All-Inorganic Metal Halide Perovskite Nanocrystals: Opportunities and Challenges.

The past decade has witnessed the growing interest in metal halide perovskites as driven by their promising applications in diverse fields. The low intrinsic stability of the early developed organic versions has however hampered their widespread applications. Very recently, all-inorganic perovskite nanocrystals have emerged as a new class of materials that hold great promise for the practical applications in solar cells, photodetectors, light-emitting diodes, and lasers, among others. In this Outlook, we first discuss the recent developments in the preparation, properties, and applications of all-inorganic metal halide perovskite nanocrystals, with a particular focus on CsPbX3, and then provide our view of current challenges and future directions in this emerging area. Our goal is to introduce the current status of this type of new materials to researchers from different areas and motivate them to explore all the potentials

An Alternating Direction Algorithm for Matrix Completion with Nonnegative Factors

This paper introduces an algorithm for the nonnegative matrix factorization-and-completion problem, which aims to find nonnegative low-rank matrices X and Y so that the product XY approximates a nonnegative data matrix M whose elements are partially known (to a certain accuracy). This problem aggregates two existing problems: (i) nonnegative matrix factorization where all entries of M are given, and (ii) low-rank matrix completion where nonnegativity is not required. By taking the advantages of both nonnegativity and low-rankness, one can generally obtain superior results than those of just using one of the two properties. We propose to solve the non-convex constrained least-squares problem using an algorithm based on the classic alternating direction augmented Lagrangian method. Preliminary convergence properties of the algorithm and numerical simulation results are presented. Compared to a recent algorithm for nonnegative matrix factorization, the proposed algorithm produces factorizations of similar quality using only about half of the matrix entries. On tasks of recovering incomplete grayscale and hyperspectral images, the proposed algorithm yields overall better qualities than those produced by two recent matrix-completion algorithms that do not exploit nonnegativity

The three-body recombination of a condensed Bose gas near a Feshbach resonance

In this paper, we study the three-body recombination rate of a homogeneous dilute Bose gas with a Feshbach resonance at zero temperature. The ground state and excitations of this system are obtained. The three-body recombination in the ground state is due to the break-up of an atom pair in the quantum depletion and the formation of a molecule by an atom from the broken pair and an atom from the condensate. The rate of this process is in good agreement with the experiment on $^{23}$Na in a wide range of magnetic fields.Comment: 10 pages, 2 figures, to be published in Phys. Rev.