A new subgroup lattice characterization of finite solvable groups

We show that if G is a finite group then no chain of modular elements in its subgroup lattice L(G) is longer than a chief series. Also, we show that if G is a nonsolvable finite group then every maximal chain in L(G) has length at least two more than that of the chief length of G, thereby providing a converse of a result of J. Kohler. Our results enable us to give a new characterization of finite solvable groups involving only the combinatorics of subgroup lattices. Namely, a finite group G is solvable if and only if L(G) contains a maximal chain X and a chain M consisting entirely of modular elements, such that X and M have the same length.Comment: 15 pages; v2 has minor changes for publication; v3 minor typos fixe

New Software for Ensemble Creation in the Spitzer Space Telescope Operations Database

Some of the computer pipelines used to process digital astronomical images from NASA's Spitzer Space Telescope require multiple input images, in order to generate high-level science and calibration products. The images are grouped into ensembles according to well-documented ensemble-creation rules by making explicit associations in the operations Informix database at the Spitzer Science Center (SSC). The advantage of this approach is that a simple database query can retrieve the required ensemble of pipeline input images. New and improved software for ensemble creation has been developed. The new software is much faster than the existing software because it uses pre-compiled database stored procedures written in Informix SPL (SQL programming language). The new software is also more flexible because the ensemble-creation rules are now stored in and read from newly defined database tables. This table-driven approach was implemented so that ensemble rules can be inserted, updated, or deleted without modifying software

Spatial adaption procedures on unstructured meshes for accurate unsteady aerodynamic flow computation

Spatial adaption procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaption procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in a high gradient region or the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational costs. A detailed description is given of the enrichment and coarsening procedures and comparisons with alternative results and experimental data are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaption for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with a computational savings of a factor of approximately fifty-three for a steady case and as much as twenty-five for the unsteady cases

Three-dimensional time-marching aeroelastic analyses using an unstructured-grid Euler method

Modifications to a three dimensional, implicit, upwind, unstructured-grid Euler code for aeroelastic analysis of complete aircraft configurations are described. The modifications involve the addition of the structural equations of motion for their simultaneous time integration with the governing flow equations. The paper presents a detailed description of the time marching aeroelastic procedure and presents comparisons with experimental data to provide an assessment of the capability. Flutter results are shown for an isolated 45 degree swept-back wing and a supersonic transport configuration with a fuselage, clipped delta wing, and two identical rearward-mounted nacelles. Comparisons between computed and experimental flutter characteristics show good agreement, giving confidence in the accuracy of the aeroelastic capability that was developed

Spatial adaptation procedures on tetrahedral meshes for unsteady aerodynamic flow calculations

Spatial adaptation procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaptation procedures were developed and implemented within a three-dimensional, unstructured-grid, upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. A detailed description of the enrichment and coarsening procedures are presented and comparisons with experimental data for an ONERA M6 wing and an exact solution for a shock-tube problem are presented to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady results, obtained using spatial adaptation procedures, are shown to be of high spatial accuracy, primarily in that discontinuities such as shock waves are captured very sharply

Unstructured-grid methods development for unsteady aerodynamic and aeroelastic analyses

The current status of unstructured grid methods development in the Unsteady Aerodynamics Branch at NASA-Langley is described. These methods are being developed for unsteady aerodynamic and aeroelastic analyses. The flow solvers are highlighted which were developed for the solution of the unsteady Euler equations and selected results are given which show various features of the capability. The results demonstrate 2-D and 3-D applications for both steady and unsteady flows. Comparisons are also made with solutions obtained using a structured grid code and with experimental data to determine the accuracy of the unstructured grid methodology. These comparisons show good agreement which thus verifies the accuracy