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Research and Advances Mar 1 1964

Digital data processor for tracking the partially illuminated moon

A study of lunar tracking techniques and fabrication of a breadboard to assess the feasibility of the best technique selected was conducted to define a tracking system for observation of the sightline to the center of a partially illuminated moon. The data processing portion of the system is presented in detail and then described in general are the operation of the tracker head assembly for data readout, the operation of the entire system and the effect data processing considerations have on the design of the tracker system. The system basically consists of an optical sensor, digital computer and tracker drive mechanism. The three system units, connected in cascade, comprise the control loop. For this application, an optical telescope with a radial mechanical scanning mechanism was used that read out lunar sightline measurement information. This information is sequentially read into a special purpose digital computer that extracts the measurements and computes the error signals that drive the tracker to the appropriate attitude.
Research and Advances Mar 1 1964

Tests on a computer method for constructing school timetables

A previously proposed computer method for constructing timetables, based on an iteration involving Boolean matrices, is described. In limited tests the method has successfully produced timetables on every trial. References are given which relate the timetable problem to theorems on matrices of zeros and ones, and to theorems on bipartite graphs. Some problems of applying the method to constructing timetables in real situations are noted.
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Research and Advances Feb 1 1964

Some effects of the 6600 computer on language structures

The problem of compiling efficient 6600 codes prompted the development of an intermediate language reflecting the structure of the machine, that is more easily manipulated in improving object program efficiency. The subject of this paper is the intermediate language and methods of manipulating it. Compilations of a series of arithmetic statements are discussed. It is assumed that all functions and exponentials have been removed from these statements, and replaced by simple variables. For purposes of simplicity the treatment of subscripts is ignored. A simplified 6600 structure is presented to illustrate the compiling method. Several assumptions are made for purposes of simplification, although there are cases in which the assumptions are violated in the actual machine.
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Research and Advances Feb 1 1964

“Structural connections” in formal languages

This paper defines the concept of “structural connection” in a mechanical language in an attempt to classify various formal languages according to the complexity of parsing structures on strings in the languages. Languages discussed vary in complexity from those with essentially no structure at all to languages which are self-defining. The relationship between some existing recognition techniques for several language classes is examined, as well as implications of language structure on the complexity of automatic recognizers.
Research and Advances Feb 1 1964

Bounded context syntactic analysis

Certain phase structure grammars define languages in which the phrasehood and structure of a substring of a sentence may be determined by consideration of only a bounded context of the substring. It is possible to determine, for any specified bound on the number of contextual characters considered, whether a given grammar is such a bounded context grammar. Such grammars are free from syntactic ambiguity. Syntactic analysis of sentences in a bounded context language may be performed by a standard process and requires a number of operations proportional to the length of sentence analyzed. Bounded context grammars form models for most languages used in computer programming, and many methods of syntactic analysis, including analysis by operator precedence, are special cases of bounded context analysis.
Research and Advances Jan 1 1964

GIT—a heuristic program for testing pairs of directed line graphs for isomorphism

Given a pair of directed line graphs, the problem of ascertaining whether or not they are isomorphic is one for which no efficient algorithmic solution is known. Since a straightforward enumerative algorithm might require 40 years of running time on a very high speed computer in order to compare two 15-node graphs, a more sophisticated approach seems called for. The situation is similar to that prevailing in areas such as game-playing and theorem-proving, where practical algorithms are unknown (for the interesting cases), but where various practical though only partially successful techniques are available. GIT—Graph Isomorphism Tester—incorporates a variety of processes that attempt to narrow down the search for an isomorphism, or to demonstrate that none exists. No one scheme is relied upon exclusively for a solution, and the program is designed to avoid excessive computation along fruitless lines. GIT has been written in the COMIT language and successfully tested on the IBM 7090.
Research and Advances Jan 1 1964

An efficient composite formula for multidimensional quadrature

A (2s+1)-point, second-degree quadrature formula for integration over an s-dimensional hyper-rectangle is presented. All but one of the points lie on the surface with weights of opposite sign attached to points on opposite faces. When a large volume is subdivided into congruent rectangular subdivisions, only one point is required in each interior subdivision to achieve second-degree accuracy.
Research and Advances Jan 1 1964

On the numerical solution of boundary value problems for linear ordinary differential equations

A numerical method is presented for the solution of boundary value problems involving linear ordinary differential equations. The method described is noniterative and makes use of any one-step numerical integration scheme to reduce the problem from one of boundary values to one of initial values. Comments are made concerning some numerical results of applying the method to a specific problem. In addition an extension of the algorithm described to more general problems is discussed.
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Research and Advances Dec 1 1961

Simulation and analysis of biochemical systems: I. representation of chemical kinetics

In the study of problems in chemical kinetics in ordinary solution, reactions which may be represented by chemical equations of the form3 A + B = C + D (1) are represented kinetically by the differential equations d(C)/dt = d(D/dt = -d(A)/dt = - d(B)/dt = k(A)(B) (2) where (A), (B), (C), ··· , are the concentrations of A, B, C, ··· , and k is the kinetic constant for the reaction (assuming it to be occurring in ordinary solution).
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Research and Advances Jun 1 1961

On a class of iteration formulas and some historical notes

The class of iteration formulas obtainable by rational approximations of “Euler's formula” is derived with the corresponding error estimates. Some historical notes on iterative procedures are followed by a derivation of Euler's formula with the associated error estimate in a new notation which simplifies the error estimate and suggests generalizations. The final section considers the Padé approximants to the “Euler polynomial” and shows how a number of known formulas may be derived from this unified approach. There is a short discussion of the “best” formula.

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