Positive Almost Periodic Solution for a Model of Hematopoiesis with Infinite Time Delays and a Nonlinear Harvesting Term

A generalized model of Hematopoiesis with infinite time delays and a nonlinear harvesting term is investigated. By utilizing a fixed point theorem of the differential equations and constructing a suitable Lyapunov functional, we establish some conditions which guarantee the existence of a unique positive almost periodic solution and the exponential convergence of the system. Finally, we give an example to illustrate the effectiveness of our results

Positive Solutions for Singular p

This paper investigates the existence of positive solutions for a class of singular p-Laplacian fractional differential equations with integral boundary conditions. By using the Leggett-Williams fixed point theorem, the existence of at least three positive solutions to the boundary value system is guaranteed

Sparsity for Ultrafast Material Identification

Mid-infrared spectroscopy is often used to identify material. Thousands of spectral points are measured in a time-consuming process using expensive table-top instrument. However, material identification is a sparse problem, which in theory could be solved with just a few measurements. Here we exploit the sparsity of the problem and develop an ultra-fast, portable, and inexpensive method to identify materials. In a single-shot, a mid-infrared camera can identify materials based on their spectroscopic signatures. This method does not require prior calibration, making it robust and versatile in handling a broad range of materials