An asymmetric Orlicz centroid inequality for probability measures

Using M-addition,an asymmetric Orlicz centroid inequality for absolutely continuous probability measures is established corresponding to Paouris and Pivovarov’s recent result on the symmetric case.As an application,we extend Haberl and Schuster’s asymmetric Lp centroid inequality from star bodies to compact sets.     

Higher integrability for nonlinear elliptic equations with variable growth and discontinuous coefficients

In this paper, based on the theory of variable exponent spaces, we study the higher integrability for a class of nonlinear elliptic equations with variable growth and discontinuous coefficients. Under suitable assumptions, we obtain a local gradient estimate in Orlicz space for weak solution.     

Brownian motion with drift on spaces with varying dimension

Many properties of Brownian motion on spaces with varying dimension (BMVD in abbreviation) have been explored in Chen and Lou (2018). In this paper, we study Brownian motion with drift on spaces with varying dimension (BMVD with drift in abbreviation). Such a process can be conveniently defined by a regular Dirichlet form that is not necessarily symmetric. Through the method of Duhamel’s principle, it is established in this paper that the transition density of BMVD with drift has the same type of two-sided Gaussian bounds as that for BMVD (without drift). As a corollary, we derive Green function estimate for BMVD with drift.     

Goniopolarimetry: Space-borne radio astronomy with imaging capabilities

The principles of space-based low-frequency radio astronomy (below 50 MHz) are briefly introduced. As the wavelength range considered does not allow the use of focusing systems, goniopolarimetric (or direction-finding) techniques have been developed. These inversion techniques provide the direction of the wave vector, the polarization state and the flux of the observed electromagnetic wave. In case of spatially extended sources, we can also infer an order of magnitude of the apparent source size. These techniques are presented, and their limitations are discussed. An example from a recent study illustrates the techniques and capabilities.     

Effect of epitaxial crystallization on packet-like space charge characteristics in low-density polyethylene under multi-field coupling conditions

In order to study the effect of epitaxial crystallization on charge transport in low-density polyethylene (LDPE) under multi-field coupling conditions, three typical epitaxial crystallizations, namely disorder (glass substrate), crossover (isotactic polypropylene substrate), and parallel (polytetrafluoroethylene substrate), were prepared and denoted as LD-G, LD-iPP, and LD-PT, respectively. Packet-like space charge through samples was analyzed by the pulsed electro-acoustic (PEA) method. It is shown that different microscopic surface morphologies appeared in the LDPE samples with different epitaxial crystallizations, which, however, do not change the crystalline structure of the bulk. Packet-like space charge phenomena were observed and the distortion field increased with the temperature which could be attributed to the larger amount of charge injection in a shorter period. The differences of the amount and injection rate of the space charge were explained and verified considering the typical chain alignment of epitaxial crystallization, which, in our opinions, contributes to the pass over of positive charge in LD-iPP samples.     

Extreme fluxes in solar energetic particle events: Methodological and physical limitations

In this study, all available data on the largest solar proton events (SPEs), or extreme solar energetic particle (SEP) events, for the period from 1561 up to now are analyzed. Under consideration are the observational, methodological and physical problems of energy-spectrum presentation for SEP fluxes (fluences) near the Earth's orbit. Special attention is paid to the study of the distribution function for extreme fluences of SEPs by their sizes. The authors present advances in at least three aspects: 1) a form of the distribution function that was previously obtained from the data for three cycles of solar activity has been completely confirmed by the data for 41 solar cycles; 2) early estimates of extremely large fluences in the past have been critically revised, and their values were found to be overestimated; and 3) extremely large SEP fluxes are shown to obey a probabilistic distribution, so the concept of an “upper limit flux” does not carry any strict physical sense although it serves as an important empirical restriction. SEP fluxes may only be characterized by the relative probabilities of their appearance, and there is a sharp break in the spectrum in the range of large fluences (or low probabilities). It is emphasized that modern observational data and methods of investigation do not allow, for the present, the precise resolution of the problem of the spectrum break or the estimation of the maximum potentialities of solar accelerator(s). This limitation considerably restricts the extrapolation of the obtained results to the past and future for application to the epochs with different levels of solar activity.     

弱Orlicz鞅空间的弱原子分解及其应用

对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理.