Integrability of superharmonic functions, uniform domains, and Hölder domains

Let denote the space of all positive superharmonic functions on a domain . Lindqvist showed that is a bounded subset of . Using this, we give a characterization of finitely connected -dimensional uniform domains and remarks on Hölder domains.

     

A criterion on weighted boundedness for rough multilinear oscillatory singular integrals

In this paper the authors give a criterion on the weighted boundedness of the multilinear oscillatory singular integral operators with rough kernels.

     

Extracting deep information from limited observations on an evolved social network

We provide empirical evidence that in a social network which evolves over time, it is possible to extract deep information about the system from limited observations. In this paper, we consider a simple piece of readily available evidence on access to financial services by individuals in the UK. Detailed statistical analysis has shown that the decisions of agents on whether or not to have a basic financial account such as a bank account is heavily influenced by other individuals on their social network. We consider a small amount of straightforward and readily accessible information. We deduce from this, using an agent-based model, the type of social network across which information and influence on behaviour flows between agents in this context. Specifically, we show that information appears to flow across a small world network.     

Structural and electronic properties of V, Nb and Ta nanoclusters by tight-binding molecular dynamics simulations

We present tight-binding molecular dynamics (TBMD) calculations on V, Nb and Ta nanoclusters with N = 15, 65, 175 and 369 atoms. We found that rhombic dodecahedra are energetically favoured over rhombic hexahedra and icosahedra, with V forming the most compact cluster with the gyration radius increasing with the cluster size. In addition, from the calculated electronic density of states we found that the cluster size plays an important role in the HOMO-LUMO gap and that an increase in cluster size results in enhancement of the electronic density around the Fermi level. Furthermore, we found that the small clusters (N = 15, 65) exhibit energy gap that persists even at 900 K. These findings originate from charge transfer occurring between the inner and outer cluster atoms; interestingly, we found that in the small N = 15, 65 clusters electronic charge accumulates at each surface site at the expense of the inner cluster atoms, while in the larger clusters, N = 175 and 369, charge is gathered on the central particles of the cluster, suggesting different sub-surface character of the clusters. These findings are in agreement with available experimental and theoretical data and promise to offer important information for creating nanostructured materials with improved properties suitable for multiple technological applications.     

Light scattering by Gaussian random ellipsoid particles: First results with discrete-dipole approximation

We introduce the stochastic geometry of a Gaussian random ellipsoid (GE) and, with the discrete-dipole approximation, carry out preliminary computations for light scattering by wavelength-scale GE particles. In the GE geometry, we describe the base ellipsoid by the three semiaxes a?b?c. The axial ratios b:a and c:a appear as two shape parameters additional to those of the Gaussian random sphere geometry (GS). We compare the scattering characteristics of GE particles to those of ellipsoids. Introducing irregularities on ellipsoids smoothens the angular scattering characteristics, in a way analogous to the smoothening of spherical particle characteristics in the case of GS particles.     

Small divisor problem for an analytic q-difference equation

Similar to the problem of linearization, the “small divisor problem” also arises in the discussion of invertible analytic solutions of a class of q-difference equations. In this paper we give the existence of such solutions under the Brjuno condition and prove that the equation may not have a nontrivial analytic solution when the Brjuno condition is violated. These results are applied to discussing a nonlinear iterative equation.     

Transition to turbulence, small disturbances, and sensitivity analysis I: A motivating problem

For over 100 years, researchers have attempted to predict transition to turbulence in fluid flows by analyzing the spectrum of the linearized Navier-Stokes equations. However, for many simple flows this approach fails to match experimental results. Recently, new scenarios for transition have been proposed that are based on the interaction of the linearized equations of motion with small disturbances to the flow system. These new “mostly linear” theories have increased our understanding of the transition process, but the role of nonlinearity has not been explored in detail. This paper is the first of a two part work in which sensitivity analysis is used to study the effects of small disturbances on transition to turbulence. In this part, we study a highly sensitive one-dimensional Burgers' equation as a motivating problem. Sensitivity analysis is used to predict the large changes in solutions in the presence of a small disturbance. Also, sensitivity analysis is shown to provide more information about the disturbed nonlinear problem than a purely linear analysis of the problem. In the second part of this work, this analysis will be extended to the three-dimensional Navier-Stokes equations to show that small disturbances have great potential to trigger transition to turbulence.     

Gradient estimates in Orlicz space for nonlinear elliptic equations

In this paper we generalize gradient estimates in Lp space to Orlicz space for weak solutions of elliptic equations of p-Laplacian type with small BMO coefficients in δ-Reifenberg flat domains. Our results improve the known results for such equations using a harmonic analysis-free technique.     

Weighted endpoint estimates for commutators of Marcinkiewicz integrals

Let μΩ^mb be the commutator generalized by μΩ, the n-dimensional Marcinkiewicz integral, and b ∈ BMO（R^n）. The author establishes the weighted weak LlogL-type estimates for μΩ^mb when Ω satisfies a kind of Dini conditions, which improves the known result essentially.     

Monte Carlo study of electron correlation functions for small molecules

A study is made of electron-electron correlation functions for use in trial wave functions for small molecules. New forms are proposed that have only a few variational parameters, and these parameters have physical meanings that are easily discerned. Total energies for H₂, LiH and Li₂ computed using these correlation functions are presented, and comparison is made with previous forms, including the Jastrow-Pade form often used in Monte Carlo studies. We further treat the possibility that correlation depends not only on the separation of a pair of electrons but also on the location of the electron pair relative to the nuclei — indicative of a density-dependent or many body correlation effect. Our results indicate that such a many-body correlation effect is weakly present.This work was supported by the Director, Office of Energy Research, Office of Basic Energy Sciences, Chemical Sciences Division of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098