Xinyu Zhang

George Washington University | GW · Department of Mathematics

In this paper we investigate existence of solutions for the system: Dtαu=div(u∇p),Dtαp=−(−Δ)sp+u2,in T3 for 0<s≤1, and 0<α≤1. The term Dtαu denotes the Caputo derivative, which models memory effects in time. The fractional Laplacian (−Δ)s represents the Lévy diffusion. We prove global existence of nonnegative weak solutions that satisfy a variation...

Object detection methods are widely adopted for computer-aided diagnosis using medical images. Anomalous findings are usually treated as objects that are described by bounding boxes. Yet, many pathological findings, e.g., bone fractures, cannot be clearly defined by bounding boxes, owing to considerable instance, shape and boundary ambiguities. Thi...

Object detection methods are widely adopted for computer-aided diagnosis using medical images. Anomalous findings are usually treated as objects that are described by bounding boxes. Yet, many pathological findings, e.g., bone fractures, cannot be clearly defined by bounding boxes, owing to considerable instance, shape and boundary ambiguities. Thi...

In this paper we investigate existence of solutions for the system: \begin{equation*} \left\{ \begin{array}{l} D^{\alpha}_tu=\textrm{div}(u \nabla p),\\ D^{\alpha}_tp=-(-\Delta)^{s}p+u^{2}, \end{array} \right. \end{equation*} in $\mathbb{T}^3$ for $0< s \leq 1$, and $0< \alpha \le 1$. The term $D^\alpha_t u$ denotes the Caputo derivative, which mod...