Origin of Stability in Branched Alkanes

The potential origins of stability in branched alkanes are investigated, paying close attention to two recent hypotheses: geminal steric repulsion and protobranching. All alkane isomers through C₆H₁₄ along with heptane and octane were investigated at the MPW1B95/6‐311++G(d,p) level. Their geminal steric repulsion, total steric repulsion, and orbital interactions were evaluated by using natural bond orbital analysis. All measures of steric repulsion fail to explain the stability of branched alkanes. The extra stability of branched alkanes and protobranching, in general, is tied to stabilizing geminal σ→σ* delocalization, particularly of the type that involves adjacent C? C bonds and, thus, preferentially stabilizes branched alkanes. This picture is corroborated by valence bond calculations that attribute the effect to additional ionic structures (e.g., CH₃⁺ :CH₂ :CH₃^? and CH₃:^? CH₂: CH₃⁺ for propane) that are not possible without protobranching.     

Weak Convergence and Banach Space-Valued Functions: Improving the Stability Theory of Feynman’s Operational Calculi

In this paper we investigate the relation between weak convergence of a sequence \(\left\{ \mu_{n}\right\} \) of probability measures on a Polish space S converging weakly to the probability measure μ and continuous, norm-bounded functions into a Banach space X. We show that, given a norm-bounded continuous function f:S→X, it follows that \(\lim_{n\to\infty}\int_{S}f\, d\mu_{n}=\int_{S}f\, d\mu\)—the limit one has for bounded and continuous real (or complex)—valued functions on S. This result is then applied to the stability theory of Feynman’s operational calculus where it is shown that the theory can be significantly improved over previous results.     

Measuring the effect of demagnetization in stacks of gadolinium plates using the magnetocaloric effect

The effect of demagnetization in a stack of gadolinium plates is determined experimentally by using spatially resolved measurements of the adiabatic temperature change due to the magnetocaloric effect. The number of plates in the stack, the spacing between them and the position of the plate on which the temperature is measured are varied. The orientation of the magnetic field is also varied. The measurements are compared to a magnetostatic model previously described. The results show that the magnetocaloric effect, due to the change in the internal field, is sensitive to the stack configuration and the orientation of the applied field. This may have significant implications for the construction of a magnetic cooling device.     

Radicals in skew polynomial and skew Laurent polynomial rings

We provide a general procedure for characterizing radical-like functions of skew polynomial and skew Laurent polynomial rings under grading hypotheses. In particular, we are able to completely characterize the Wedderburn and Levitzki radicals of skew polynomial and skew Laurent polynomial rings in terms of ideals in the coefficient ring. We also introduce the T-nilpotent radideals, and perform similar characterizations.     

The Atlas power-flow system-a status report

Atlas is a high-energy, pulsed-power facility under development to study materials properties and hydrodynamics under extreme conditions. Atlas will implode heavy liner loads (m ~ 45 gm) with a peak current of 27-32 MA delivered in 4 μs, and it is energized by 96, 240-kV Marx generators storing a total of 23 MJ. The power-flow system transports current from the Marx generators to the load. It includes a load protection switch to protect the load in case of a prefire; 24 oil-insulated, vertically oriented, radially converging, triplate transmission lines; a transition region that couples the transmission lines to the power-flow channel; and a radially converging, dielectric-insulated, horizontal and conical, power-flow channel. Proposed experiments, the design of the power-flow system, test results, and status are presented