The Rates of Second-Order Gas Reactions

It has been shown that the most accurate existing measurements of the rates of second-order gas reactions show deviations from pure exponential temperature dependence, which can be empirically represented by a linear increase of the energy of activation with temperature. It is pointed out that this requires the chance of reaction to increase with the energy of the collision in a continuous fashion. Assuming a particular form for this variation, a theory is worked out which predicts that this linear increase shall fail at temperatures only slightly higher than those yet reached in the hydrogen iodide decomposition. There is reason to believe that the numerical results of this theory are substantially correct, even though the detailed assumptions are doubtless far from right

On an action of the braid group B_{2g+2} on the free group F_{2g}

We construct an action of the braid group B_{2g+2} on the free group F_{2g} extending an action of B_4 on F_2 introduced earlier by Reutenauer and the author. Our action induces a homomorphism from B_{2g+2} into the symplectic modular group Sp_{2g}(Z). In the special case g=2 we show that the latter homomorphism is surjective and determine its kernel, thus obtaining a braid-like presentation of Sp_4(Z).Comment: 11 pages. Minor changes in v

Twisting algebras using non-commutative torsors

Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can be used to twist comodule algebras. After surveying and extending the literature on the subject, we prove a theorem that affords a presentation by generators and relations for the algebras obtained by such twisting. We give a number of examples, including new constructions of the quantum affine spaces and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised. Sections 1 and 2 were thoroughly restructured. The presentation theorem in Section 3 is now put in a more general framework and has a more general formulation. Section 4 was shortened. All examples (quantum affine spaces and tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are left unchange

New types of bialgebras arising from the Hopf equation

New types of bialgebras arising from the Hopf equation (pentagonal equation) are introduced and studied. They will play from the Hopf equation the same role as the co-quasitriangular do from the quantum Yang Baxter equation.Comment: Latex2e, Comm Algebra, in pres

Cleft Extensions and Quotients of Twisted Quantum Doubles

Given a pair of finite groups $F, G$ and a normalized 3-cocycle $\omega$ of $G$, where $F$ acts on $G$ as automorphisms, we consider quasi-Hopf algebras defined as a cleft extension $\Bbbk^G_\omega\#_c\,\Bbbk F$ where $c$ denotes some suitable cohomological data. When $F\rightarrow \overline{F}:=F/A$ is a quotient of $F$ by a central subgroup $A$ acting trivially on $G$, we give necessary and sufficient conditions for the existence of a surjection of quasi-Hopf algebras and cleft extensions of the type $\Bbbk^G_\omega\#_c\, \Bbbk F\rightarrow \Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{F}$. Our construction is particularly natural when $F=G$ acts on $G$ by conjugation, and $\Bbbk^G_\omega\#_c \Bbbk G$ is a twisted quantum double $D^{\omega}(G)$. In this case, we give necessary and sufficient conditions that Rep($\Bbbk^G_\omega\#_{\overline{c}} \, \Bbbk \overline{G}$) is a modular tensor category.Comment: LaTex; 14 page

Method and apparatus for determining time, direction, and composition of impacting space particles

A space particle collector for recording the time specific particles are captured, and its direction at the time of capture, utilizes an array of targets, each comprised of an MOS capacitor on a chip charged from an external source and discharged upon impact by a particle through a tab on the chip that serves as a fuse. Any impacting particle creates a crater, but only the first will cause a discharge of the capacitor. A substantial part of the metal film around the first crater is burned off by the discharge current. The time of the impulse which burns the tab, and the identification of the target, is recorded together with data from flight instruments. The metal film is partitioned into pie sections to provide a plurality of targets on each of an array of silicon wafers, thus increasing the total number of identified particles that can be collected. It is thus certain which particles were captured at what specific times

The equilibrium between matter and radiation

The equilibrium concentration of electrons and protons is recalculated on the basis of Dirac's new theory of the nature of the proton; it is found to be exceedingly small, of the same order of magnitude as had been found in previous calculations

Persistence of velocity and the theory of second order GAS reactions

R. H. Fowler has stated that if, in second order gas reactions, it is supposed that reaction occurs whenever two reactant molecules collide with sufficient velocity, then the deviation from the Maxwell distribution law which would result is so great that this law cannot be used in calculating the rate of the reaction. It is shown that this view is sometimes in error, and that in a mixture of molecules of nearly equal mass reacting in this way the molecular velocities do not diverge appreciably from the predictions of the Maxwell law

The heat of dissociation of oxygen

It has recently been suggested by Gerhard Herzberg (Zeits. f. phys. Chem. 4B, 223 (1929)) that the currently accepted value for the heat of dissociation of oxygen is too high. Herzberg concludes that the correct value is not 7.0 volts, but somewhere between 5 and 6 volts; the basis for the conclusion is a re-interpretation of the Lyman-Runge bands on the basis of a theory developed by Wigner and Witmer