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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：C1,1/3- very weak solutions to the two dimensional Monge–Ampère equation
二维 Monge–Ampère方程 C1,1/3极弱解
2023/11/29
For any θ<1/3 , we show that very weak solutions to the two-dimensional Monge–Ampère equation with regularity C1,θ are dense in the space of continuous functions. This result is shown by a convex inte...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Weak values as statistical estimation
统计估计 弱值 量子可观测值 最小方差
2023/11/15
Given a quantum observable and a state, one can construct a classical observable, such that it is the optimal estimate of the quantum observable, in the sense of minimum variance. We demonstrate how t...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Convex integration and non-uniqueness of weak solutions for viscous fluids
粘性流体弱解 凸积分 非唯一性
2023/4/23
In this talk, I will discuss the method of convex integration and its applications on non-uniqueness of weak solutions to the hyper-viscous incompressible Navier-Stokes equations as well as the hypo-v...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Energy Concentration and Weak Stability in Fluid Dynamics
流体动力学 能量集中 弱稳定性
2023/4/14
The weak stability is an important issue in fluid dynamics. We will discuss the mathematical understudying of concentration phenomena in the framework of weak solutions with either critical or subcrit...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Many-body localization and quantum many-body scars: The strong and weak form of ergodicity breaking
多体定位 量子多体疤痕 遍历性断裂 强弱形式
2023/4/23
The fate of an isolated quantum many-body system has attracted much attention in the past decade. One of the most important issues is whether such a system can reach thermalization under its own dynam...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Weak multisymplectic spectral integrators with a resolution of Gibbs phenomenon
吉布斯现象 分辨率 弱多辛谱 积分器
2023/4/28
We will report our recent work on weak multisymplectic spectral integrators for a wide range of nonsmooth Hamiltonian partial differential equations, which appear in quite a few physical applications ...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Prediction When Factors are Weak
因素较弱 预测 宏观经济预测
2023/5/5
In macroeconomic forecasting, principal component analysis (PCA) has been the most prevalent approach to the recovery of factors, which summarize information in a large set of macro predictors. Nevert...
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：The spectral collocation method for the nonlocal problem with weak singularity
弱奇点 非局部问题 光谱搭配
2023/5/6
介绍求解一维弱奇异非局部扩散问题的谱配位法，建立了相应的Gauss-Jacobi 积分公式，并将其推广至高维非局部问题的谱配置点法，相关的理论与实验检验了算法的精度和渐进相容性。
Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Peakon Models II: Weak-kink, interactions with peakon, and Remedies
Peakon模型 弱扭结 相互作用 补救措施
2023/5/8
In the 2nd part of the series talks, I will introduce the new phenomena of weak-kink and its interaction with regular peakons which we recently developed. Such models include cubic Camassa-Holm (CH) t...
In the Standard Model of particle physics, the Brout–Englert–Higgs mechanism provides mass to elementary particles. While physicists are carrying out direct studies of the Higgs boson to test this mec...
Planckian metals have the potential to power high-temperature superconductors, quantum computers and a host of other next-generation technologies. However, these “strange” metals – in which electrical...
Weak Keys in the Rekeying Paradigm: Attacks on COMET-128 and mixFeed
weak keys authenticated encryption comet
2019/8/6
In this article, we analyze two of the NIST Round 1 Candidates for the Lightweight Cryptography Standardization Process: COMET and mixFeed. We show how AEAD modes that are based on rekeying can be mod...
Invariant subspaces (Crypto'11) and subspace trails (FSE'17) are two related recent cryptanalytic approaches that led to new results on, e. g. PRINTCipher and AES. We extend the invariant subspace app...
Indistinguishability Obfuscation Without Multilinear Maps: New Paradigms via Low Degree Weak Pseudorandomness and Security Amplification
PFG iO
2019/6/4
The existence of secure indistinguishability obfuscators (iO) has far-reaching implications, significantly expanding the scope of problems amenable to cryptographic study. All known approaches to cons...
Biased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies
Hidden number problem ECDSA Lattices
2019/1/10
In this paper, we compute hundreds of Bitcoin private keys and dozens of Ethereum, Ripple, SSH, and HTTPS private keys by carrying out cryptanalytic attacks against digital signatures contained in pub...