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open problemµconstruction of Cauchy-Szegö kernel on theunit ball
Dirichlet problem on the classical domains
�EÑ4 a;.�aصBergman Ø£´ BergmanÝþ£PoincaréÝþ�pí2¤�³¤§Cauchy-SzegöاPoissonØ"
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• Lu, QiKengµAn inequality of the holomorphic invariantforms. Sci. China Math. 56 (2013);
• Lu, Qi KengµOn the curvature conjecture of Hua Loo-Keng. Acta Math. Sin. (Engl. Ser.) 28 (2012);
• Lu, Qi-KengµPoisson kernel and Cauchy formula of a non-symmetric transitive domain. Sci. China Math. 53 (2010);
• Lu, QikengµThe conjugate points of CP∞ and the zeroesof Bergman kernel. Acta Math. Sci. Ser. B Engl. Ed. 29(2009);
• Lu, QiKengµHolomorphic invariant forms of a boundeddomain. Sci. China Ser. A 51 (2008)
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Kobayashi embedding: k.áE�Km
Lu embedding: k.áGrassmann6/
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/fundamental inequalities for holomorphically invariantforms0
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Dieudonneµ/´¤kêÆÆ�¥�!(J�nØ0, in /The Work of Nicholas Bourbaki0, TheAmerican Math. Monthly, 1970
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Niccolo Fontana (Tartaglia), Gerolamo Cardano
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x3 + px = q;
x3 = px + q, where p, q > 0
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Tartaglia-Cardano formula:Cardano1545cuL/Ars Magna0(Îoc§+^Z1¤
)x3 + px = q
Sµ(u− v)3 + 3uv(u− v) = u3 − v3
-3uv = p, u3 − v3 = qu3,−v3´y2 − qy − p3/27 = 0�
x = u− v =3
√q/2 +
√q2/4 + p3/27 + 3
√−q/ +
√q2/4 + p3/27
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)x3 = px + q
Sµ(u + v)3 = 3uv(u + v) + u3 + v3
-3uv = p, u3 + v3 = q
u3, v3´y2 − qy + p3/27 = 0�
x = u + v =3
√q/2 +
√q2/4− p3/27 + 3
√q/2−
√q2/4− p3/27
~µx3 = 15x + 4, x = 4 is obviously a solution.,lúª%ÑyJê
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