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Object detection is a focal point in remote sensing applications. Remote sensing images typically contain a large number of small objects and a wide range of orientations across objects. This results in great challenges to small object detection approaches based on remote sensing images. Methods directly employ channel relations with equal weights to construct information features leads to inadequate feature representation in complex image small object detection tasks. Multiscale detection methods improve the speed and accuracy of detection, while small objects themselves contain limited information, and the features are easily lost following down-sampling. During the detection, the feature images are independent across scales, resulting in a discontinuity at the detection scale. In this article, we propose the multiscale context and enhanced channel attention (MSCCA) model. MSCCA employs PeleeNet as the backbone network. In particular, the feature image channel attention is enhanced and the multiscale context information is fused with multiscale detection methods to improve the characterization ability of the convolutional neural network. The proposed MSCCA method is evaluated on two real datasets. Results show that for 512 × 512 input images, MSCCA was able to achieve 80.4% and 94.4% mAP on the DOTA and NWPU VHR-10, respectively. Meanwhile, the model size of MSCCA is 21% smaller than that of its predecessor. MSCCA can be considered as a practical lightweight oriented object detection model in remote sensing images.

In this paper, we derive the Liouville theorem of D-solutions to the stationary MHD system under the asymptotic assumption: one of the velocity field and the magnetic field approaches zero and the other approaches a non zero constant vector at infinity. Our result extends the corresponding one of D-solutions to the Navier–Stokes equations when the velocity approaches a non zero constant vector at infinity.

In this paper, we derive Schauder estimates to the solutions of the following uniformly elliptic equation with a inverse-square potential and nonhomogeneous term (0.1) − a i j ( x ) ∂ i j u ( x ) + A | x | 2 u ( x ) = f ( x ) , in B , which lead to the existence and sharp regularity results of the classical solutions. More precisely, we prove that u ∈ C n + 2 , γ provided f ∈ C n , γ , a i j ∈ C n , γ and A > Λ ( 2 + n + γ ) ( d + n + γ ) .

Exploiting stretchable solar cells that can accommodate large strain and feature high cyclic mechanical endurance is challenging for wearable and skin-interfaced electronics application. In this work, we demonstrated such solar cells using the kirigami design. Experiments and mechanical simulations showed that the kirigami structure effectively imparted stretchability to perovskite solar cells (PSCs) through out-of-plane deformation, which significantly reduced the stress in devices. The kirigami-based PSCs with optimal geometric parameters exhibited high mechanical deformability, including stretchability (strain up to 200%), twistability (angle up to 450°), and bendability (radius down to 0.5 mm). More importantly, the kirigami PSCs revealed high mechanical endurance with almost unchanged performance even after 1000 repetitive stretching, twisting, and bending cycles. This kirigami design for stretchable PSCs presented here provides a promising strategy to achieve high deformability for solar cells as well as other optoelectronic devices.

In this paper, we study the stationary magnetohydrodynamics system in $\mathbb{R}^2\times\mathbb{T}$. We prove trivialness of D-solutions (the velocity field $u$ and the magnetic field $h$) when they are swirl-free. Meanwhile, this Liouville type theorem also holds provided $u$ is swirl-free and $h$ is axially symmetric, or both $u$ and $h$ are axially symmetric. Our method is also valid for certain related boundary value problems in the slab $\mathbb{R}^2\times[-\pi,\,\pi]$., Comment: 16 pages

In the paper \cite{KNSS:1}, the authors make the following conjecture: {\it any bounded ancient mild solution of the 3D axially symmetric Navier-Stokes equations is constant.} And it is proved in the case that the solution is swirl free. Our purpose of this paper is to improve their result by allowing that the solution can grow with a power smaller than 1 with respect to the distance to the origin. Also, we will show that such a power is optimal to prove the Liouville type theorem since we can find counterexamples for the Navier-Stokes equations such that the Liouville theorem fails if the solution can grow linearly., Comment: 10 pages

Two main results will be presented in our paper. First, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a $log$ supercritical assumption on the horizontally radial component $u^r$ and vertical component $u^z$, accompanied by a $log$ subcritical assumption on the horizontally angular component $u^\theta$ of the velocity. Second, the precise Green function for the operator $-(\Delta-\frac{1}{r^2})$ under the axially symmetric situation, where $r$ is the distance to the symmetric axis, and some weighted $L^p$ estimates of it will be given. This will serve as a tool for the study of axially symmetric Navier-Stokes equations. As an application, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a critical (or a subcritical) assumption on the angular component $w^\theta$ of the vorticity., Comment: Final version, to appear in Comm. Pure Appl. Anal

We prove H\"older continuity of weak solutions of the uniformly elliptic and parabolic equations %$\Delta u-\frac{A}{|x|^{2+\beta}}u=0,\,\,(\beta\geq 0)$, and variable second order term coefficients case $%% \begin{equation}\label{01} \partial_{i} (a_{ij}(x) \partial_{j}u(x)) - \frac{A}{|x|^{2+\beta}} u(x) =0\quad (A>0,\quad\beta\geq 0), \end{equation} \begin{equation}\label{02} \partial_{i} (a_{ij}(x,t) \partial_{j}u(x,t)) - \frac{A}{|x|^{2+\beta}} u(x,t)-\partial_{t}u(x,t) =0\quad (A>0,\quad\beta\geq 0), \end{equation} with critical or supercritical 0-order term coefficients which are beyond De Giorgi-Nash-Moser's Theory. We also prove, in some special cases, weak solutions are even differentiable. Previously P. Baras and J. A. Goldstein \cite{Baras1984} treated the case when $A0$, $\beta=0$ and $(a_{ij})=I$, P. D. Milman and Y. A. Semenov \cite{Milman2003}\cite{Milman2004} obtain bounds for the heat kernel., Comment: 32 pages