Results 11 to 20 of about 8,612,691 (178)
Milnor Number Equals Tjurina Number for Functions on Space Curves [PDF]
Journal of the London Mathematical Society, 2001 In many situations in complex geometry one can define a Milnor number, \(\mu\), that describes the rank of some vanishing homology, and a Tjurina number, \(\tau\), the dimension of the base of a semi-universal deformation. For example, for a hypersurface singularity \(X=V(f)\), one has \[ \mu=\dim {\mathcal O}/J_f,\quad \tau=\dim {\mathcal O}/(f,J_f), \
Mond, D. (David), Straten, Duco van
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On Sextic Curves with Big Milnor Number [PDF]
, 2002 In this work we present an exhaustive description, up to projective isomorphism, of all irreducible sextic curves in ℙ2 having a singular point of type , A n ,n⩾15 n ≥ 15, only rational singularities and global Milnor number at least 18. Moreover, we develop a method for an explicit construction of sextic curves with at least eight — possibly ...
Artal Bartolo, Enrique +2 more
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A formula for the Milnor Number
, 1995 We give a formula for the Milnor number of a germ (X,0) subset of (C-n+1,0) defined by f=0, f=f(d)+f(d+k)+...epsilon C {x(0),...,x(n)}, and such that Sing(D) boolean AND Z (f(d+k)) = circle divide, where D=Z (f(d)) subset of P-C(n). We prove that the topological type of (X,0) is determined by the d+k-jet of f.
Melle Hernández, Alejandro +1 more
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Finite Jumps in Milnor Number Imply Vanishing Folds [PDF]
Proceedings of the American Mathematical Society, 1983 Let { X t
Donal B. O’Shea
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Milnor number of pairs and pencils of plane holomorphic germs
Bulletin de la Société mathématique de France, 2015 Summary: We introduce a Milnor number of pairs of plane holomorphic germs and investigate the relation between the Milnor numbers in a pencil of such functions.
Szawlowski, Adrian
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Presentation of preload and afterload to isolated heart preparations. [PDF]
J PhysiolAbstract figure legend The heart can be isolated, and when this is so, it must be subjected to loading conditions. Over the past few decades, various loading methods have been developed to prescribe preload and afterload to isolated working‐heart preparations.
Mhandu E +4 more
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Proximal Pulmonary Artery Stiffening as a Biomarker of Cardiopulmonary Aging. [PDF]
Aging CellMouse models revealed age‐associated increased circumferential stiffness of the proximal pulmonary artery that was associated with reorientation of collagen and decreased function of the lung and right ventricle. Age‐related transcriptional changes were indicative of senescence, ECM turnover, TGFβ signaling, and altered intercellular signaling among ...
De Man R +22 more
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TJURINA AND MILNOR NUMBERS OF MATRIX SINGULARITIES [PDF]
Journal of the London Mathematical Society, 2005 LaTeX file; 23 pages; minor ...
Goryunov, Victor V., Mond, D. (David)
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On the Milnor number of non-isolated singularities of holomorphic foliations and its topological invariance [PDF]
, 2021 We define the Milnor number -- as the intersection number of two holomorphic sections -- of a one-dimensional holomorphic foliation $\mathscr{F}$ with respect to a compact connected component $C$ of its singular set.
Rosas, Rudy +2 more
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Deformations of functions and F-manifolds [PDF]
, 2004 We study deformations of functions on isolated singularities. A unified proof of the equality of Milnor and Tjurina numbers for functions on isolated complete intersections singularities and space curves is given.
De Gregorio, Ignacio +1 more
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