On the analyticity and the almost periodicity of the solution to the Euler equations with non-decaying initial velocity

AbstractThe Cauchy problem of the Euler equations in the whole space is considered with non-decaying initial velocity in the frame work of B∞,11. It is proved that if the initial velocity is real analytic then the solution is also real analytic in spatial variables. Furthermore, a new estimate for the size of the radius of convergence of Taylor's expansion is established. The key of the proof is to derive the suitable estimates for the higher order derivatives of the bilinear terms. It is also shown the propagation of the almost periodicity in spatial variables

X-raying the Birth of Binary Neutron Stars and Neutron Star-Black Hole Binaries

We consider fallback accretion after an ultra-stripped supernova (USSN) that accompanies formation of a binary neutron star (BNS) or a neutron star-black hole binary (NS-BH). The fallback matter initially accretes directly to the nascent NS, while it starts to accrete to the circumbinary disk, typically 0.1\mbox{-}1\, \mathrm{day} after the onset of the USSN explosion. The circumbinary disk mass further accretes, forming mini disks around each compact object, with a super-Eddington rate up to a few years. We show that such a system constitutes a binary ultraluminous X-ray source (ULX), and a fraction of the X rays can emerge through the USSN ejecta. We encourage follow-up observations of USSNe within $\lesssim 100\,\rm Mpc$ and \sim 100\mbox{-}1,000\,\mathrm{day} after the explosion using Chandra, XMM Newton and NuSTAR, which could detect the X-ray counterpart with time variations representing the properties of the nascent compact binary, e.g., the orbital motion of the binary, the spin of the NS, and/or the quasiperiodic oscillation of the mini disks.Comment: 12 pages, 5 figure

Open Multi-Access Network Platform with Dynamic Task Offloading and Intelligent Resource Monitoring

We constructed an open multi-access network platform using open-source hardware and software. The open multi-access network platform is characterized by the flexible utilization of network functions, integral management and control of wired and wireless access networks, zero-touch provisioning, intelligent resource monitoring, and dynamic task offloading. We also propose an application-driven dynamic task offloading that utilizes intelligent resource monitoring to ensure effective task processing in edge and cloud servers. For this purpose, we developed a mobile application and server applications for the open multi-access network platform. To investigate the feasibility and availability of our developed platform, we experimentally and analytically evaluated the effectiveness of application-driven dynamic task offloading and intelligent resource monitoring. The experimental results demonstrated that application-driven dynamic task offloading could reduce real-time task response time and traffic over metro and core networks