The aim of the paper is twofold. First, some results of Shiota and Plaza-Mart́ın on Prym varieties of curves with an involution are generalized to the general case of an arbitrary automorphism of prime order. Second, the equations defining the moduli space of curves with an automorphism of prime order as a subscheme of the Sato Grassmannian are given.

The analytic calculation of the three-loop QCD β-function and anomalous dimensions within the minimal subtraction scheme in an arbitrary covariant guage is presented. The result for the β-function coincides with the previous calculation [1]. on leave from Institute for Nuclear Research (INR) of the Russian Academy of Sciences, Moscow 117312, USSR.

See [Oli04]. In [AdKech00], Adams and Kechris showed that the relation of equality on Borel sets (and therefore, any Borel equivalence relation whatsoever) is Borel reducible to the equivalence relation of Borel bireducibility. (In somewhat finer terms, they showed that the partial order of inclusion on Borel sets is Borel reducible to the quasi-order of Borel reducibility.) Their technique was...

The paper mentioned above is a contribution of the authors to volume 18(2002) of this journal, see [1] . Recently J. Domsta pointed out to us that the proof of Theorem 4.2 in that paper contains an error. The purpose of this note is to present a correct argument for it. §

On the basis of order statistics, Baker (2008) proposed a method for constructing multivariate distributions with fixed marginals. This is another representation of the Bernstein copula. According to the construction of Baker’s distribution, the Bernstein copula can be regarded as a finite mixture distribution. In this paper, we propose expectationmaximization (EM) algorithms to estimate the Be...

A new formula expressing explicitly the derivatives of Bernstein polynomials of any degree and for any order in terms of Bernstein polynomials themselves is proved, and a formula expressing the Bernstein coefficients of the general-order derivative of a differentiable function in terms of its Bernstein coefficients is deduced. An application of how to use Bernstein polynomials for solving high ...

This paper is devoted to the comparison of various shape properties of triangular Bézier surfaces and of their Bézier nets, such as polyhedral convexity, axial convexity and subharmonicity. In order to better compare these properties, the different notations used by different authors are unified. It also includes counterexamples for the results that are not true.  1999 Elsevier Science B.V. Al...

In this note we present a new characterization of Bernstein operators by showing that they are the only solution of a certain extremal relation. © 2006 Elsevier Inc. All rights reserved.

We discuss the long-time behavior of Andreoli's differential equation for genetic algebras and for Bernstein algebras and show convergence to an equilibrium in both cases. For a class of Bernstein algebras this equilibrium is determined explicitly.

Let B be the Borel σ-algebra of R, and let B be the Borel σ-algebra of [−∞,∞] = R ∪ {−∞,∞}: the elements of B are those subsets of R of the form B,B ∪ {−∞}, B ∪ {∞}, B ∪ {−∞,∞}, with B ∈ B. Let (X,A , μ) be a measure space. It is a fact that if fn is a sequence of A → B measurable functions then supn fn and infn fn are A → B measurable, and thus if fn is a sequence of A → B measurable functions...