Hermitian matrices have real eigenvalues. The Cauchy interlace theorem states that the eigenvalues of a Hermitian matrix A of order n are interlaced with those of any principal submatrix of order n − 1. Theorem 1 (Cauchy Interlace Theorem). Let A be a Hermitian matrix of order n, and let B be a principal submatrix of A of order n − 1. If λ n ≤ λ n−1 ≤ · · · ≤ λ 2 ≤ λ 1 lists the eigenvalues of ...

In this paper, we investigate the existence of solutions of some three-point boundary value problems for n-th order nonlinear fractional differential equations with higher boundary conditions by using a fixed point theorem on cones.

Big data processing systems often employ batched updates and sketches to estimate certain properties of large data. For example, a CountMin sketch approximates the frequencies at which elements occur in stream, counter counts events batches. This paper focuses on correctness criteria for concurrent implementations such objects. Specifically, we consider quantitative objects, whose return values...

We introduce a general technique to create an extended formulation of a mixed-integer program. We classify the integer variables into blocks, each of which generates a finite set of vector values. The extended formulation is constructed by creating a new binary variable for each generated value. Initial experiments show that the extended formulation can have a more compact complete description ...