ISOMETRY

作品数：65被引量：151H指数：6
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相关领域：理学更多>>
相关作者：马玉梅王见勇更多>>
相关机构：常熟高等专科学校大连民族学院电子科技大学更多>>
相关期刊：《Science Bulletin》《Annals of Applied Mathematics》《Science China(Information Sciences)》《Communications and Network》更多>>
相关基金：国家自然科学基金国家重点基础研究发展计划国家教育部博士点基金福建省自然科学基金更多>>
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Large-scale self-normalizing neural networks
《Journal of Automation and Intelligence》2024年第2期101-110,共10页Zhaodong Chen Weiqin Zhao Lei Deng Yufei Ding Qinghao Wen Guoqi Li Yuan Xie 
National Key R&D Program of China(2018AAA0102600);National Natural Science Foundation of China(No.61876215,62106119);Beijing Academy of Artificial Intelligence(BAAI),China;Chinese Institute for Brain Research,Beijing,and the Science and Technology Major Project of Guangzhou,China(202007030006).
Self-normalizing neural networks(SNN)regulate the activation and gradient flows through activation functions with the self-normalization property.As SNNs do not rely on norms computed from minibatches,they are more fr...
关键词：Self-normalizing neural network Mean-field theory Block dynamical isometry Activation function 
ON A UNIVERSAL INEQUALITY FOR APPROXIMATE PHASE ISOMETRIES
《Acta Mathematica Scientia》2024年第3期823-838,共16页戴端旭 阙海新 孙龙发 郑本拓 
supported by the NSFC(12126329,12171266,12126346);the NSF of Fujian Province of China(2023J01805);the Research Start-Up Fund of Jimei University(ZQ2021017);supported by the NSFC(12101234);the NSF of Hebei Province(A2022502010);the Fundamental Research Funds for the Central Universities(2023MS164);the China Scholarship Council;supported by the Simons Foundation(585081)。
Let X and Y be two normed spaces.Let U be a non-principal ultrafilter on N.Let g:X→Y be a standard ε-phase isometry for someε≥ 0,i.e.,g(0)=0,and for all u.v ∈ X,||‖g(u)+g(v)‖±‖g(u)-g(v)‖|-|‖u+v‖±‖u-v‖| ...
关键词：ε-phase isometry phase isometry Banach space 
Specht Triangle Approximation of Large Bending Isometries
《Annals of Applied Mathematics》2023年第4期544-569,共26页Xiang Li Pingbing Ming 
supported by National Natural Science Foundation of China through Grants No.11971467 and No.12371438.
We propose a Specht triangle discretization for a geometrically nonlinear Kirchhoff plate model with large bending isometry.A combination of an adaptive time-stepping gradient flow and a Newton’s method is employed t...
关键词：Specht triangle plate bending isometry constraint adaptive time-stepping gradient flow 
ISOMETRY AND PHASE-ISOMETRY OF NON-ARCHIMEDEAN NORMED SPACES
《Acta Mathematica Scientia》2023年第6期2377-2386,共10页王瑞东 姚文婷 
supported by the Natural Science Foundation of China (12271402);the Natural Science Foundation of Tianjin City (22JCYBJC00420)。
In this paper,we study isometries and phase-isometries of non-Archimedean normed spaces.We show that every isometry f:Sr(X)→Sr(X),where X is a finite-dimensional non-Archimedean normed space and Sr(X)is a sphere with...
关键词：non-Archimedean normed spaces isometry extension Wigner's theorem 
Surjective Lp-isometries on Grassmann spaces
《Science China Mathematics》2023年第9期2105-2118,共14页Wenhua Qian Junhao Shen Weijuan Shi Wenming Wu Wei Yuan 
supported by the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN2021000529);the Natural Science Foundation of Chongqing Science and Technology Commission(Grant No.cstc2020jcyj-msxm X0723);supported by Young Talent Fund of University Association for Science and Technology in Shaanxi(Grant No.20210507);supported by National Natural Science Foundation of China(Grant Nos.11871127and 11971463);supported by National Natural Science Foundation of China(Grant Nos.11971463,11871303 and 11871127)。
Letϕ:Pc(M1)→Pc(M2)be a surjective Lp-isometry between Grassmann spaces of projections with the trace value c in semifinite factors M1 and M2.Based on the characterization of surjective Lp-isometries of unitary groups...
关键词：surjective L^(p)-isometry unitary group Grassmann space semifinite factor 
ON THE FIGIEL TYPE PROBLEM AND EXTENSION OFε-ISOMETRY BETWEEN UNIT SPHERES
《Acta Mathematica Scientia》2023年第4期1503-1517,共15页刘锐 尹际富 
the National Nature Science Foundation of China(11671214,11971348,12071230);the Hundred Young Academia Leaders Program of Nankai University(63223027,ZB22000105);the Undergraduate Education and Teaching Project of Nankai University(NKJG2022053);the National College Students’Innovation and Entrepreneurship Training Program of Nankai University(202210055048)。
This paper studies two isometric problems between unit spheres of Banach spaces.In the first part,we introduce and study the Figiel type problem of isometric embeddings between unit spheres.However,the classical Figie...
关键词：unit spheres isometric embedding Figiel type problem ε-isometry EXTENSION 
The Minkowski norm and Hessian isometry induced by an isoparametric foliation on the unit sphere被引量：1
《Science China Mathematics》2022年第7期1485-1516,共32页Ming Xu 
supported by Beijing Natural Science Foundation(Grant No.Z180004);National Natural Science Foundation of China(Grant Nos.11771331 and 11821101);Capacity Building for SciTech Innovation—Fundamental Scientific Research Funds(Grant No.KM201910028021)。
Let M_(t) be an isoparametric foliation on the unit sphere(S^(n−1)(1),g^(st))with d principal curvatures.Using the spherical coordinatesinduced by M_(t),we construct a Minkowski norm with the representation F=r√2f(t)...
关键词：Minkowski norm Hessian isometry Hessian metric isoparametric foliation Laugwitz Conjecture Legendre transformation 
COARSE ISOMETRIES BETWEEN FINITE DIMENSIONAL BANACH SPACES
《Acta Mathematica Scientia》2021年第5期1493-1502,共10页Yuqi SUN Wen ZHANG 
Supported by National Natural Science Foundation of China(11731010 and 12071388)。
Assume that X and Y are real Banach spaces with the same finite dimension.In this paper we show that if a standard coarse isometry f:X→Y satisfies an integral convergence condition or weak stability on a basis,then t...
关键词：coarse isometry linear isometry finite dimensional Banach spaces 
Isometries for the modulus metric in higher dimensions are conformal mappings
《Science China Mathematics》2021年第9期1951-1958,共8页Xiaohui Zhang 
supported by National Natural Science Foundation of China(Grant Nos.11771400 and 11911530457);Science Foundation of Zhejiang Sci-Tech University(Grant No.16062023Y)。
for a proper subdomain D of R^(n) and for all x,y∈D defineμD(x,y)=infC_(xy)Cap(D,C_(xy)),where the infimum is taken over all curves Cxy=γ[0,1]in D withγ(0)=x andγ(1)=y,and Cap denotes the conformal capacity of co...
关键词：capacity modulus metric ISOMETRY M?bius transformation 
STABILITY OF ε-ISOMETRIES ON L_∞-SPACES
《Acta Mathematica Scientia》2019年第6期1733-1742,共10页Duanxu DAI 
supported by the Natural Science Foundation of China(11601264);the Natural Science Foundation of Fujian Province of China(2019J05103);the Outstanding Youth Scientific Research Personnel Training Program of Fujian Province;the High level Talents Innovation and Entrepreneurship Project of Quanzhou City(2017Z032)
In this article,we discuss the stability ofε-isometries for L∞,λ-spaces.Indeed,we first study the relationship among separably injectivity,injectivity,cardinality injectivity and universally left stability of L∞,...
关键词：STABILITY ε-isometry L∞-space 
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