Categories in Computer Science and Logic by John W. Gray, Andre Scedrov

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By John W. Gray, Andre Scedrov

Class conception has had vital makes use of in good judgment because the invention of topos idea within the early Sixties, and good judgment has continuously been a major part of theoretical machine technological know-how. a brand new improvement has been the rise in direct interactions among type thought and desktop technology. In June 1987, an AMS-IMS-SIAM summer season study convention on different types in desktop technology and good judgment was once held on the college of Colorado in Boulder. the purpose of the convention was once to collect researchers engaged on the interconnections among type conception and laptop technology or among machine technological know-how and common sense. The convention emphasised the ways that the final equipment built in class thought may be utilized to express questions and be used for category-theoretic reviews of concrete difficulties. This quantity represents the complaints of the convention. (Some of the contributors' contributions were released elsewhere.) The papers released the following relate to 3 diversified features of the convention. the 1st matters issues suitable to all 3 fields, together with, for instance, Horn good judgment, lambda calculus, general shape discount rates, algebraic theories, and specific types for computability idea. within the region of common sense, subject matters contain semantical ways to proof-theoretical questions, inner homes of particular items in (pre-) topoi and their representations, and specific sprucing of model-theoretic notions. ultimately, within the sector of machine technology, using class concept in formalizing elements of laptop programming and software layout is mentioned.

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Lambert [42] stated that the minimum measurable amount of uranium or plutonium in aluminum was 500 ppm_ For plutonium the sample was sandwiched between two l/rmil Mylar sheets to prevent contamination of the sample chamber. These limits seem high since aluminum is not a strong X-ray absorber for radiation in the I-A range. Fluorescent X-ray Spectrography 43 Oxides In many instances it may be necessary to convert metal samples of irregular shapes or sizes to oxides before analysis. The intensity of a metal Ka line should be approximately the same whether measured on a pure metal or its oxide, assuming an infinite thickness of sample.

Absorption of Zn Ka by cobalt. added to the solution was then washed, dried, and subjected to X-ray analysis. The standard deviation for starting samples of 1 g was ±10% at 5 to 6 ppm. Campbell, Leon, and Thatcher [16] determined microgram quantities of iron and copper in low-grade copper ores, using cationexchange membranes. Results obtained by this method and by chemical techniques agreed. Zemany, Welbon, and Gaines [60] determined the quantity of potassium liberated from the surface of ground-mica samples by ionexchange-membrane techniques.

However, Sandell [51 J states, "There is no reason for making this boundary a rigid one. It is sometimes convenient to consider as a trace constituent one that occurs to the extent of a few hundredths of a percent. 05% (500 ppm) is emphasized. SAMPLE CLASSIFICATION Liebhafsky, Pfeiffer, Winslow, and Zemany [44J suggest that trace analysis can be conveniently subdivided according to sample type: (1) traces as minor constituents in samples not unusually small and (2) traces as major constituents of a minute sample.

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