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Historical Comments on Monge’s Ellipsoid and the Configurations of Lines of Curvature on Surfaces

Jorge SotomayorRonaldo A. Garcia — 2016

Antiquitates Mathematicae

This is an essay on the historical landmarks leading to the study of principal confgurations on surfaces in R^3 , their structural stability and further generalizations. Here it is pointed out that in the work of Monge, 1796, are found elements of the qualitative theory of differential equations, founded by Poincaré in 1881. Recent development concerning the space R^4 are mentioned. Two open problems are proposed at the end.

Note on stability estimation in sequential hypothesis testing

E. GordienkoJ. Ruiz de ChávezA. García — 2013

Applicationes Mathematicae

We introduce a quantitative measure Δ of stability in optimal sequential testing of two simple hypotheses about a density of observations: f=f₀ versus f=f₁. The index Δ represents an additional cost paid when a stopping rule optimal for the pair (f₀,f₁) is applied to test the hypothesis f=f₀ versus a "perturbed alternative" f=f̃₁. An upper bound for Δ is established in terms of the total variation distance between f₁(X)/f₀(X) and f̃₁(X)/f₀(X) with X∼f₀.

Semigroup-theoretical characterizations of arithmetical invariants with applications to numerical monoids and Krull monoids

Víctor BlancoPedro A. García-SánchezAlfred Geroldinger — 2010

Actes des rencontres du CIRM

Arithmetical invariants—such as sets of lengths, catenary and tame degrees—describe the non-uniqueness of factorizations in atomic monoids.We study these arithmetical invariants by the monoid of relations and by presentations of the involved monoids. The abstract results will be applied to numerical monoids and to Krull monoids.

Numerical semigroups with a monotonic Apéry set

José Carlos RosalesPedro A. García-SánchezJuan Ignacio García-GarcíaM. B. Branco — 2005

Czechoslovak Mathematical Journal

We study numerical semigroups S with the property that if m is the multiplicity of S and w ( i ) is the least element of S congruent with i modulo m , then 0 < w ( 1 ) < < w ( m - 1 ) . The set of numerical semigroups with this property and fixed multiplicity is bijective with an affine semigroup and consequently it can be described by a finite set of parameters. Invariants like the gender, type, embedding dimension and Frobenius number are computed for several families of this kind of numerical semigroups.

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