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On the bit-based division property of S-boxes

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Science China(Information Sciences) 2022年第4期65卷 261-263页

作者： Zejun XIANG Xiangyong ZENG Shasha ZHANG Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied MathematicsHubei University

Dear editor,The S-box, which is one of the most popular cipher components, has been extensively applied in modern symmetrickey primitives. Moreover, it is often the case that S-boxes are the only nonlinear components ... 详细信息

关键词： division property Sbox ANF divisional optimal divisional suboptimal

CURRENTS CARRIED BY THE SUBGRADIENT GRAPHS OF SEMI-CONVEX FUNCTIONS AND APPLICATIONS TO HESSIAN MEASURES

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Acta Mathematica Scientia 2018年第1期38卷 315-332页

作者：涂强陈文艺 Faculty of Mathematics and Statistics Hubei University School of mathematics and statistics Wuhan University

In this paper we study integer multiplicity rectifiable currents carried by the subgradient （subdifferential） graphs of semi-convex functions on an n-dimensional convex domain, and show a weak continuity theorem with respect to pointwise convergence for such currents. As an application, the structure theorem of the Lagrangian currents for semi-convex functions is given and the k-Hessian measures are calculated by a different method in terms of currents.

关键词： semi-convex function subgradient Cartesian current Hessian measure

A STABILITY RESULT FOR TRANSLATINGSPACELIKE GRAPHS IN LORENTZ MANIFOLDS

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Acta Mathematica Scientia 2024年第2期44卷 474-483页

作者：高雅毛井吴传喜 Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei ProvinceHubei UniversityWuhan430062China

In this paper,we investigate spacelike graphs defined over a domain Ω⊂M^(n) in the Lorentz manifold M^(n)×ℝ with the metric−ds^(2)+σ,where M^(n) is a complete Riemannian n-manifold with the metricσ,Ωhas piecewise smooth boundary,and ℝ denotes the Euclidean 1-space.We prove an interesting stability result for translating spacelike graphs in M^(n)×ℝ under a conformal transformation.

关键词： mean curvature flow spacelike graphs translating spacelike graphs maximal spacelike graphs constant mean curvature Lorentz manifolds

A Class of New Quadratic Vectorial Bent Functions

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Chinese Journal of Electronics 2020年第5期29卷 873-879页

作者： PANG Tingting ZENG Xiangyong LI Nian XU Yunge The Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University

A class of quadratic vectorial bent functions having the form F（x）=Tr;(ax;2;+1))+Tr;(bx;2;+1)) is investigated,where n,m,s;,s;are positive integers and the coefficients a,b belong to the finite field F;.Through some discussions on the permutation property of certain linearized polynomials over F;,several classes of quadratic vectorial bent functions are presented for special cases of n,and it is also verified by computer that some vectorial bent functions proposed are extended affine inequivalent to all known quadratic vectorial bent functions.

关键词： Vectorial bent function Permutation polynomial Extended affine equivalence Finite field

A Note on Supersaturated Design

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Acta Mathematicae Applicatae Sinica 2022年第3期38卷 729-739页

作者： Na ZOU Hong QIN School of statistics and mathematics Zhongnan University of Economics and LawWuhan 430073China Faculty of Mathematics and Statistics Central China Normal UniversityWuhan 430079China

Supersaturated designs are common choice for screening experiments.This paper studies the properties of supersaturated designs.We give new lower bounds of E(s^(2))-criterion and E(f_(NOD))-criterion.Some linkages between the combined/double design and its original design are firstly provided,and the lower bounds of E(s^(2)) and E(f_(NOD)) for the combined/double design are also given.Furthermore,the close relationship between the minimum Lee-moment aberration criterion and the criteria for optimal supersaturated designs is revealed.These theoretical results can be used to construct or search for optimal supersaturated designs in practice.Numerical results are also provided,which lend further support to our theoretical findings.

关键词： supersaturated design E(s^(2))-criterion E(f_(NOD))-criterion minimum Lee-moment aberration criterion foldover double

On the monomorphism category of n-cluster tilting subcategories

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Science China mathematics 2022年第7期65卷 1343-1362页

作者： Javad Asadollahi Rasool Hafezi Somayeh Sadeghi Department of Pure mathematics Faculty of Mathematics and StatisticsUniversity of IsfahanIsfahan 81746-73441Iran School of mathematics and statistics Nanjing University of Information Science&TechnologyNanjing 210044China

Let M be an n-cluster tilting subcategory of mod-Λ,whereΛis an Artin algebra.Let S(M)denote the full subcategory of S(Λ),the submodule category of Λ,consisting of all the monomorphisms in M.We construct two functors from S(M)to mod-Λ,the category of finitely presented additive contravariant functors on the stable category of M.We show that these functors are full,dense and objective and hence provide equivalences between the quotient categories of S(M)and mod-Λ.We also compare these two functors and show that they differ by the n-th syzygy functor,provided M is an n Z-cluster tilting subcategory.These functors can be considered as higher versions of the two functors studied by Ringel and Zhang(2014)in the case Λ=k[x]/and generalized later by Eiríksson(2017)to self-injective Artin algebras.Several applications are provided.

关键词： submodule categories n-abelian categories n-cluster tilting subcategories

Translating Solutions of the Nonparametric Mean Curvature Flow with Nonzero Neumann Boundary Data in Product Manifold M^(n)×R^(*)

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Chinese Annals of mathematics,Series B 2022年第4期43卷 601-620页

作者： Ya GAO Yi-Juan GONG Jing MAO Faculty of Mathematics and Statistics Key Laboratory of Applied Mathematics of Hubei ProvinceHubei UniversityWuhan 430062China

In this paper,the authors can prove the existence of translating solutions to the nonparametric mean curvature flow with nonzero Neumann boundary data in a prescribed product manifold M^(n)×R,where M^(n) is an n-dime... 详细信息

关键词： Translating solutions Singularity Nonparametric mean curvature flow Convexity Ricci curvature

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

Fully nonlinear equations of Krylov type on Riemannian manifolds with totally geodesic boundary

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Acta Mathematica Sinica,English Series 2023年

作者： Li CHEN Yan HE Faculty of Mathematics and Statistics Hubei Key Laboratory of Applied Mathematics Hubei University

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 equa...

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 equations and establish an existence result.

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