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

Preparation of ordered poly /arylenesiloxane/ polymers

Preparation of ordered poly/arylenesiloxane/ polymer

Putting wind resource atlases to use

An assessment of an area's wind resource and proper site selection are critical to the successful utilization of wind energy. How the twelve recently published wind energy resource atlases for the United States and its territories can be used to evaluate in the atlas on various geographic scales (regional, state and station) and time scales (annual, seasonal and diurnal) is discussed. In addition to techniques for extracting the magnitude of the wind resource, methods are presented for estimating the seasonal and diurnal variations of the wind resource for an area, the certainty with which the resource has been estimated and the fraction of land area with a given wind resource

A compactness lemma and its application to the existence of minimizers for the liquid drop model

The ancient Gamow liquid drop model of nuclear energies has had a renewed life as an interesting problem in the calculus of variations: Find a set $\Omega \subset \mathbb R^3$ with given volume A that minimizes the sum of its surface area and its Coulomb self energy. A ball minimizes the former and maximizes the latter, but the conjecture is that a ball is always a minimizer -- when there is a minimizer. Even the existence of minimizers for this interesting geometric problem has not been shown in general. We prove the existence of the absolute minimizer (over all $A$) of the energy divided by $A$ (the binding energy per particle). A second result of our work is a general method for showing the existence of optimal sets in geometric minimization problems, which we call the `method of the missing mass'. A third point is the extension of the pulling back compactness lemma from $W^{1,p}$ to $BV$.Comment: 16 page

Sharp constants in several inequalities on the Heisenberg group

We derive the sharp constants for the inequalities on the Heisenberg group H^n whose analogues on Euclidean space R^n are the well known Hardy-Littlewood-Sobolev inequalities. Only one special case had been known previously, due to Jerison-Lee more than twenty years ago. From these inequalities we obtain the sharp constants for their duals, which are the Sobolev inequalities for the Laplacian and conformally invariant fractional Laplacians. By considering limiting cases of these inequalities sharp constants for the analogues of the Onofri and log-Sobolev inequalities on H^n are obtained. The methodology is completely different from that used to obtain the R^n inequalities and can be (and has been) used to give a new, rearrangement free, proof of the HLS inequalities.Comment: 30 pages; addition of Corollary 2.3 and some minor changes; to appear in Annals of Mathematic

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

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