Nonlinear obstacle problems with double phase in the borderline case

In this paper we study a double phase problem with an irregular obstacle. The energy functional under consideration is characterized by the fact that both ellipticity and growth switch between a type of polynomial and a type of logarithm, which can be regarded as a borderline case of the double phase functional with $(p,q)$-growth. We obtain an optimal global Calderón–Zygmund type estimate for the obstacle problem with double phase in the borderline case.     

Controllable 1D Patterned Assembly of Colloidal Quantum Dots on PbSO4 Nanoribbons

Control of the 1D self‐assembly pattern of colloidal quantum dots (QDs) on PbSO₄ nanoribbon (NRb) templates is achieved. The internal structure of the NRbs is investigated by X‐ray diffraction, revealing the isotropic packing of the PbSO₄ nanoclusters in the NRbs. Colloidal QDs in a chloroform/hexane mixture are adsorbed onto the region close to the edges of the NRbs and form a 1D assembly of straight single line or double lines by controlling the amount of OAm. This is the first demonstration of a densely packed 1D self‐assembly of colloidal QDs with a straight line pattern without the use of any molecular bridge or adhesive. Atomic force microscopy measurements of the NRbs show depressions in the phase profile along the width of the NRbs, corresponding to the position of the 1D QD chain. The amount of adsorbed QDs on the NRbs in solution decreases as the addition of OAm increases, suggesting that additional OAm prevents interaction between the QDs and NRbs but facilitates the uniform adsorption of the 1D assembly. The low‐dimensional self‐assembly of colloidal QDs in this study opens up the possibility for the creation of anisotropically assembled QD superstructures.     

Weighted estimates for the multilinear maximal function on the upper half‐spaces

For a general dyadic grid, we give a Calderón–Zygmund type decomposition, which is the principle fact about the multilinear maximal function on the upper half‐spaces. Using the decomposition, we study the boundedness of . We obtain a natural extension to the multilinear setting of Muckenhoupt's weak‐type characterization. We also partially obtain characterizations of Muckenhoupt's strong‐type inequalities with one weight. Assuming the reverse Hölder's condition, we get a multilinear analogue of Sawyer's two weight theorem. Moreover, we also get Hytönen–Pérez type weighted estimates.     

Sharp Reilly-type inequalities for a class of elliptic operators on submanifolds

Let M be an $n(>2)$-dimensional closed orientable submanifold in an $(n+p)$-dimensional space form ${\mathbb{R}}^{n+p}(c)$. We obtain an optimal upper bound for the second eigenvalue of a class of elliptic operators on M defined by $L_{T}f=-\text{div}(T\mathrm{\nabla }f)$, where T is a general symmetric, positive definite and divergence-free $(1,1)$-tensor on M. The upper bound is given in terms of an integration involving tr T and $|H_T{|}^2$, where tr T is the trace of the tensor T and $H_T={\sum }_{i=1}^{n}A(T{e}_i,e_i)$ is a normal vector field associated with T and the second fundamental form A of M. Furthermore, we give the sufficient and necessary conditions when the upper bound is attained. Our main theorem can be viewed as an extension of the famous “Reilly inequality”. The operator $L_T$ can be regarded as a natural generalization of the well-known operator $L_r$ which is the linearized operator of the first variation of the $(r+1)$-th mean curvature for hypersurfaces in a space form. As applications of our main theorem, we generalize the results of Grosjean [17] and Li–Wang [20] in codimension one to arbitrary codimension.     

靶场媒体资产管理系统发展趋势

随着科学技术的飞速发展和靶场信息化建设的需要,靶场声像信息媒体资源的整合被提升了前所未有的高度。靶场的声像信息管理争议媒体资产为中心,向数字化、网络化迈进。主要介绍了靶场媒体资产管理系统的构成和关键技术。展望了媒体资产管理系统的发展趋势,并对现在媒体资产管理系统有待完善的方面提出了几点建议。     

An inverse problem for Maxwell's equations in isotropic and non-stationary media

In this article, we consider Maxwell's equations in an isotropic, inhomogeneous and non-stationary medium. We discuss an inverse problem of determining the t-independent components of the coefficients ?, μ in the constitutive relations from a finite number of interior measurements. We prove a Lipschitz stability estimate for the inverse problem by applying the argument on the basis of Carleman estimate.     

电力机车牵引电机在全速度范围的控制策略研究

本文主要对电力机车牵引点击在全速度范围内的控制方法进行阐述讨论,下文为具体内容.     

The relation between structure changes and thermal expansion in liquid indium

The structure of liquid indium in a wide temperature range has been investigated by means of X-ray diffraction and reverse Monte Carlo methods. Analysis of temperature dependence of the interatomic distances and coordination numbers allowed us to determine the existence of structural transformation in a liquid state. Moreover, it was found that at a temperature of 640 K thermal expansion coefficients, estimated from temperature dependence of interatomic distances, change its sign from negative to positive confirming the transformations in structure of liquid indium which are observed by temperature variations.