We study the multiplicity modulo 2 of real analytic hypersurfaces. We prove that, under some assumptions on the singularity, the multiplicity modulo 2 is preserved by subanalytic bi-Lipschitz homeomorphisms of R. In the first part of the paper, we find a subset of the tangent cone which determines the multiplicity mod 2 and prove that this subset of S is preserved by the antipodal map. The stud...

We propose an extension of visibly pushdown automata by means of weights (represented as positive integers) associated with transitions, called visibly pushdown automata with multiplicities. The multiplicity of a computation is the product of the multiplicities of the transitions used along this computation. The multiplicity of an input is the sum of the ones of all its successful computations....

We analyze the criterion of the multiplicity-free theorem of representations [5, 6] and explain its generalization. The criterion is given by means of geometric conditions on an equivariant holomorphic vector bundle, namely, the “visibility” of the action on a base space and the multiplicity-free property on a fiber. Then, several finite dimensional examples are presented to illustrate the gene...

‎By considering a degenerate $p(x)-$Laplacian equation‎, ‎a generalized compact embedding in weighted variable‎ ‎exponent Sobolev space is presented‎. ‎Multiplicity of positive solutions are discussed by applying fibering map approach for the‎ ‎corresponding Nehari manifold‎. 

We examine the phenomenology of particle multiplicity distributions, with special emphasis on the low multiplicities that are a background to the study of rapidity gaps. In particular, we analyze the multiplicity distribution in a rapidity interval between two jets, using the HERWIG QCD simulation with some necessary modifications. The distribution is not of the “negative binomial” form, and di...

We find upper and lower bounds of the multiplicities of irreducible admissible representations π of a semisimple Lie group G occurring in the induced representations IndH τ from irreducible representations τ of a closed subgroup H. As corollaries, we establish geometric criteria for finiteness of the dimension of HomG(π, Ind G H τ) (induction) and of HomH(π|H , τ) (restriction) by means of the ...

Models generalizing the su(2) XX spin-chain were recently introduced. These XXC models also have an underlying su(2) structure. Their construction method is shown to generalize to the chains based on the fundamental representations of the Am Lie algebras. Integrability of the new models is shown in the context of the quantum inverse scattering method. Their R-matrix is found and shown to yield ...

The heart of intersection theory resides in the following situation. Given a purely d-dimensional analytic set X, and subsets V and W intersecting at a point x ∈ X, V and W given by i and j equations respectively where i + j = d, then the correct number of times to count x is the multiplicity of the ideal I in the local ring of X at x, where I is the ideal generated by the equations of V and W....

When asked the direction between Phildadelphia and Rome, most people err. They say that Philadelphia is north of Rome when in fact, it is south of Rome. This cannot be dismissed as the weather, because when asked the direction between Boston and Rio, a majority of people erroneously say that Boston is east of Rio. Nor are these errors a simple consequence of randomness, nor of ignorance of geog...