By George Biddell Airy

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2) where D, L, and U are n X n matrices with D nonsingular. Here, we do not assume that D is diagonal, nor that L and U are triangular. 3) for all complex relaxation factors w with w sufficiently smaU4 and the extrapolated Jacobi matrix *Research accomplished while on leave at Kent State Universit~ **Research supported in part by the Air Force Office of Scientific Research, and by the Department of Energy. 4) A. 4), when J is ass~ed to be a nonnegative matrix (written J 1 ~ ~) anA when D- L and n-lu are respectively strictly 1ower tr1angular and strictly upper triangu1ar.

2? 1. So far we have considered completeness theorems connected L 'i -approximation. What about co -approximation? A ~ formed by the functions u. of Li(~) such that there exist two measure functions ~ and ß both defined on the G' -ring of all the Borel sets of '<> 4 such that wi th (8) J u. >Gr'\f' cl(! V "'t ( C. 00 (X>t). 35 FICHERA Co Completeness of S [ of Sv J in Co (~4} [in ('d4 l ] amounts in proving that o( = o ( ß 2 o ) in (8) implies u.. = o For this proof see [34], (35]. ::. f . ~ P}, where P is an arbi trary polynomial in the variables x~, ...

Von Papyrus- und Lederrollen, die bis zu 4000 Jahre alt sind, wissen wir, daß die Xgypter des Altertums auf der Grundzahl Zehn aufbauend eine für das numerische Rechnen wenig geeignete additive Zahlenschreibweise - ähnlich der späteren römischen - benutzt, daß HEINRICH 48 sie eine eigenartige, ziemlich schwerfällige Bruchrechnung geschaffen und sich beim praktischen Rechnen gewisser vorbereiteter Hilfetafeln bedient haben. z. gelegen hat und denen man die Erfindung der Keilschrift zuschreibt, aus einem ursprUngliehen Zehnersystem durch BUndelung eine sexagesimale Zahlenschreibweise entwickelt, die schon die Keime für ein Stellenwertsystem in sich getragen hat.

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