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Compute sequence of multiplicities of reduced plane curve singularity .
C]] will reveal sharp differences between tube and non-tube types, giving new characterization of tube type domains from the viewpoint of multiplicities in some branching laws and also from the viewpoint of visibility of holomorphic actions.
A multiplicity, depending on its threshold, continues to transform itself into a series of other multiplicities.
Gross [7] extended the study by considering preimages of sets counting multiplicities.
Let [psi]([not equivalent to] 0) be a holomorphic function in D and which has zeros only of multiplicities at most p.
For a positive integer m we denote by N(r, a; f l< m) (N(r, a; f |[greater than or equal to] m)) the counting function of those a-points of f whose multiplicities are not greater (not less) than m where each a-point is counted according to its multiplicity.
I am trying here to raise the brackets and parentheses, syntheses, whereby we shove multiplicities under unities that is the object of this book: the multiple.
So the fundamental idea of this work (to create a virtual garden from the interaction between the spectator and real plants) leads to a multiplicity of multiplicities set inside of each other.
In a persuasive comparative reading, Rhu argues that the episode of Errour's den in Book I, canto 1 of The Faerie Queene, with its connotations of a Reformation textual "nightmare" (65) resonates with Tasso's anxieties in the face of the kind of multiplicities of plot found in Ariosto, multiplicities that he seeks to avoid through the justifying principles of neo-Aristotelian theory.
For example, the tensor product of two irreducible unitary principal series representations of a simple group such as SL(n, R) (n [greater than or equal to] 3) involves infinite multiplicities in the irreducible decomposition.
A curve C in a linear system [absolute value of L] on a surface, passing through r points with multiplicities [m.