Multiple-Square-Root Minimization Problem

Kato’s Square Root Problem in Banach Spaces

Abstract. Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X-valued functions on Rn. We characterize Kato’s square root estimates ‖ √ Lu‖p h ‖∇u‖p and the H-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp spac...

Border Length Minimization Problem on a Square Array

Protein/peptide microarrays are rapidly gaining momentum in the diagnosis of cancer. High-density and high-throughput peptide arrays are being extensively used to detect tumor biomarkers, examine kinase activity, identify antibodies having low serum titers, and locate antibody signatures. Improving the yield of microarray fabrication involves solving a hard combinatorial optimization problem ca...

Square - Root Algorithmsfor the Discrete Logarithm Problem ( a Survey )

Square Root Problem of Kato for the Sum of Operators

This paper is concerned with the square root problem of Kato for the ”sum” of linear operators in a Hilbert space H. Under suitable assumptions, we show that if A and B are respectively m-scetroial linear operators satisfying the square root problem of Kato. Then the same conclusion still holds for their ”sum”. As application, we consider perturbed Schrödinger operators.

Square-root rule of two-dimensional bandwidth problem

The bandwidth minimization problem is of significance in network communication and related areas. Let G be a graph of n vertices. The two-dimensional bandwidth B2(G) of G is the minimum value of the maximum distance between adjacent vertices when G is embedded into an n × n grid in the plane. As a discrete optimization problem, determining B2(G) is NP-hard in general. However, exact results for...