The numerical range of a nonnegative matrix

We offer an almost self-contained development of Perron–Frobenius type results for the numerical range of an (irreducible) nonnegative matrix, rederiving and completing the previous work of Issos, Nylen and Tam, and Tam and Yang on this topic. We solve the open problem of characterizing nonnegative matrices whose numerical ranges are regular convex polygons with center at the origin. Some related results are obtained and some open problems are also posed.     

Wall boundary conditions for high-order finite-difference schemes in computational aeroacoustics

High-order finite-difference schemes are less dispersive and dissipative but, at the same time, more isotropic than low-order schemes. They are well suited for solving computational acoustics problems. High-order finite-difference equations, however, support extraneous wave solutions which bear no resemblance to the exact solution of the original partial differential equations. These extraneous wave solutions, which invariably degrade the quality of the numerical solutions, are usually generated when solid-wall boundary conditions are imposed. A set of numerical boundary conditions simulating the presence of a solid wall for high-order finite-difference schemes using a minimum number of ghost values is proposed. The effectiveness of the numerical boundary conditions in producing quality solutions is analyzed and demonstrated by comparing the results of direct numerical simulations and exact solutions.This work was supported by the NASA Lewis Research Center Grant NAG 3-1267 and in part by the NASA Langley Research Center Grant NAG 1-1479 and the Florida State University through time granted on its Cray-YMP Supercomputer.     

Geodesic precession in the (Ω,A ab)-field theory

This paper aims to determine the geodesic precession in Yu’s (Ω, A_ab)-field theory[1], and to compare the result with that of the Schwarzschild orbit.     

Structural Characterization of O‐ and C‐Glycosylating Variants of the Landomycin Glycosyltransferase LanGT2

The structures of the O‐glycosyltransferase LanGT2 and the engineered, C? C bond‐forming variant LanGT2S8Ac show how the replacement of a single loop can change the functionality of the enzyme. Crystal structures of the enzymes in complex with a nonhydrolyzable nucleotide‐sugar analogue revealed that there is a conformational transition to create the binding sites for the aglycon substrate. This induced‐fit transition was explored by molecular docking experiments with various aglycon substrates.     

Facile Synthesis of Novel Selenium‐Containing Benzopyrans

4,4‐Dimethylchromeno[4,3‐d]selenadiazoles 8 with insecticide activities have been synthesized via oxidative ring closure of the corresponding semicarbazone derivatives 7 by treatment with selenium dioxide. Reaction of various alkoxy‐2,2‐dimethyl‐2H‐benzopyrans with phenylselenyl chloride was utilized to prepare different phenylselenyl‐ and 3‐chloro precocene analogs.     

On the shape of solution sets of systems of (functional) equations

Solution sets of systems of linear equations over fields are characterized as being affine subspaces. But what can we say about the “shape” of the set of all solutions of other systems of equations? We study solution sets over arbitrary algebraic structures, and we give a necessary condition for a set of n-tuples to be the set of solutions of a system of equations in n unknowns over a given algebra. In the case of Boolean equations we obtain a complete characterization, and we also characterize solution sets of systems of Boolean functional equations.     

A polynomial primal-dual affine scaling algorithm for symmetric conic optimization

The primal-dual Dikin-type affine scaling method was originally proposed for linear optimization and then extended to semidefinite optimization. Here, the method is generalized to symmetric conic optimization using the notion of Euclidean Jordan algebras. The method starts with an interior feasible but not necessarily centered primal-dual solution, and it features both centering and reducing the duality gap simultaneously. The method’s iteration complexity bound is analogous to the semidefinite optimization case. Numerical experiments demonstrate that the method is viable and robust when compared to SeDuMi, MOSEK and SDPT3.