Fluorinated esters of polycarboxylic acids

Fluorine containing esters of polycarboxylic acids are discussed. The use of these esters as extreme temperature lubricants and base fluids for greases is investigated

Separation of gas from liquid in a two-phase flow system

Separation system causes jets which leave two-phase nozzles to impinge on each other, so that liquid from jets tends to coalesce in center of combined jet streams while gas phase is forced to outer periphery. Thus, because liquid coalescence is achieved without resort to separation with solid surfaces, cycle efficiency is improved

Norms of quantum Gaussian multi-mode channels

We compute the $\mathcal S^p \to \mathcal S^p$ norm of a general Gaussian gauge-covariant multi-mode channel for any $1\leq p<\infty$, where $\mathcal S^p$ is a Schatten space. As a consequence, we verify the Gaussian optimizer conjecture and the multiplicativity conjecture in these cases.Comment: 9 pages; minor changes; to appear in J. Math. Phy

Development of lubricating oils suitable for use with liquid oxidizers Quarterly progress report, 1 Jun. - 31 Aug. 1970

Investigating ester and alkyl compounds as lubricating oils for use with liquid oxidizer

Inversion positivity and the sharp Hardy-Littlewood-Sobolev inequality

We give a new proof of certain cases of the sharp HLS inequality. Instead of symmetric decreasing rearrangement it uses the reflection positivity of inversions in spheres. In doing this we extend a characterization of the minimizing functions due to Li and Zhu.Comment: 15 pages; references added and minor change

Hardy-Lieb-Thirring inequalities for fractional Schrödinger operators

We show that the Lieb-Thirring inequalities on moments of negative eigenvalues of Schrödinger-like operators remain true, with possibly different constants, when the critical Hardy-weight C │x│^(-2) is subtracted from the Laplace operator. We do so by first establishing a Sobolev inequality for such operators. Similar results are true for fractional powers of the Laplacian and the Hardy-weight and, in particular, for relativistic Schrödinger operators. We also allow for the inclusion of magnetic vector potentials. As an application, we extend, for the first time, the proof of stability of relativistic matter with magnetic fields all the way up to the critical value of the nuclear charge Zɑ = 2/π, for ɑ less than some critical value

The resistible effects of Coulomb interaction on nucleus-vapor phase coexistence

We explore the effects of Coulomb interaction upon the nuclear liquid vapor phase transition. Because large nuclei (A>60) are metastable objects, phases, phase coexistence, and phase transitions cannot be defined with any generality and the analogy to liquid vapor is ill-posed for these heavy systems. However, it is possible to account for the Coulomb interaction in the decay rates and obtain the coexistence phase diagram for the corresponding uncharged system.Comment: 5 pages, 5 figure