1. Linear series on curves 1.1. Terminology and notation 1.2. Morphisms from linear series; Castelnuovo’s genus bound 1.3. Linear series from morphisms 1.4. Relation between linear series and morphisms 1.5. Hermitian invariants; Weierstrass semigroups I 2. Weierstrass point theory 2.1. Hasse derivatives 2.2. Order sequence; Ramification divisor 2.3. D-Weierstrass points 2.4. D-osculating spaces...

In this paper, the universal approximation property of one of the most frequently used type of fuzzy systems is proved. The type of fuzzy system in the present work employs triangle-shaped fuzzy membership functions (TSMF) for its input variables. The proof of the universal approximation property does not use the Stone-Weierstrass theorem because the TSMFs are not closed for the product; instea...

We prove an effective Weierstrass Division Theorem for algebraic restricted power series with p-adic coefficients. The complexity of such power series is measured using a certain height function on the algebraic closure of the field of rational functions over Q. The paper includes a construction of this height function, following an idea of Kani. We apply the effective Weierstrass Division Theo...

The two main results in this paper are analogues of the Stone-Weierstrass theorem for real-valued functions, obtained by using different function space topologies. The first (Theorem 2.3) is a Stone-Weierstrass theorem for unbounded functions. The second (Theorem 3.6) is a theorem for bounded functions ; it is stronger than the usual theorem because the topology is larger than the uniform topol...

Let T be a compact Hausdorff topological space and let M denote an n–dimensional subspace of the space C(T ), the space of real–valued continuous functions on T and let the space be equipped with the uniform norm. Zukhovitskii [7] attributes the Basic Theorem to E.Ya.Remez and gives a proof by duality. He also gives a proof due to Shnirel’man, which uses Helly’s Theorem, now the paper obtains a...

We define the notion of rational presentation of a complete metric space, in order to study metric spaces from the algorithmic complexity point of view. In this setting, we study some representations of the space C[0, 1] of uniformly continuous real functions over [0,1] with the usual norm : ‖ f ‖∞= Sup{| f(x) |; 0 ≤ x ≤ 1}. This allows us to have a comparison of global kind between complexity ...

which are now called Bernstein polynomials, in order to present a short proof of the Weierstrass Approximation Theorem. The subsequent history is well documented, see, e.g., [29] for the period up to 1955, the monograph [18] published in 1953, and the survey article [9] which appeared on the occasion of the hundredth anniversary of the above paper by Bernstein. Since the latter publication prov...