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Fully Nonlinear Equations of Krylov Type on Riemannian Manifolds with Totally Geodesic Boundary

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Acta Mathematica Sinica,English Series 2024年第5期40卷 1293-1307页

作者： Li CHEN Yan HE Faculty of mathematics and Statistics Hubei Key Laboratory of Applied MathematicsHubei UniversityWuhan 430000P.R.China

In this paper,we study fully nonlinear equations of Krylov type in conformal geometry on compact smooth Riemannian manifolds with totally geodesic boundary.We prove the a priori estimates for solutions to these equati... 详细信息

关键词： The modified Schouten tensor k-convex Hessian type equation

Burning Numbers of Barbells

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Acta Mathematicae Applicatae Sinica 2024年第2期40卷 526-538页

作者： Hui-qing LIU Rui-ting ZHANG Xiao-lan HU hubei key laboratory of applied mathematics&Faculty of mathematics and Statistic Hubei UniversityWuhan 430062China hubei key laboratory of Mathematical Sciences&School of mathematics and Statistics Central China Normal UniversityWuhan 430079China

Motivated by a discrete-time process intended to measure the speed of the spread of contagion in a graph,the burning number b(G)of a graph G,is defined as the smallest integer k for which there are vertices x1,…xk su... 详细信息

关键词： burning number short/long barbell isometric subtree cycle

Polynomial-Time key-Recovery Attacks Against NTRURe Encrypt from ASIACCS'15

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Journal of Systems Science & Complexity 2024年第3期37卷 1308-1325页

作者： LIU Zhen PAN Yanbin ZHENG Jinwei School of Cyber Science and Technology Hubei Key Laboratory of Applied MathematicsHubei UniversityWuhan 430062China key laboratory of mathematics Mechanization Academy of Mathematics and Systems ScienceChinese Academy of SciencesBeijing 100190China School of Mathematical Sciences University of Chinese Academy of SciencesBeijing 100190China

In ASIACCS 2015, Nu nez, et al. proposed a proxy re-encryption scheme, named NTRURe Encrypt, based on NTRU, which allows a proxy to translate ciphertext under the delegator’s public key into a re-encrypted ciphertext that can be decrypted correctly by delegatee’s private key. Because of the potential resistance to quantum algorithm, high efficiency and various applications in real life,NTRURe Encrypt has drawn lots of attention and its security has been widely discussed and analyzed.In PQCrypto2019, Liu, et al. proposed two key recovery attacks against it. However, their first attack heavily relies on a weaken decryption oracle, and the second attack needs to collect about 260ciphertexts from the same message by theoretical analysis, which makes both of the attacks unrealistic. In this paper, inspired by the broadcast attack against NTRU, the authors find out that for NTRURe Encrypt the delegator and the delegatee can efficiently recover each other’s private key in polynomial time without any unrealistic assumptions. In addition, the authors also show how to fix NTRURe Encrypt to resist the proposed attacks. As a by-product, the authors also show how to commit broadcast attacks against NTRU 2001 with even dg, which was thought infeasible before.

关键词： Broadcast attack key recovery NTRU NTRUReEncrypt

The Orthogonal Bases of Exponential Functions Based on Moran–Sierpinski Measures

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Acta Mathematica Sinica,English Series 2024年第7期40卷 1804-1824页

作者： Qi Rong DENG Xing Gang HE Ming Tian LI Yuan Ling YE School of mathematics and Statistics Center for Applied Mathematics of Fujian Province & Key Laboratory of Analytical Mathematics and Applications (Ministry of Education)Fujian Normal University School of mathematics and Statistics Key Lab NAA-MOE and Hubei Key Lab-Math.Sci.Central China Normal University School of Mathematical Sciences & South China Research Center for applied mathematics and Interdisciplinary Studies South China Normal University

Let A_n ∈ M2（Z） be integral matrices such that the infinite convolution of Dirac measures with equal weights ■ is a probability measure with compact support, where D = {（0, 0）~t,（1, 0）~t,（0, 1）~t} is the Sierpinski digit.We prove that there exists a set Λ ? R2such that the family ■ is an orthonormal basis of L2(μ{An,n≥1}) if and only if 1/3（1,-1）A_n ∈ Z2for n ≥ 2 under some metric conditions on A_n.

关键词： Moran-Sierpinski measures orthonormal basis of exponential functions self-affine measures spectral measures 28A33 42C05 28A80 42C30

THE WEIGHTED KATO SQUARE ROOT PROBLEMOF ELLIPTIC OPERATORS HAVING A BMOANTI-SYMMETRICPART

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Acta Mathematica Scientia 2024年第2期44卷 532-550页

作者：马文贤杨四辈 School of mathematics and Statistics Gansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou730000China

Let n≥2 and let L be a second-order elliptic operator of divergence form with coefficients consisting of both an elliptic symmetric part and a BMO anti-symmetric part in ℝ^(n).In this article,we consider the weighted Kato square root problem for L.More precisely,we prove that the square root L^(1/2)satisfies the weighted L^(p)estimates||L^(1/2)(f)||L_(ω)^p(R^(n))≤C||■f||L_(ω)^p(R^(n);R^(n))for any p∈(1,∞)andω∈Ap(ℝ^(n))(the class of Muckenhoupt weights),and that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,2+ε)andω∈Ap(ℝ^(n))∩RH_(2+ε/p),(R^(n))(the class of reverse Hölder weights),whereε∈(0,∞)is a constant depending only on n and the operator L,and where(2+ε/p)'denotes the Hölder conjugate exponent of 2+ε/p.Moreover,for any given q∈(2,∞),we give a sufficient condition to obtain that||■f||L_(ω)^p(R^(n);R^(n))≤C||L^(1/2)(f)||L_(ω)^p(R^(n))for any p∈(1,q)andω∈A_(p)(R^(n))∩pRH_(q/p),(R^(n)).As an application,we prove that when the coefficient matrix A that appears in L satisfies the small BMO condition,the Riesz transform∇L^(−1/2)is bounded on L_(ω)^(p)(ℝ^(n))for any given p∈(1,∞)andω∈Ap(ℝ^(n)).Furthermore,applications to the weighted L^(2)-regularity problem with the Dirichlet or the Neumann boundary condition are also given.

关键词： elliptic operator Kato square root problem Muckenhoupt weight Riesz transform reverse Hölder inequality

Multiscale control of MnO2 growth via [WO6]-perturbed[MnO6] assembly toward a favorable balance between capacitance and rate performance

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Rare Metals 2024年第4期43卷 1658-1671页

作者： Jin-Kang Liu Tian-Shuo Yang Zhi-Bin Ren Adekunle-Adedapo Obisanya Xin-Yi Tan Yan-Di Rao Jun-Shuang Zhou Fa-Ming Gao Jian-Ren Wang Hebei key laboratory of applied Chemistry Yanshan University

Although pseudocapacitive manganese dioxide（MnO2） integrates the high-power merit of carbonaceous materials with the high-energy merit of battery-type materials,it still has a long way to go in achieving a more satisfactory balance of higher energy and power density,and in decoupling the relationship of structural characteristics with energy storage performance.To realize such goals,a bottom-up [WO6]-perturbed [MnO6] assembly strategy has been developed here due to their similar structure,yet mismatched lattice parameters.This facile protocol is capable of finely controlling the morphology and crystal structure of MnO2by adjusting its internal[WO6] concentration.Therefore,the as-prepared WxMnO2is treated as an ideal platform to scrutinize the correlations of the structure with the energy storage performance.The operando Raman spectra and finite element analysis have fully demonstrated the superiority of the locally ordered defects-enriched structure of W0.02-MnO2,which could reach a favorable balance between the ion diffusion equilibrium time and the number of active sites.As a result,the W0.02-MnO2is able to deliver a high capacitance of 292 F·g-1at a current density of 1 A·g-1and a remarkable rate performance with a 60% capacity retention at a current density of 50 A·g-1.The further unveiled structure-performance relationship provides a guideline for the design of better pseudocapacitive energy storage devices.

关键词： Supercapacitors Pseudocapacitive materials MnO 2 Tungsten doping Crystal structure regulation

NONMONOTONE LOCAL MINIMAX METHODS FOR FINDING MULTIPLE SADDLE POINTS

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Journal of Computational mathematics 2024年第3期42卷 851-884页

作者： Wei Liu Ziqing Xie Wenfan Yi South China Research Center for applied mathematics and Interdisciplinary Studies South China Normal UniversityGuangzhou 510631China key laboratory of Computing and Stochastic mathematics(Ministry of Education) Hunan Normal UniversityChangshaHunan 410081China Hunan Provincial key laboratory of Intelligent Information Processing and applied mathematics School of MathematicsHunan UniversityChangshaHunan 410082China

In this paper,by designing a normalized nonmonotone search strategy with the BarzilaiBorwein-type step-size,a novel local minimax method(LMM),which is a globally convergent iterative method,is proposed and analyzed to find multiple(unstable)saddle points of nonconvex functionals in Hilbert spaces.Compared to traditional LMMs with monotone search strategies,this approach,which does not require strict decrease of the objective functional value at each iterative step,is observed to converge faster with less computations.Firstly,based on a normalized iterative scheme coupled with a local peak selection that pulls the iterative point back onto the solution submanifold,by generalizing the Zhang-Hager(ZH)search strategy in the optimization theory to the LMM framework,a kind of normalized ZH-type nonmonotone step-size search strategy is introduced,and then a novel nonmonotone LMM is constructed.Its feasibility and global convergence results are rigorously carried out under the relaxation of the monotonicity for the functional at the iterative sequences.Secondly,in order to speed up the convergence of the nonmonotone LMM,a globally convergent Barzilai-Borwein-type LMM(GBBLMM)is presented by explicitly constructing the Barzilai-Borwein-type step-size as a trial step-size of the normalized ZH-type nonmonotone step-size search strategy in each iteration.Finally,the GBBLMM algorithm is implemented to find multiple unstable solutions of two classes of semilinear elliptic boundary value problems with variational structures:one is the semilinear elliptic equations with the homogeneous Dirichlet boundary condition and another is the linear elliptic equations with semilinear Neumann boundary conditions.Extensive numerical results indicate that our approach is very effective and speeds up the LMMs significantly.

关键词： Multiple saddle points Local minimax method Barzilai-Borwein gradient method Normalized nonmonotone search strategy Global convergence

Navigation Finsler metrics on a gradient Ricci soliton

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applied mathematics(A Journal of Chinese Universities) 2024年第2期39卷 266-275页

作者： LI Ying MO Xiao-huan WANG Xiao-yang Department of applied mathematics Zhejiang University of TechnologyHangzhou 310023China key laboratory of Pure and applied mathematics School of Mathematical SciencesPeking UniversityBeijing 100871China School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

In this paper,we study a class of Finsler metrics defined by a vector field on a gradient Ricci soliton.We obtain a necessary and sufficient condition for these Finsler metrics on a compact gradient Ricci soliton to be of isotropic S-curvature by establishing a new integral inequality.Then we determine the Ricci curvature of navigation Finsler metrics of isotropic S-curvature on a gradient Ricci soliton generalizing result only known in the case when such soliton is of Einstein type.As its application,we obtain the Ricci curvature of all navigation Finsler metrics of isotropic S-curvature on Gaussian shrinking soliton.

关键词： gradient Ricci soliton navigation Finsler metric isotropic S-curvature Ricci curvature Gaussian shrinking soliton

A new quantity in Finsler geometry

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Science China mathematics 2024年第4期67卷 883-890页

作者： Xiaohuan Mo Xiaoyang Wang key laboratory of Pure and applied mathematics School of Mathematical SciencesPeking UniversityBeijing 100871China School of mathematics and Statistics Beijing Institute of TechnologyBeijing 100081China

In this paper,we study a new Finslerian quantity■defined by the T-curvature and the angular metric tensor.We show that the■-curvature not only gives a measure of the failure of a Finsler metric to be of scalar flag curvature but also has a vanishing trace.We find that the■-curvature is closely related to the Riemann curvature,the Matsumoto torsion and theΘ-curvature.We solve Z.Shen’s open problem in terms of the■-curvature.Finally,we give a global rigidity result for Finsler metrics of negative Ricci curvature on a compact manifold via the■-curvature,generalizing a theorem previously only known in the case of negatively curved Finsler metrics of scalar flag curvature.

关键词： Finsler metric Finslerian quantity T-curvature -curvature Randers metric