A 1-prefix normal word is a binary word with the property that no factor has more 1s than the prefix of the same length; a 0-prefix normal word is defined analogously. These words arise in the context of indexed binary jumbled pattern matching, where the aim is to decide whether a word has a factor with a given number of 1s and 0s (a given Parikh vector). Each binary word has an associated set ...

The aim of bioequivalence studies is the evaluation of bioequivalence of pharmaceutical products. The products are usually two and basic pharmacokinetic parameters such as AUC, C max and t max are used. These studies aim at investigating the “closeness” of the distributions of the pharmacokinetic parameters (responses) for the two products, which is made mainly by comparing the average values o...

In this paper we construct a large class of new normal forms for Levi-nondegenerate real hypersurfaces in complex spaces. We adopt a general approach illustrating why these normal forms are natural and which role is played by the celebrated Chern-Moser normal form [CM74]. The latter appears in our class as the one with the ”maximum normalization” in the lowest degree. However, there are other n...

This paper describes and analyzes a method for computing border bases of a zero-dimensional ideal I . The criterion used in the computation involves specific commutation polynomials and leads to an algorithm and an implementation extending the one provided in [29]. This general border basis algorithm weakens the monomial ordering requirement for Gröbner bases computations. It is up to date the ...

1 2 D. ZAITSEV

Let δ(P) = (δ0, δ1, . . . , δd) be the δ-vector of an integral polytope P ⊂ R of dimension d. Following the previous work of characterizing the δvectors with ∑d i=0 δi ≤ 3, the possible δ-vectors with ∑d i=0 δi = 4 will be classified. And each possible δ-vectors can be obtained by simplices. We get this result by studying the problem of classifying the possible integral simplices with a given δ...

Very recently, the second author showed that the question whether an equation over a trace monoid has a solution or not is decid-able 11,12]. In the original proof this question is reduced to the solv-ability of word equations with constraints, by induction on the size of the commutation relation. In the present paper we give another proof of this result using lexicographical normal forms. Our ...

Matrix pencils, or pairs of matrices, may be used in a variety of applications. In particular, a pair of matrices (E,A) may be interpreted as the differential equation Ex′ + Ax = 0. Such an equation is invariant by changes of variables, or linear combination of the equations. This change of variables or equations is associated to a group action. The invariants corresponding to this group action...