1. |
Telegraphic Reviews |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 57-64
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971880
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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2. |
Ludwig Bieberbach's Conjecture and its Proof by Louis de Branges |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 505-514
KorevaarJ.,
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摘要:
Summary1984 has been an exciting year for complex analysis. It even brought strong rumors that the Riemann hypothesis had been proved, but so far, the rumor has not been confirmed. However, we know for sure that the difficult Bieberbach conjecture has been settled this year. As many of you know, this famous conjecture of 1916 concerns the classSof normalized injective holomorphic functions. That class consists of the 1–1 holomorphic functions from the unit discUinto the complex plane C with a power series of the formf(z)=z+ a2z2+…+anzn+…,|z|<1.The conjecture asserts that |an|⩽nfor veryfinSand everyn. Louis de Branges has proved this conjecture as well as some stronger conjectures for the classS.Each of the following items has played an essential role in the proof:(i)Löwner's partial differential equation for so-called Löwner chains {f,(z)} of injective holomorphic functions fromUto C.(ii)The observations of Lebedev and I. M. Milin, especially their inspired conjecture for the so-called logarithmic coefficients offinS, that is, the coefficients in the expansionfor a branch of log {f(z)/z}.(iii)De Branges' striking breakthrough, namely, the creation of a functional associated with the Lebedev-Milin conjecture which varies monotonically along Löwner chains.(iv)De Branges' introduction and solution of a system of differential equations which he devised to make the functional manageable.(v)A positivity result for hypergeometric functions which is a tool in establishing the monotonicity of the functional.Of the above, (i) dates back to 1923, while (ii) and (v) are relatively recent. The Lebedev-Milin observations date from the years 1965–1970 and became well known in the West only around 1977. The hypergeometric functions result occurs in work of Askey and Gasper of 1976.
ISSN:0002-9890
DOI:10.1080/00029890.1986.11971872
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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3. |
Non-Sexist Solution of the Ménage Problem |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 514-518
BogartKenneth P.,
DoylePeter G.,
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971873
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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4. |
Photo |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 519-519
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971874
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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5. |
Chance Expectancy with Trial-By-Trial Feedback and Random Sampling Without Replacement |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 520-530
PattersonJames C.,
GardnerBeatrix T.,
GardnerR. Allen,
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971875
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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6. |
Miscellanea |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 530-584
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971876
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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7. |
A Note on Alternating Series in Several Dimensions |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 531-539
BorweinDavid,
BorweinJonathan M.,
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971877
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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8. |
Infinitesimals, Microsimplexes and Elementary Homology Theory |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 540-544
ŽivaljevićRade T.,
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971878
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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9. |
Is there an all-Purpose Tile? |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 545-551
GrünbaumBranko,
ShephardG. C.,
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971879
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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10. |
Forms of the Resultant of Two Polynomials |
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The American Mathematical Monthly,
Volume 93,
Issue 7,
1986,
Page 551-552
BarnettS.,
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ISSN:0002-9890
DOI:10.1080/00029890.1986.11971881
出版商:Taylor&Francis
年代:1986
数据来源: Taylor
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