Andrew M. Gleason's The William Lovell Putnam Mathematical Competition. Problems PDF

By Andrew M. Gleason

ISBN-10: 0883854287

ISBN-13: 9780883854280

Ebook by means of Gleason, Andrew M.

Show description

Read or Download The William Lovell Putnam Mathematical Competition. Problems and solutions 1938-1964 PDF

Best mathematics books

Recreations mathematiques et problemes des temps anciens et - download pdf or read online

Nous publions une nouvelle édition de l. a. traduction française de l'ouvrage si remarquable de Rouse-Ball, faite sur los angeles 4e édition anglaise. M. Filz Patrick ne s'est pas borné au rôle de traducteur, il a enrichi F ouvrage d'additions nombreuses et importantes. Dans cette première partie, notamment, il a introduit une histoire originale cl anecdotique des nombres, et plus de cent problèmes extrêmement curieux, dont los angeles resolution, bien qu'élémentaire, est parfois délicate.

Ullrich Rüde's Mathematical and computational techniques for multilevel PDF

Multilevel adaptive equipment play an more and more very important position within the resolution of many clinical and engineering difficulties. speedy adaptive equipment innovations are familiar by way of experts to execute and research simulation and optimization difficulties. This monograph offers a unified method of adaptive equipment, addressing their mathematical idea, effective algorithms, and versatile info constructions.

Higher Mathematics for Physics and Engineering: Mathematical - download pdf or read online

As a result of quick growth of the frontiers of physics and engineering, the call for for higher-level arithmetic is expanding each year. This booklet is designed to supply obtainable wisdom of higher-level arithmetic demanded in modern physics and engineering. Rigorous mathematical buildings of vital matters in those fields are absolutely lined, with a view to be precious for readers to develop into accustomed to yes summary mathematical options.

Additional info for The William Lovell Putnam Mathematical Competition. Problems and solutions 1938-1964

Sample text

Furthermore. 17). 2 that llHyf-Qy fll~ ~ l[0fll~ ~ 321]fI]~ < +~ . and thus llHyf -Qy f]I2 § 0 as y ~0+ by dominated convergence. 14). P2yf dx . 15). 16). 4. 16). 13) proved . 39 Proof. 13). is of weak type is of type 1 . 15) in 2 , and hence also of weak type 2 . e. Hf dx[ = < cp llfllp llgllq we conclude fs and all and g~Lq(R) H . Hgdx[ = llfIlp<__l proving that (I

Is continuous. 20) is unaffected, if we from any continuous function fo f subtract of compact support. , proving the lena. 4. e. the operator Proof. P for all P Y is of strong type p Using H~ider's inequality we get for for all p ~ ]I,+ ~] p ~ ]I,+~[ IPyf(x)]P< ([ +~k (x-t). 5. 2. In fact, llPyfllp ~ II0 flip ~ Cpllfllp , p E ]I,+~] However~ we do not get that the constant may be chosen equal I . 6. (5. If fE for some ~) p e ]I, + ~[ , then lim llPyf - fIlp= 0 y~O+ and (5. ~S) Proof. 23) are obvious if tinuous function of compact support.

Due to the facts that f has compact support and gx(t) tends to 0 as Itl ->+~ vals mentioned we shall never need to consider the two infinite inter- above. We define g(x) = ~I J f(t)dt 9 x-c(J) I and gj (x) = ~I J . = j The function J f(t)dt 9 x-c(J) 36 g(x) - gj(x) ffi i f(t)dt 9 x-c(J) Jn J is clearly decreasing in the interval get for x=c(lj) I. 10) we J , g(c(lj)) - gj(c(lj)) > (I-6)X , for x in the left half of I.. I ~m(lj) < m({x I g(x) > 89 ~=i = + n I m({x ] gj(x) < j=l - ~(I-~)}) 2 . llm(lj)< __ 2 11 j =~(--(T~-6)J ~ 2 ~i fJ f(t)dt+ j=l~~ X(I-~) J I.

Download PDF sample

The William Lovell Putnam Mathematical Competition. Problems and solutions 1938-1964 by Andrew M. Gleason

by Thomas

Rated 4.63 of 5 – based on 9 votes