2.(Mathematics)mathsa set of components, functions of the coordinates of any point in space, that transform linearly between coordinate systems. For three-dimensional space there are 3rcomponents, whereris the rank. A tensor of zero rank is a scalar, of rank one, a vector ...
liquid structuremolecular configurationsnematic liquid crystalspolymer solutionspolymerisationThe free energy of semiflexible polymers is calculated as a functional of the compositional scalar order parameter phi and the orientational order parameter of second-rank tensor S ij on the basis of a microscopic ...
The αij and βij are the components of second-rank tensors $$\begin{array}{*{20}{c}} {\alpha = \left( {\begin{array}{*{20}{c}} {\alpha _{xx}} & {\alpha _{xy}} \\ {\alpha _{yx}} & {\alpha _{yy}} \end{array}} \right)\sim \left( {\begin{array}{*{20}{c...
Botanists usually use the term “form” to designate a category lower in rank than a variety; zoologists use the term as a synonym for variety. Sometimes the term “form” is used in the same sense as the term “taxon,” that is, to designate a systematic unit of any rank. In ...
DeepRank: a deep learning framework for data mining 3D protein-protein interfaces Article Open access 03 December 2021 ScanNet: an interpretable geometric deep learning model for structure-based protein binding site prediction Article 30 May 2022 SurfDock is a surface-informed diffusion generative...
Tensors of Minimal Border Rank - Joseph Landsberg 01:06:59 Standard Monomials for Positroid Varieties - Daoji Huang 57:05 Simple High Dimensional Expanders from Cayley Graphs - Yotam Dikstein 01:01:53 A canonical basis for cosmological correlators from the positive geometry of cut 15:12 ...
We determine the local structure of all pseudo-Riemannian manifolds of dimensions greater than 3 whose Weyl conformal tensor is parallel and has rank 1 whe... D Andrzej,R Witold - 《東北數學雜誌. second series》 被引量: 35发表: 2007年 A classification of locally homogeneous affine connections...
Let G be a group given by a free presentation G=F/R, where F is a non- cyclic free group, and let γ c R be the c-th term of the lower central series of the normal subgroup R. Conjugation in F induces on each lower central quotient of R the structure of a right G-module gi...
Proof. Consider left A-module M and a family of rank 1 free right A-modules Fi ∼= A. We shall consider all left (respectively, right) A-modules to be always endowed with the right (respec- tively, left) K-module structure identical to the left (respectively, right) K-module ...
JournalofStatisticalMechanics:TheoryandExperiment,2010,P06003.5.DarongLai,HongtaoLuandChristineNardini,FindingcommunitiesindirectednetworksbyPageRankrandomwalkinducednetworkembedding,PhysicaA:StatisticalMechanicsanditsApplications,vol.389,pp.2443-2454,20106.WuX,LuH.“Generalizedprojectivesynchronizationbetweentwodifferent...