Unnormalized associated Legendre functions: A compendium of graphs, expansions, properties, and integrals
Compendium of graphs, expansions, propertites, and integrals for unnormalized associated Legendre functions
Heffron, W. G.↗
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Bond graph for modeling valves and switches
Digital graph element represents two-state devices. It can be used in modeling mechanical stops, backlash, and other discontinuities that occur whenever subsystems are connected or disconnected.
Gebben, V. D.↗
A graph-theoretic method to quantify the airline route authority
The paper introduces a graph-theoretic method to quantify the legal statements in route certificate which specifies the airline routing restrictions. All the authorized nonstop and multistop routes, including the shortest time routes, can be obtained, and the method suggests profitable route structure alternatives to airline analysts. This method to quantify the C.A.B. route authority was programmed in a software package, Route Improvement Synthesis and Evaluation, and demonstrated in a case study with a commercial airline. The study showed the utility of this technique in suggesting route alternatives and the possibility of improvements in the U.S. route system.
Chan, Y.↗
Linking of the BENSON graph-plotter with the Elektronika-1001 computer
A device, developed by the Institute of Space Research of the Academy of Sciences of the USSR, for linking the Elektronika-100I computer with the BENSON graph-plotter is described. Programs are compiled which provide display of graphic and alphanumeric information. Instructions for their utilization are given.
Valtts, I. Y.↗
Semantic definitions of space flight control center languages using the hierarchical graph technique
In this paper a method is described by which the semantic definitions of the Goddard Space Flight Control Center Command Languages can be specified. The semantic modeling facility used is an extension of the hierarchical graph technique, which has a major benefit of supporting a variety of data structures and a variety of control structures. It is particularly suited for the semantic descriptions of such types of languages where the detailed separation between the underlying operating system and the command language system is system dependent. These definitions were used in the definition of the Systems Test and Operation Language (STOL) of the Goddard Space Flight Center which is a command language that provides means for the user to communicate with payloads, application programs, and other ground system elements.
Zaghloul, M. E.↗
Graph theory approach to the eigenvalue problem of large space structures
Graph theory is used to obtain numerical solutions to eigenvalue problems of large space structures (LSS) characterized by a state vector of large dimensions. The LSS are considered as large, flexible systems requiring both orientation and surface shape control. Graphic interpretation of the determinant of a matrix is employed to reduce a higher dimensional matrix into combinations of smaller dimensional sub-matrices. The reduction is implemented by means of a Boolean equivalent of the original matrices formulated to obtain smaller dimensional equivalents of the original numerical matrix. Computation time becomes less and more accurate solutions are possible. An example is provided in the form of a free-free square plate. Linearized system equations and numerical values of a stiffness matrix are presented, featuring a state vector with 16 components.
Reddy, A. S. S. R.↗
An evaluation of the directed flow graph methodology
The applicability of the Directed Graph Methodology (DGM) to the design and analysis of special purpose image and signal processing hardware was evaluated. A special purpose image processing system was designed and described using DGM. The design, suitable for very large scale integration (VLSI) implements a region labeling technique. Two computer chips were designed, both using metal-nitride-oxide-silicon (MNOS) technology, as well as a functional system utilizing those chips to perform real time region labeling. The system is described in terms of DGM primitives. As it is currently implemented, DGM is inappropriate for describing synchronous, tightly coupled, special purpose systems. The nature of the DGM formalism lends itself more readily to modeling networks of general purpose processors.
Snyder, W. E.↗
When Is a Bernstein-bezier Curve the Graph of a Function?
The question of determining when a Bernstein-Bezier cubic curve in the plane can be represented as the graph of function in some fixed orthogonal coordinate system is considered. The notion of a curve being monotone in a given direction is introduced to aid in the analysis.
Mclaughlin, H. W.↗
Multiple degree of freedom object recognition using optical relational graph decision nets
Multiple-degree-of-freedom object recognition concerns objects with no stable rest position with all scale, rotation, and aspect distortions possible. It is assumed that the objects are in a fairly benign background, so that feature extractors are usable. In-plane distortion invariance is provided by use of a polar-log coordinate transform feature space, and out-of-plane distortion invariance is provided by linear discriminant function design. Relational graph decision nets are considered for multiple-degree-of-freedom pattern recognition. The design of Fisher (1936) linear discriminant functions and synthetic discriminant function for use at the nodes of binary and multidecision nets is discussed. Case studies are detailed for two-class and multiclass problems. Simulation results demonstrate the robustness of the processors to quantization of the filter coefficients and to noise.
Casasent, David P.↗
Planning repair sequences using the AND/OR graph representation of assembly plans
A simple modification is shown in the set of goal nodes of the AND/OR graph that allows its use in planning repairs such as the replacement of a part or a subassembly. An algorithm for the generation of all feasible sequences for disassembly and reassembly of parts that will achieve a repair is shown. This approach has been demonstrated for the example of the repair of space-based satellite equipment.
Homem De Mello, L. S.↗
Optimal trajectories for the aeroassisted flight experiment. Part 4: Data, tables, and graphs
The determination of optimal trajectories for the aeroassisted flight experiment (AFE) is discussed. Data, tables, and graphs relative to the following transfers are presented: (IA) indirect ascent to a 178 NM perigee via a 197 NM apogee; and (DA) direct ascent to a 178 NM apogee. For both transfers, two cases are investigated: (1) the bank angle is continuously variable; and (2) the trajectory is divided into segments along which the bank angle is constant. For case (2), the following subcases are studied: two segments, three segments, four segments, and five segments; because the time duration of each segment is optimized, the above subcases involve four, six, eight, and ten parameters, respectively. Presented here are systematic data on a total of ten optimal trajectories (OT), five for Transfer IA and five for Transfer DA. For comparison purposes and only for Transfer IA, a five-segment reference trajectory RT is also considered.
Miele, A.↗
Optimal trajectories for an aerospace plane. Part 2: Data, tables, and graphs
Data, tables, and graphs relative to the optimal trajectories for an aerospace plane are presented. A single-stage-to-orbit (SSTO) configuration is considered, and the transition from low supersonic speeds to orbital speeds is studied for a single aerodynamic model (GHAME) and three engine models. Four optimization problems are solved using the sequential gradient-restoration algorithm for optimal control problems: (1) minimization of the weight of fuel consumed; (2) minimization of the peak dynamic pressure; (3) minimization of the peak heating rate; and (4) minimization of the peak tangential acceleration. The above optimization studies are carried out for different combinations of constraints, specifically: initial path inclination that is either free or given; dynamic pressure that is either free or bounded; and tangential acceleration that is either free or bounded.
Miele, Angelo↗
Coverability graphs for a class of synchronously executed unbounded Petri net
After detailing a variant of the concurrent-execution rule for firing of maximal subsets, in which the simultaneous firing of conflicting transitions is prohibited, an algorithm is constructed for generating the coverability graph of a net executed under this synchronous firing rule. The omega insertion criteria in the algorithm are shown to be valid for any net on which the algorithm terminates. It is accordingly shown that the set of nets on which the algorithm terminates includes the 'conflict-free' class.
Stotts, P. David↗
Software For Generating Graphs And Charts
Common Graphics Library (CGL) computer program designed to enable users to generate graphs and charts of quality sufficient for publication or optical projection. Quickly and easily generates linear, logarithmic, bar, pie, and composite charts. Features of linear charts include automatic scaling, increasing or decreasing numerical axes, and character axes. Features of pie charts include segment labels, exploded segments, and chart keys. One of general features, horizontal or vertical orientation of figures. Written in ANSI FORTRAN 77.
Hammond, Dana P.↗
The alignment-distribution graph
Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.
Chatterjee, Siddhartha↗
The alignment-distribution graph
Implementing a data-parallel language such as Fortran 90 on a distributed-memory parallel computer requires distributing aggregate data objects (such as arrays) among the memory modules attached to the processors. The mapping of objects to the machine determines the amount of residual communication needed to bring operands of parallel operations into alignment with each other. We present a program representation called the alignment-distribution graph that makes these communication requirements explicit. We describe the details of the representation, show how to model communication cost in this framework, and outline several algorithms for determining object mappings that approximately minimize residual communication.
Chatterjee, Siddhartha↗
Weighted graph based ordering techniques for preconditioned conjugate gradient methods
We describe the basis of a matrix ordering heuristic for improving the incomplete factorization used in preconditioned conjugate gradient techniques applied to anisotropic PDE's. Several new matrix ordering techniques, derived from well-known algorithms in combinatorial graph theory, which attempt to implement this heuristic, are described. These ordering techniques are tested against a number of matrices arising from linear anisotropic PDE's, and compared with other matrix ordering techniques. A variation of RCM is shown to generally improve the quality of incomplete factorization preconditioners.
Clift, Simon S.↗
Graph Embedding Techniques for Bounding Condition Numbers of Incomplete Factor Preconditioning
We extend graph embedding techniques for bounding the spectral condition number of preconditioned systems involving symmetric, irreducibly diagonally dominant M-matrices to systems where the preconditioner is not diagonally dominant. In particular, this allows us to bound the spectral condition number when the preconditioner is based on an incomplete factorization. We provide a review of previous techniques, describe our extension, and give examples both of a bound for a model problem, and of ways in which our techniques give intuitive way of looking at incomplete factor preconditioners.
Guattery, Stephen↗