Isolated singularities of binary differential equations of degree n
... classification, but just as a description of the phase portrait of the foliations around the singular point. One of the main ingredients of the classification is the index of an isolated singular point. It is defined as a rational number of the form k/n, where k ∈ Z and it can be interpreted as the ...
... classification, but just as a description of the phase portrait of the foliations around the singular point. One of the main ingredients of the classification is the index of an isolated singular point. It is defined as a rational number of the form k/n, where k ∈ Z and it can be interpreted as the ...
SMALL BALL PROBABILITIES FOR LINEAR IMAGES OF HIGH
... purposes, we will start by presenting a version of Ball-Nazarov’s argument in dimension d = 1 in Sections 3 and 4. The higher-dimensional argument will be presented in Sections 5–7. There turned out to be an unexpected difference between dimension d = 1 and higher dimensions, which presents us with ...
... purposes, we will start by presenting a version of Ball-Nazarov’s argument in dimension d = 1 in Sections 3 and 4. The higher-dimensional argument will be presented in Sections 5–7. There turned out to be an unexpected difference between dimension d = 1 and higher dimensions, which presents us with ...
Topological Pattern Recognition for Point Cloud Data
... of f is a subspace of W , and we write θ(f ) for the quotient space W/im(f ). Proposition 2.2 Let g : V → V and h : W → W be invertible linear transformations. Then θ(f ) is isomorphic to θ(hf g). It follows that if we have the matrix equation A(f � ) = A(h)A(f )A(g), then θ(f � ) is isomorphic to θ ...
... of f is a subspace of W , and we write θ(f ) for the quotient space W/im(f ). Proposition 2.2 Let g : V → V and h : W → W be invertible linear transformations. Then θ(f ) is isomorphic to θ(hf g). It follows that if we have the matrix equation A(f � ) = A(h)A(f )A(g), then θ(f � ) is isomorphic to θ ...
AAN_15
... It follows from Thm II.8 that the projections z→x and z→y are linear continuous and surjective. ...
... It follows from Thm II.8 that the projections z→x and z→y are linear continuous and surjective. ...
