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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Inverse problems for elliptic PDE" (8)
椭圆偏微分方程 反问题 Calderón问题
2023/11/29
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars："Inverse problems for elliptic PDE" (7)
椭圆偏微分方程 反问题 Calderón问题
2023/11/29
This course will give an introduction to inverse problems for elliptic partial differential equations. The most famous example of such problems is the Calderón problem, which arises in seismic and med...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Pseudorandomness of Sato-Tate Distributions for Elliptic Curves
椭圆曲线 佐藤-泰特分布 伪随机性
2023/4/13
Equidistribution is an important theme in number theory. The Sato-Tate conjecture, which was established by Richard Taylor et.al. in 2008, asserts that given an elliptic curve over Q without complex m...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Two families of $n$-rectangle nonconforming finite elements for sixth-order elliptic equations
六阶椭圆方程 矩形 有限元族
2023/4/13
We propose two families of nonconforming finite elements on $n$-rectangle meshes of any dimension to solve the sixth-order elliptic equations. The unisolvent property and the approximation ability of ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Twisted Real quasi-elliptic cohomology
扭曲 实拟椭圆 上同调
2023/4/13
Quasi-elliptic cohomology is closely related to Tate K-theory. It is constructed as an object both reflecting the geometric nature of elliptic curves and more practicable to study than most elliptic c...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Two Approaches towards elliptic cohomology
椭圆 上同调 两种方法
2023/4/14
An elliptic cohomology theory is an even periodic multiplicative generalized cohomology theory whose associated formal group is the formal completion of an elliptic curve. It is at the intersection of...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Deep neural network approximation to inverse conductivity problems for elliptic equations
椭圆方程 反电导率 深度神经网络
2023/4/14
The focus of this talk is on the numerical methods used to identify parameters in partial differential equations. Typically, an optimization approach is used to solve this class of inverse problems, w...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：A posteriori error estimate for a WG method of H(curl)-elliptic problems
H（卷曲） 椭圆问题 WG方法 后验误差估计
2023/4/23
In this paper, a posteriori error estimate of a weak Galerkin (WG) finite element method for solving H(curl)-elliptic problems is designed and analyzed. Firstly, a WG method for H(curl)-elliptic probl...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Regularity of sub-elliptic harmonic map into non-positively curved metric space
亚椭圆谐波 非正曲线 度量空间 规律性
2023/4/28
We prove the Holder continuity of a harmonic map from a domain of a sub-Riemannian manifold into a locally compact manifold with non-positive curvature, and more generally into a non-positively curved...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Nontrivial solutions for a quasilinear elliptic system with weight functions
权重函数 准线性 椭圆系统 非平凡解
2023/4/28
In this talk, we consider nontrivial solutions of a quasilinear elliptic system with the weight functions h(x) and f_i (x) (i = 1, 2) by applying the Nehari manifold method along with the fibrering ma...
A new elliptic curve point compression method based on Fp-rationality of some generalized Kummer surfaces
elliptic cryptography point compression Barreto-Naehrig curves
2019/9/19
In the article we propose a new compression method (to 2log2(p)+32log2(p)+3 bits) for the Fp2Fp2-points of an elliptic curve Eb:y2=x3+bEb:y2=x3+b (for b∈F∗p2b∈Fp2∗) of jj-invariant ...
A New Attack on RSA and Demytko's Elliptic Curve Cryptosystem
RSA Cryptanalysis Coppersmith's method
2019/9/19
Let N=pqN=pq be an RSA modulus and ee be a public exponent. Numerous attacks on RSA exploit the arithmetical properties of the key equation ed−k(p−1)(q−1)=1ed−k(p−1)(q...
Improved Cryptanalysis of the KMOV Elliptic Curve Cryptosystem
public-key cryptography KMOV
2019/9/19
This paper presents two new improved attacks on the KMOV cryptosystem. KMOV is an encryption algorithm based on elliptic curves over the ring ZNZN where N=pqN=pq is a product of two large primes of eq...
A New Method for Geometric Interpretation of Elliptic Curve Discrete Logarithm Problem
Intersection of Curves Grobner Basis Vanishing Ideals
2019/9/19
In this paper, we intend to study the geometric meaning of the discrete logarithm problem defined over an Elliptic Curve. The key idea is to reduce the Elliptic Curve Discrete Logarithm Problem (EC-DL...
Algorithmic aspects of elliptic bases in finite field discrete logarithm algorithms
discrete logarithm problem finite fields elliptic representation
2019/7/10
Elliptic bases, introduced by Couveignes and Lercier in 2009, give an elegant way of representing finite field extensions. A natural question which seems to have been considered independently by sever...