The Lp dual Minkowski problem for p > 1 and q > 0

General $L_p$ dual curvature measures have recently been introduced by Lutwak, Yang and Zhang [24]. These new measures unify several other geometric measures of the Brunn–Minkowski theory and the dual Brunn–Minkowski theory. $L_p$ dual curvature measures arise from qth dual intrinsic volumes by means of Alexandrov-type variational formulas. Lutwak, Yang and Zhang [24] formulated the $L_p$ dual Minkowski problem, which concerns the characterization of $L_p$ dual curvature measures. In this paper, we solve the existence part of the $L_p$ dual Minkowski problem for $p>1$ and $q>0$, and we also discuss the regularity of the solution.     

Direct analysis in real time mass spectrometry (DART‐MS) of highly non‐polar low molecular weight polyisobutylenes

Low molecular weight polyisobutylenes (PIB) with chlorine, olefin and succinic acid end‐groups were studied using direct analysis in real time mass spectrometry (DART‐MS). To facilitate the adduct ion formation under DART conditions, NH₄Cl as an auxiliary reagent was deposited onto the PIB surface. It was found that chlorinated adduct ions of olefin and chlorine telechelic PIBs, i.e. [M + Cl]^? up to m/z 1100, and the deprotonated polyisobutylene succinic acid [M? H]^? were formed as observed in the negative ion mode. In the positive ion mode formation of [M + NH₄]⁺, adduct ions were detected. In the tandem mass (MS/MS) spectra of [M + Cl]^?, product ions were absent, suggesting a simple dissociation of the precursor [M + Cl]^? into a Cl^? ion and a neutral M without fragmentation of the PIB backbones. However, structurally important product ions were produced from the corresponding [M + NH₄]⁺ ions, allowing us to obtain valuable information on the arm‐length distributions of the PIBs containing aromatic initiator moiety. In addition, a model was developed to interpret the oligomer distributions and the number average molecular weights observed in DART‐MS for PIBs and other polymers of low molecular weight. Copyright © 2015 John Wiley & Sons, Ltd.     

Gravity-Related Wave Function Collapse

The gravity-related model of spontaneous wave function collapse, a longtime hypothesis, damps the massive Schrödinger Cat states in quantum theory. We extend the hypothesis and assume that spontaneous wave function collapses are responsible for the emergence of Newton interaction. Superfluid helium would then show significant and testable gravitational anomalies.     

Variance-reduced DSMC for binary gas flows as defined by the McCormack kinetic model

A variance-reduced direct simulation Monte Carlo method is presented for binary gas flows as defined by the McCormack kinetic model. Two types of flow configuration, namely pressure driven flow between two parallel plates and through rectangular channels, are considered. The kinetic model is transformed into one- and two-dimensional projected formalisms. Both cases are modeled by the variance-reduced DSMC. Simulations are performed to compare the method to the analytical discrete ordinate and discrete velocity methods. For both flow configurations, very good agreement is obtained between the results of different approaches. The results of the approach are also compared to the prediction of the moment method and the results of hard-sphere gases. The model can be beneficial for computing slow rarefied gaseous mixture flows, especially in nano- and microscale devices.     

Weak invariance principles for sums of dependent random functions

Motivated by problems in functional data analysis, in this paper we prove the weak convergence of normalized partial sums of dependent random functions exhibiting a Bernoulli shift structure.