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System for computer construction, enumeration and notation of organic molecules as tree structures and cyclic graphs
An algorithmic language, GRAAL, is presented for describing and implementing graph algorithms of the type primarily arising in applications. The language is based on a set algebraic model of graph theory which defines the graph structure in terms of morphisms between certain set algebraic structures over the node set and arc set. GRAAL is modular in the sense that the user specifies which of these mappings are available with any graph. This allows flexibility in the selection of the storage representation for different graph structures. In line with its set theoretic foundation, the language introduces sets as a basic data type and provides for the efficient execution of all set and graph operators. At present, GRAAL is defined as an extension of ALGOL 60 (revised) and its formal description is given as a supplement to the syntactic and semantic definition of ALGOL. Several typical graph algorithms are written in GRAAL to illustrate various features of the language and to show its applicability.
A computer algorithm is developed that provides efficient means to compute transmittances directly from a signal flow graph or a block diagram. Signal flow graphs are cast as directed graphs described by adjacency matrices. Nonsearch computation, designed for compilers without symbolic capability, is used to identify all arcs that are members of simple cycles for use with Mason's gain formula. The routine does not require the visual acumen of an interpreter to reduce the topology of the graph, and it is particularly useful for analyzing control systems described for computer analyses by means of interactive graphics.
The FORTRAN version FGRAAL of the graph algorithmic language GRAAL as it has been implemented for the Univac 1108 is described. FBRAAL is an extension of FORTRAN 5 and is intended for describing and implementing graph algorithms of the type primarily arising in applications. The formal description contained in this report represents a supplement to the FORTRAN 5 manual for the Univac 1108 (UP-4060), that is, only the new features of the language are described. Several typical graph algorithms, written in FGRAAL, are included to illustrate various features of the language and to show its applicability.
Given a directed graph, a natural topology is defined and relationships between standard topological properties and graph theoretical concepts are studied. In particular, the properties of connectivity and separatedness are investigated. A metric is introduced which is shown to be related to separatedness. The topological notions of continuity and homeomorphism. A class of maps is studied which preserve both graph and topological properties. Applications involving strong maps and contractions are also presented.
Graphs have been developed for rapid evaluation of air-induction systems from considerations of their aerodynamic-performance parameters in combination with power-plant characteristics. The graphs cover the range of supersonic Mach numbers to 3.0. Examples are presented for an air-induction system and engine combination of two Mach numbers and two altitudes in order to illustrate the method and application of the graphs. The examples show that jet-engine characteristics impose restrictions on the use of fixed inlets if the maximum net thrusts are to be realized at all flight conditions. (author)
This Handbook contains a series of maps, graphs, and tables which will be of use to the preliminary design analyst in scheduling round-trip interplanetary missions to Mars and Venus in the time period 1965-1999. It constitutes the third in a series of space flight manuals prepared for the George C. Marshall Space Flight Center, NASA. The present Handbook, denoted as Volume 3 of this series, is divided into three Parts. Part 3-1 presents maps for obtaining departure and arrival speeds for trips to these planets, a listing of useful constants, planetary ephemerides, tables of important occurrences, and a number of auxiliary graphs. Although most of the basic calculations were performed for the period 1965 -1980, much of the information is also applicable to the years 1980- 1999, as is explained in the text.
Graph determines effect of stalled motor on a distribution system and eliminates hand calculation of amperage in emergencies. Graph is useful to any manufacturer, contractor, or maintenance department involved in electrical technology.
Let G be a finite undirected graph with no loops or multiple edges. The Laplacian matrix of G, Delta(G), is defined by Delta sub ii = degree of vertex i and Delta sub ij = -1 if there is an edge between vertex i and vertex j. The structure of the graph G is related to the eigenvalues of Delta(G); in particular, it is proved that all the eigenvalues of Delta(G) are nonnegative, less than or equal to the number of vertices, and less than or equal to twice the maximum vertex degree. Precise conditions for equality are given.
Number of terms in general gain formulas for Coates and Mason signal flow graphs
Coding graphs and information lossless automata
Systematics of organic molecules, graph topology and Hamilton circuits
Information-theoretic concepts in theory of random graphs - entropy functions for probability distributions and Markov chains
Air radiation graphs - spectrally integrated fluxes including line contributions and self- absorption
Geometric interpretation of product form of inverse applied to sparse matrices in linear programming, using graph theory
Simple transparent overlay with interpolation scale facilitates accurate, rapid reading of graph coordinate points. This device can be used for enlarging drawings and locating points on perspective drawings.
Computer construction, enumeration, and notation of organic molecules as tree structures and cyclic graphs