Nucleation and Growth Synthesis of Siloxane Gels to Form Functional,Monodisperse, and Acoustically Programmable Particles

Nucleation and growth methods offer scalable means of synthesizing colloidal particles with precisely specified size for applications in chemical research, industry, and medicine. These methods have been used to prepare a class of silicone gel particles that display a range of programmable properties and narrow size distributions. The acoustic contrast factor of these particles in water is estimated and can be tuned such that the particles undergo acoustophoresis to either the pressure nodes or antinodes of acoustic standing waves. These particles can be synthesized to display surface functional groups that can be covalently modified for a range of bioanalytical and acoustophoretic sorting applications.     

On the crystallization of two-dimensional electron system in strong magnetic field

The possibility of the two-dimensional electron crystallization in the strong magnetic field is discussed by comparison between electron free energies in liquid and crystal states. The electron free energy in the liquid state is determined in Hartree-Fock approximation, while the correlation phenomena are proved to be negligible. The electron free energy in the crystal state is calculated in the harmonic approximation. The magnetic field is shown to “nonmonotonously” affect the crystal formation. From one hand, an electron crystal may exist in an interval of the strong magnetic field H at rather high density, where that is impossible at H=0. From the other hand, at any density the sufficiently strong field forces electron lattice to melt at finite temperature.     

Continuous wave NMR of submonolayer 3He adsorbed on grafoil

NMR linewidths and magnetic susceptibilities of ³He adsorbed on Grafoil have been measured by a continuous wave technique between 0.40 K to 4.21 K for five fractional monolayer coverages, x, between 0.20 and 0.96. Interpretations in terms of the phases of the submonolayers are presented.     

Improved calculation of distributions sensitive to the three gluon vertex ine + e −→4-jets using a coherent parton shower simulator

The calculation of hadron distributions ine ⁺ e ^?→4-jets using the 4-parton matrix element diverges unless cuts are imposed on the parton phase space. Experimentally cuts can be applied only on the hadron spectrum and not at the 4-parton level. Test observables for the three gluon vertex relying on jet-jet angular correlations are found to be particularly sensitive to these parton cuts. The contribution from the parton phase space below the cut region is calculated to modified logarithmic approximation accuracy using a Monte Carlo simulator HERWIG and is found to be of order 45%. This modifies the predictions of the tests so that differences between QCD and ‘QED’ are diminished significantly. A tagging method based on the average energy of particles in a jet is found to be best at identifying both gluon jets with a possible 9:1 success to failure ratio and it allows the presence of the three gluon vertex to be verified.     

The last subconstituent of the Hemmeter graph

We prove that when q is any odd prime power, the distance-2 graph on the set of vertices at maximal distance D from any fixed vertex of the Hemmeter graph Hem_D(q) is isomorphic to the graph Quad_D-1(q) of quadratic forms on .     

The boundary value problem and the Jensen inequality for an entropy functional of a Markov diffusion process

The paper introduces the recent results related to an entropy functional on trajectories of a controlled diffusion process, expressed through an additive functional of the diffusion process, with a Lagrangian, determined by the parameters of a controlled stochastic equation. These results include a minimum condition for the entropy functional and the functional's Jensen inequality, which both are useful for the solution of important mathematical and applied problems.     

Network ensemble clustering using latent roles

We present a clustering method for collections of graphs based on the assumptions that graphs in the same cluster have a similar role structure and that the respective roles can be founded on implicit vertex types. Given a network ensemble (a collection of attributed graphs with some substantive commonality), we start by partitioning the set of all vertices based on attribute similarity. Projection of each graph onto the resulting vertex types yields feature vectors of equal dimensionality, irrespective of the original graph sizes. These feature vectors are then subjected to standard clustering methods. This approach is motivated by social network concepts, and we demonstrate its utility on an ensemble of personal networks of migrants, where we extract structurally similar groups and show their resemblance to predicted acculturation strategies.     

On Sharp Aperture-Weighted Estimates for Square Functions

Let \(S_{\alpha ,\psi }(f)\) be the square function defined by means of the cone in \({\mathbb R}^{n+1}_{+}\) of aperture \(\alpha \) , and a standard kernel \(\psi \) . Let \([w]_{A_p}\) denote the \(A_p\) characteristic of the weight \(w\) . We show that for any \(1<p<\infty \) and \(\alpha \ge 1\) , $$\begin{aligned} \Vert S_{\alpha ,\psi }\Vert _{L^p(w)}\lesssim \alpha ^n[w]_{A_p}^{\max \left( \frac{1}{2},\frac{1}{p-1}\right) }. \end{aligned}$$ For each fixed \(\alpha \) the dependence on \([w]_{A_p}\) is sharp. Also, on all class \(A_p\) the result is sharp in \(\alpha \) . Previously this estimate was proved in the case \(\alpha =1\) using the intrinsic square function. However, that approach does not allow to get the above estimate with sharp dependence on \(\alpha \) . Hence we give a different proof suitable for all \(\alpha \ge 1\) and avoiding the notion of the intrinsic square function.