The multiplicity ofφPhe revisited

The Algebraic Multiplicity of Eigenvalues and the Evans Function Revisited

This paper is related to the spectral stability of traveling wave solutions of partial differential equations. In the first part of the paper we use the Gohberg-Rouche Theorem to prove equality of the algebraic multiplicity of an isolated eigenvalue of an abstract operator on a Hilbert space, and the algebraic multiplicity of the eigenvalue of the corresponding Birman-Schwinger type operator pe...

QUICKSELECT Revisited

We give an overview of the running time analysis of the random divide-and-conquer algorithm FIND or QUICKSELECT. The results concern moments, distribution of FIND’s running time, the limiting distribution, a stochastic bound and the key: a stochastic fixed point equation.

PENDRED\'S SYNDROME REVISITED

Pendred's syndrome is defined as a triad of congenital perceptive hearing loss, goiter, and abnormal perchlorate test. Three brothers with Pendred's syndrome [P.S.] are reported. The oldest brother has hearing loss (he has been deaf and mute since childhood) and has a large goiter. A thyroid scan revealed euthyroid multinodular goiter and a perchlorate test was performed, and reported abno...

Multiplicity of Resonances Equals Multiplicity of the Scattering Matrix

Extensions of the Multiplicity

The Multiplicity conjecture of Herzog, Huneke, and Srinivasan states an upper bound for the multiplicity of any graded k-algebra as well as a lower bound for Cohen-Macaulay algebras. In this note we extend this conjecture in several directions. We discuss when these bounds are sharp, find a sharp lower bound in case of not necessarily arithmetically Cohen-Macaulay one-dimensional schemes of 3-s...