Fields Medallists' Lectures by Michael Francis Atiyah, Daniel Iagolnitzer

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By Michael Francis Atiyah, Daniel Iagolnitzer

Even though the Fields Medal doesn't have a similar public attractiveness because the Nobel Prizes, they percentage the same highbrow status. it's limited to 1 box - that of arithmetic - and an age restrict of forty has turn into an authorized culture. arithmetic has in general been interpreted as natural arithmetic, and this isn't so unreasonable considering significant contributions in a few utilized components might be (and were) famous with Nobel Prizes. a listing of Fields Medallists and their contributions presents a bird's-eye view of arithmetic over the last 60 years. It highlights the parts within which, at numerous occasions, maximum growth has been made. This quantity doesn't fake to be accomplished, neither is it a ancient rfile. however, it provides contributions from Fields Medallists and so presents a hugely attention-grabbing and sundry photo. the second one variation of Fields Medallists' Lectures beneficial properties extra contributions from the next Medallists: Kunihiko Kodaira (1954), Richard E Borcherds (1998), William T Gowers (1998), Maxim Kontsevich (1998), Curtis T McMullen (1998) and Vladimir Voevodsky (2002).

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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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