The lecture is motivated by the regularity criteria, showing that some particular quantities (one or two components of velocity, two components of vorticity, some chosen components of the gradient of velocity, etc) control the regularity of a weak solution to the Navier–Stokes equations. We show that a certain spectral projection of vorticity, or even one its component, also belong to such quan...

Complete coverage of the in vivo proton metabolite spectrum, including downfield resonances, requires a spectral bandwidth of approximately 9 ppm. Spectral bandwidth of in vivo echo-planar spectroscopic imaging (EPSI) is primarily limited by gradient strength of the oscillating readout gradient, gradient slew rate, and limits on peripheral nerve stimulation for human subjects. Furthermore, conv...

This paper addresses the positive semi-deffnite procrustes problem (PSDP). The PSDP corresponds to a least squares over set of symmetric and matrices. These kinds problems appear in many applications such as structure analysis, signal processing, among others. A non-monotone spectral projected gradient algorithm is proposed obtain numerical solution for PSDP. employs Zhang Hager's technique com...

Phase retrieval problem has been studied in various applications. It is an inverse problem without the standard uniqueness guarantee. To make complete theoretical analyses and devise efficient algorithms to recover the signal is sophisticated. In this paper, we come up with a model called phase retrieval with background information which recovers the signal with the known background information...

We consider the problem of minimizing a Lipschitz differentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize 1/L satisfies the L-stationarity optimality condition that was introduced in [3]. In this paper we ...

We consider the problem of minimizing a Lipschitz di erentiable function over a class of sparse symmetric sets that has wide applications in engineering and science. For this problem, it is known that any accumulation point of the classical projected gradient (PG) method with a constant stepsize 1/L satis es the L-stationarity optimality condition that was introduced in [3]. In this paper we in...

We present a new numerical method for computing the pure-point spectrum associated with the linear stability of coherent structures. In the context of the Evans function shooting and matching approach, all the relevant information is carried by the flow projected onto the underlying Grassmann manifold. We show how to numerically construct this projected flow in a stable and robust manner. In pa...