منابع مشابه
Sharpening the LYM inequality
More detailed information about the s t ructure of Sperner families can be obtained by considering their level sequences. The level sequence of a family 4 , f ( ~ ) = {fi(Y)}, has f i (~) equal to the number of members of ~ with exac t ly ' / e l emen t s . Sperner 's theorem asserts tha t ~fi(2~)<_ ([~j) . A stronger restriction on the level i sequence was proved independent ly by Lubell, Yama...
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A. Moriwaki proved the following arithmetic analogue of the Bogomolov unstability theorem. If a torsion-free hermitian coherent sheaf on an arithmetic surface has negative discriminant then it admits an arithmetically destabilising subsheaf. In the geometric situation it is known that such a subsheaf can be found subject to an additional numerical constraint and here we prove the arithmetic ana...
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The famous Erdös-Mordell inequality in geometric inequalities states the following: Let P be an interior point of a triangle ABC. Let R1, R2, R3 be the distances from P to the vertices A,B,C, and let r1, r2, r3 be the distance from P to the sides BC,CA,AB, respectively. Then R1 +R2 +R3 ≥ 2(r1 + r2 + r3), (1.1) with equality if and only if △ABC is equilateral and P is its center. This equality w...
متن کاملSharpening and Generalizations of Carlson’s Inequality for the Arc Cosine Function
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ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1995
ISSN: 0022-247X
DOI: 10.1006/jmaa.1995.1465