منابع مشابه
Geometric Height Inequalities
0. The Results. Let f : X → B be a fibration of a compact smooth algebraic surface over a compact Riemann surface B, denote by g ≥ 2 the genus of a generic fiber of f and by q the genus of B. Let s be the number of singular fibers of f and ωX/B be the relative dualizing sheaf. Let C1, · · · , Cn be n mutually disjoint sections of f , and denote by D the divisor ∑n j=1Cj. Then the main result we...
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In this paper, using the extended Holder- -McCarthy inequality, several inequalities involving the α-weighted geometric mean (0<α<1) of two positive operators are established. In particular, it is proved that if A,B,X,Y∈B(H) such that A and B are two positive invertible operators, then for all r ≥1, ‖X^* (A⋕_α B)Y‖^r≤‖〖(X〗^* AX)^r ‖^((1-α)/2) ‖〖(Y〗^* AY)^r ‖^((1-α)/2) ‖〖(X〗^* BX)^r ‖^(α/2) ‖〖(Y...
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This lecture is concerned with apriori bounds on the size of solutions to Diophantine equations. We will present a rather random collection of results with the intention to provide a flavor of the subject, with only a glimpse of something like a unifying principle. In the next lecture, we will make a better attempt to give coherence to our exposition, by describing the relation to canonical cla...
متن کاملIMO/KKK/Geometric Inequality/1 Geometric Inequalities
Notation and Basic Facts a, b, and c are the sides of ∆ABC opposite to A, B, and C respectively. [ABC] = area of ∆ABC s = semi-perimeter =) c b a (2 1 + + r = inradius R = circumradius Sine Rule: R 2 C sin c B sin b A sin a = = = Cosine Rule: a 2 = b 2 + c 2 − 2bc cos A [ABC] = B sin ac 2 1 A sin bc 2 1 C sin ab 2 1 = = = R 4 abc =) c s)(b s)(a s (s − − − (Heron's Formula) = 2 cr 2 br 2 ar + + ...
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ژورنال
عنوان ژورنال: Mathematical Research Letters
سال: 1996
ISSN: 1073-2780,1945-001X
DOI: 10.4310/mrl.1996.v3.n5.a10