890 resultados para problems in the real line


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Trigonometrical problems.--Hydrostatical problems.--Optical problems.--Problems from Newton's Principia.--Astronomical problems.

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"October 5, 1909."

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Includes index.

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The Johns Hopkins university in its beginning.--The utility of universities.--The characteristics of a university.--The Sheffield scientific school of Yale university, New Haven.--The University of California in its infancy.--Knowledge and charity.--Modern progress in medicine.--University libraries.--The Teachers' college of Columbia university.--Washington and Lee university.--Higher education in the United States.--The proposals for a national university in Washington.

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"September 1942."

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ACCESS: May only be used at the Armenian Research Center ; please call 313 593-5181 for Center hours.

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The real-time refinement calculus is a formal method for the systematic derivation of real-time programs from real-time specifications in a style similar to the non-real-time refinement calculi of Back and Morgan. In this paper we extend the real-time refinement calculus with procedures and provide refinement rules for refining real-time specifications to procedure calls. A real-time specification can include constraints on, not only what outputs are produced, but also when they are produced. The derived programs can also include time constraints oil when certain points in the program must be reached; these are expressed in the form of deadline commands. Such programs are machine independent. An important consequence of the approach taken is that, not only are the specifications machine independent, but the whole refinement process is machine independent. To implement the machine independent code on a target machine one has a separate task of showing that the compiled machine code will reach all its deadlines before they expire. For real-time programs, externally observable input and output variables are essential. These differ from local variables in that their values are observable over the duration of the execution of the program. Hence procedures require input and output parameter mechanisms that are references to the actual parameters so that changes to external inputs are observable within the procedure and changes to output parameters are externally observable. In addition, we allow value and result parameters. These may be auxiliary parameters, which are used for reasoning about the correctness of real-time programs as well as in the expression of timing deadlines, but do not lead to any code being generated for them by a compiler. (c) 2006 Elsevier B.V. All rights reserved.