra.Comment: 6 pages + reference

A study of Na(x)Pt3O4 as an O2 electrode bifunctional electrocatalyst

The present study suggests that polytetrafluoroethylene (PTFE) bonded Na(X)Pt3O4 gas porous diffusion electrodes may be a viable candidate for bifunctional O2 reduction and evolution activity. The electrodes exhibited Tafel slopes of about 0.06 V/decade for both O2 reduction an evolution. For O2 reduction, the 0.06 slope doubled to 0.12 V/decade at larger current densities. Preliminary stability testing at 24 C suggest that the Na(x)Pt3O4 electrodes were relatively stable at reducing and oxidizing potentials typically encountered at the O2 electrodes in a regenerative fuel cell

Oxygen electrode bifunctional electrocatalyst NiCo2O4 spinel

A significant increase in energy density may be possible if a two-unit alkaline regenerative H2-O2 fuel cell is replaced with a single-unit system that uses passive means for H2O transfer and thermal control. For this single-unit system, new electrocatalysts for the O2 electrode will be required which are not only bifunctionally active but also chemically and electrochemically stable between the voltage range of about 0.7 and 1.5 V. NiCo2O4 spinel is reported to have certain characteristics that make it useful for a study of electrode fabrication techniques. High surface area NiCo2O4 powder was fabricated into unsupported, bifunctional, PTFE-bonded, porous gas fuel cell electrodes by commercial sources using varying PTFE contents and sintering temperatures. The object of this study is to measure the bifunctional activities of these electrodes and to observe what performance differences might result from different commercial electrode fabricators. O2 evolution and O2 reduction data were obtained at 80 C (31 percent KOH). An irreversible reaction (i.e., aging) occurred during O2 evolution at potentials greater than about 1.5 V. Anodic Tafel slopes of 0.06 and 0.12 V/decade were obtained for the aged electrodes. Within the range of 15 to 25 percent, the PTFE content was not a critical parameter for optimizing the electrode for O2 evolution activity. Sintering temperatures between 300 and 340 C may be adequate but heating at 275 C may not be sufficient to properly sinter the PTFE-NiCo2O4 mixture. Electrode disintegration was observed during O2 reduction. Transport of O2 to the NiCo2O4 surface became prohibitive at greater than about -0.02 A/sq cm. Cathodic Tafel slopes of -0.6 and -0.12 V/decade were assumed for the O2 reduction process. A PTFE content of 25 percent (or greater) appears to be preferable for sintering the PTFE-NiCo2O4 mixture

Corrosion testing of candidates for the alkaline fuel cell cathode

It is desirable to employ a corrosion screening test for catalyst or support candidates for the fuel cell cathode before entering upon optimization of the candidate or of the catalytic electrode. To this end, corrosion test electrodes, intended for complete immersion and maximum wetting, have been made with 30 to 40 vol. pct Teflon; with perovskites this is about 10 to 15 pct. The candidates were synthesized by methods intended for single-phase product without special emphasis on high surface area, although the substances tested were no coarser than 2 m squared/g. A typical loading was 25 mg/cm sq of the pure substance, usually on gold screen, a few mm squared of which were left bare for contacting. Contact to the gold lead wire was made by welding with a micro-torch or a spot-welder. Corrosion testing consisted of obtaining current-voltage data under flowing inert gas in the potential region for reduction of O2. The electrode was immersed in 30 pct KOH. Observations were made at 20 C and 80 C, and the results compared with data from gold standards. Results with some perovskites, pyrochlores, spinels, and interstitial compounds will be discussed

O2 reduction at the IFC orbiter fuel cell O2 electrode

O2 reduction Tafel data were obtained for the IFC Orbiter fuel cell O2 electrode (Au-10 percent Pt catalyst) at temperatures between 24 and 81 C. BET measurements gave an electrode surface area of about 2040 sq cm per sq cm of geometric area. The Tafel data could be fitted to three straight line regions. For current densities less than 0.001 A/sq cm, the slope was essentially independent of temperature with a value of about 0.032 V/decade. Above 0.001 A/sq cm, the two regions, designated in the present study as the 0.04 and 0.12 V/decate regions, were temperature dependent. The apparent energies of activation for these two regions were about 9.3 and 6.5 kcal/mol, respectively. Tafel data (1 atmosphere O2) were extrapolated to 120 C for predicting changes in overpotential with increasing temperature. A mechanism is presented for O2 reduction

Corrosion testing of candidates for the alkaline fuel cell cathode

Current/voltage data was obtained for specially made corrosion electrodes of some oxides and of gold materials for the purpose of developing a screening test of catalysts and supports for use at the cathode of the alkaline fuel cell. The data consists of measurements of current at fixed potentials and cyclic voltammograms. These data will have to be correlated with longtime performance data in order to fully evaluate this approach to corrosion screening. Corrosion test screening of candidates for the oxygen reduction electrode of the alkaline fuel cell was applied to two substances, the pyrochlore Pb2Ru2O6.5 and the spinel NiCo2O4. The substrate gold screen and a sample of the IFC Orbiter Pt-Au performance electrode were included as blanks. The pyrochlore data indicate relative stability, although nothing yet can be said about long term stability. The spinel was plainly unstable. For this type of testing to be validated, comparisons will have to be made with long term performance tests

Oxidation of basaltic tephras: Influence on reflectance in the 1 micron region

As part of a ongoing study into the products of hydrovolcanism, tuffs were examined from the Cerro Colorado and Pavant Butte tuff cones. The former resides in the northeastern corner of the Pinacate Volcanic Field in Sonara, Mexico and the latter is in the Black Rock Desert of southern Utah. Numerous samples were collected and many of these had their Vis/IR reflectance measured. It seems likely that in the palagonite tuffs there is a combination of nanocrystalline ferric oxide phases contributing to the UV absorption edge, but not to the 1 micron band, plus more crystalline ferric oxides which do contribute to that band as well as ferrous iron within unaltered sideromelane which is skewing the band center to longer wavelengths. This work has implications for the study of Mars. The present work indicates that when ferrous and ferric iron phases are both present, their combined spectral contribution is a single band in the vicinity of 1 micron. The center, depth, and width of that feature has potential to be used to gauge the relative proportions of ferrous and ferric iron phases

Things that We Would Like to Take for Granted: Minimum Standards for the Legal Framework of a Free and Democratic Society

We live in an age that glorifies the free market, small government and freedom of contract. Regulations are viewed as interferences with liberty and mandatory terms in contracts are derided as paternalistic interferences with autonomy. This free market model fails adequately to describe either our settled social values or our law. If we recognize the truism that there is no liberty without law, we will see that even our most libertarian states have comprehensive networks of regulations that set minimum standards for economic relationships. Rather than asking, Why interfere with freedom of contract? We would do better to recognize that all contracts are subject to minimum standards regulations and ask, What are the minimum standards for transactions of this sort? Some minimum standards merely set rules of the road; others, however, shape the contours of our way of life. We impose minimum standards regulations, not because government officials know better than individuals what is in their own best interest, but because we live in a free and democratic society and such a society promotes social relations of a certain type; this means that certain contract terms are out of line and certain contract demands must be taken off the table. Mandatory contract terms do limit our freedom to agree to contrary terms but we as a society demand those mandatory terms to create the legal framework of a free and democratic society that treats each person with equal concern and respect. We cannot create such a society by deferring to preferences, whatever they happen to be; some preferences cannot be indulged in a free and democratic society. Identifying appropriate minimum standards requires us to go beyond economic and legal theory by using useful aspects of moral and political philosophy, in conjunction with law, to shape the contours of our way of life