Let E/F be a quadratic extension of p-adic fields. We compute the multiplicity of the space of SL2(F )-invariant linear forms on a representation of SL2(E). This multiplicity varies inside an L-packet similar in spirit to the multiplicity formula for automorphic representations due to Labesse and Langlands.

The j-multiplicity is an invariant that can be defined for any ideal in a Noetherian local ring (R, m). It is equal to the Hilbert-Samuel multiplicity if the ideal is m-primary. In this paper we explore the computability of the j-multiplicity, giving another proof for the length formula and the additive formula.

employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of neumann two-point boundary valuesturm-liouville type equations. using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.

If A is an nxn complex matrix and λ is an eigenvalue of A with geometric multiplicity k, then λ is in at least k of the Geršgorin discs Di of A. Let k, r, t be positive integers with k ≤ r ≤ t . Then there is a t x t complex matrix A and an eigenvalue λ of A such that λ has geometric multiplicity k and algebraic multiplicity t, and λ is in precisely r Geršgorin Discs of A. Some examples and rel...

In this paper, we present a theoretical approach for the problem of learning multiplicity tree automata. These automata allows one to define functions which compute a number for each tree. They can be seen as a strict generalization of stochastic tree automata since they allow to define functions over any field K. A multiplicity automaton admits a support which is a non deterministic automaton....

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...

using the fixed point theorem in a‎ ‎cone‎, ‎the existence and multiplicity of radial convex solutions of‎ ‎singular system of monge-amp`{e}re equations are established‎.‎