Scattering below ground state of 3D focusing cubic fractional Schordinger equation with radial data

The aim of this note is to adapt the strategy in [4][See,B.Dodson, J.Murphy, a new proof of scattering below the ground state for the 3D radial focusing cubic NLS, arXiv:1611.04195 ] to prove the scattering of radial solutions below sharp threshold for certain focusing fractional NLS with cubic nonlinearity. The main ingredient is to apply the fractional virial identity proved in [11][See,T.Boulenger, D.Himmelsbach,E.Lenzmann, Blow up for fractional NLS,J.Func.Anal,271(2016),2569-2603] to exclude the concentration of mass near the origin.Comment: This version is an extension of the last version by the first and fourth author, where the dimensional case $d=3$ is treate

Aircraft turbine engine control systems development : historical perspective

This paper describes the development of aircraft turbine engine control systems from the historical point of view to the present. With the increasing emphasis on aircraft safety, enhanced performance, and affordability, as well as the need to reduce the environmental effect caused by aircraft, there are many new challenges being faced by the designers of aircraft propulsion systems. The paper provides an overview of the various technological development activities in aircraft engine control and diagnostics, both current and some accomplished in the recent past. The motivations for each of the research efforts, the research approach, technical challenges, and the key progress to date are summarized

非线性系统有限时间受限控制

Any realistic system is restricted in one form or another. One of the restrictions is the lack of sensors and actuators. This paper addresses the problem of restricted control of nonlinear systems with a finite time approach. Important results are obtained on the design of controllers for stabilizing nonlinear systems in a finite time. Practical issues on control implementation are also discussed. The proposed design method is validated through its application to a Lorenz chaotic system

Performance cycle analysis on turbo fan engine PW4000

This paper describes an effort to investigate and better define the capabilities of a modern mathematical solver in predicting the in on-design performance of a turbo fan engine PW4000. The results will validate the use of commercially available Object Oriented Programming (OOP) with C++ software tools for these problems and lead to a better understanding of the flow phenomenon within the inlet to the outlet in the engine. Better engine designs that enhance design-point operation and improve performance could result once confidence is gained in applying performance analysis tools to the component section of the PW4000 engine design process

Two characterizations of switched nonlinear systems with average dwell time

This note aims to establish the fast switching condition with average dwell time satisfying an upper bound. Important results are obtained on the behaviour of switched nonlinear dynamical systems. In specific, this note contributes in the following three aspects: (1) establish the condition of fast switching of switched nonlinear systems; (2) obtain the condition of arbitrary switching stability of switched nonlinear dynamical systems using a weak Lyapunov functions approach; and (3) prove the necessity of the average dwell time condition associated with the conventional multiple Lyapunov functions’ framework

非线性系统的限制有限时间控制

Any realistic system is restricted in one form or another. One of the restrictions is the lack of sensors and actuators. This paper addresses the problem of restricted control of nonlinear systems with a finite time approach. Important results are obtained on the design of controllers for stabilizing nonlinear systems in a finite time. Practical issues on control implementation are also discussed. The proposed design method is validated through its application to a Lorenz chaotic system