In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles ...In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.展开更多
A new elliptic curve scalar multiplication algorithm is proposed. Thealgorithm uses the Frobenius map on optimal extension field (OEF) and addition sequence We introducea new algorithm on generating addition sequence ...A new elliptic curve scalar multiplication algorithm is proposed. Thealgorithm uses the Frobenius map on optimal extension field (OEF) and addition sequence We introducea new algorithm on generating addition sequence efficiently and also give some analysis about it.Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over anOEF is presented. The new method is more efficient than the traditional scalar multiplicationalgorithms of elliptic curve over OEF. Thecomparisons of traditional method and the new method arealso given.展开更多
Elliptic curve cryptosystem is the focus of public key cryptology nowadays, for it has many advantages RSA lacks. This paper introduced a new heuristic algorithm on computing multiple scalar multiplications of a given...Elliptic curve cryptosystem is the focus of public key cryptology nowadays, for it has many advantages RSA lacks. This paper introduced a new heuristic algorithm on computing multiple scalar multiplications of a given point. Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over optimal extension field (OEF) using Frobenius map was presented. The new method is more efficient than the traditional ones. In the last part of this paper, the comparison was given in the end.展开更多
In this paper, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll′ar and Jonsson-Mustat?a implies th...In this paper, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll′ar and Jonsson-Mustat?a implies the truth of twisted versions of the strong openness conjecture; our optimal L^2 extension implies Berndtsson's positivity of vector bundles associated to holomorphic fibrations over a unit disc.展开更多
In this paper, we discuss our most recent results on the optimal L-2 extension problem and Siu＇s lemma as applications of the strong openness property of multiplier ideal sheaves obtained by Guan and Zhou.
基金the National Natural Science Foundation of China(11688101 and 11431013)the National Natural Science Foundation of China(12022110,11201347 and 11671306).
文摘In this paper,we give a survey of our recent results on extension theorems on Kähler manifolds for holomorphic sections or cohomology classes of(pluri)canonical line bundles twisted with holomorphic line bundles equipped with singular metrics,and also discuss their applications and the ideas contained in the proofs.
文摘A new elliptic curve scalar multiplication algorithm is proposed. Thealgorithm uses the Frobenius map on optimal extension field (OEF) and addition sequence We introducea new algorithm on generating addition sequence efficiently and also give some analysis about it.Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over anOEF is presented. The new method is more efficient than the traditional scalar multiplicationalgorithms of elliptic curve over OEF. Thecomparisons of traditional method and the new method arealso given.
文摘Elliptic curve cryptosystem is the focus of public key cryptology nowadays, for it has many advantages RSA lacks. This paper introduced a new heuristic algorithm on computing multiple scalar multiplications of a given point. Based on this algorithm, a new method of computing scalar multiplication of elliptic curve over optimal extension field (OEF) using Frobenius map was presented. The new method is more efficient than the traditional ones. In the last part of this paper, the comparison was given in the end.
文摘In this paper, we reveal that our solution of Demailly's strong openness conjecture implies a matrix version of the conjecture; our solutions of two conjectures of Demailly-Koll′ar and Jonsson-Mustat?a implies the truth of twisted versions of the strong openness conjecture; our optimal L^2 extension implies Berndtsson's positivity of vector bundles associated to holomorphic fibrations over a unit disc.
基金supported by the National Natural Science Foundation of China(Grant Nos.11688101 and11431013)supported by the National Natural Science Foundation of China(Grant Nos.11201347 and 11671306)
文摘In this paper, we discuss our most recent results on the optimal L-2 extension problem and Siu＇s lemma as applications of the strong openness property of multiplier ideal sheaves obtained by Guan and Zhou.
