Frobenius theoremcontinuous tangent sub-bundlesintegrabilityordinary differential equationspartial differential equationsWe formulate a notion of(uniform) asymptotic involutivityand show that it implies (unique) integrability of corank-1 continuous distributions in dimensions three or less. This generalizes and...
We prove a Frobenius-type theorem for singular distributions generated by a family of locally Lipschitz continuous vector fields satisfying almost everywhere a quantitative finite type condition. Keywords Frobenius theorem; Singular distribution; Orbits of vector fields Corresponding author. Copyright ©...
读书报告 | 谱图理论 Ch2: Eigenvalues and Optimization: The Courant-Fischer Theorem 读书报告 | 谱图理论 Ch3: The Laplacian and Graph Drawing 读书报告 | 谱图理论 Ch4: Adjacency matrices, Eigenvalue Interlacing, and the Perron-Frobenius Theorem 读书报告 | 谱图理论 Ch5: Comparing Graphs 读书报告 ...
Other blocks, such as block OM3, appear to divide into two halves with different functions for each half; for block OM3, only half projects to the ABD, whereas the other half provides the strongest projection to the \({{\rm{O}}}_{{{\rm{Ve}}}^{2}}\) block. We separately applied...
We present several proofs of the result, some of which use the Perron-Frobenius Theorem. Structure of max eigenvalues and max eigenvectors is described. Possible ways to unify the Perron-Frobenius Theorem and its max version are indicated. Some inequalities for μ(A) are proved....
Footnote 2 One computes the eigenvector-based centralities of nodes for a time-independent network as the entries of the “dominant” eigenvector, which is associated with the largest positive eigenvalue (by the Perron–Frobenius theorem, the eigenvalue with the largest magnitude is guaranteed to ...
23 Positivity preservers forbidden to operate on diagonal blocks 54:41 Predicting rain and lightning using statistical and machine learning techniques 1:03:20 Projections and circles 1:01:20 Recent advances in dynamical optimal transport_ Lecture 2 1:32:26 Small prime k-th power residues modulo p...
However, the additional requirement for all entries in the eigenvector to be non-negative implies (by the Perron-Frobenius theorem) that only the eigenvector associated with the greatest eigenvalue is the desired centrality measure. Then, the \(v^{th}\) component of the related eigenvector ...
23 Positivity preservers forbidden to operate on diagonal blocks 54:41 Predicting rain and lightning using statistical and machine learning techniques 1:03:20 Projections and circles 1:01:20 Recent advances in dynamical optimal transport_ Lecture 2 1:32:26 Small prime k-th power residues modulo p...
In Section 3, we show the Brauer categories of b and b0 are the same if Q is cyclic (Theorem 3 below). Next we consider local structure of blocks with cyclic hyperfocal subgroups (Lemma 6, Lemma 7 below). In order to prove Theorem 1, we use lower defect groups of blocks. Theorem ...