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## On the completion of measures

### Archiv der Mathematik (1988-05-01) 50: 259-263 , May 01, 1988

## The Hilbert function of generic plane sections of curves of ℙ3

### Inventiones mathematicae (1988-06-01) 91: 253-258 , June 01, 1988

### Summary

A characteristic condition is given on a zero-dimensional differentiable 0-sequence*H={h*_{i}}_{i≧0},*h*_{1}≦3, in order to be the Hilbert function of a generic plane section of a reduced irreducible curve of ℙ^{3}, hence of points of ℙ^{2} with the uniform position property. In this way an answer is given to some question stated by Harris in [Ha_{2}].

The result is obtained by constructing a smooth irreducible arithmetically Cohen-Macaulay curve in ℙ^{3} whose generic plane section has an assigned Hilbert function satisfying that condition.

## Mutual derivability of operations in program algebras. I

### Cybernetics (1988-01-01) 24: 41-47 , January 01, 1988

## Weakly compact operators on Jordan triples

### Mathematische Annalen (1988-08-01) 281: 451-458 , August 01, 1988

## A fluctuation theorem for solutions of certain random evolution equations

### Probability Theory and Mathematical Statistics (1988-01-01) 1299: 339-347 , January 01, 1988

## Stochastic mechanics of free scalar fields

### Stochastic Mechanics and Stochastic Processes (1988-01-01) 1325: 40-60 , January 01, 1988

## Regularity of generalized solutions of Monge-Ampère equations

### Mathematische Zeitschrift (1988-09-01) 197: 365-393 , September 01, 1988

## Probability Theory of Completely Labelled Random Multigraphs

### Graphs as Structural Models (1988-01-01): 115-156 , January 01, 1988

The roots of graph theory are obscure. The famous eighteenth-century Swiss mathematician Leonard Euler was perhaps the first to solve a problem using graphs when he was asked to consider the problem of the Königsberg bridges (in the 1730s). Problems in (finite) graph theory are often enumeration problems, and thus can become rather intricate to be solved. However, in the late 1950s and early 1960s the Hungarian mathematicians Paul Erdös and Alfred Rényi founded the theory of random graphs and used probabilistic methods (limit theorems) to by-pass enumeration problems. These problems also became secondary with the emergence of powerful computers. Thus, perhaps no topic in mathematics has enjoyed such explosive growth in recent years as graph theory. This stepchild of combinatorics and topology has emerged as a fascinating topic for research in its own right. Moreover, during the last two decades, calculus of graph theory has proved to be a valuable tool in applied mathematics and life sciences as well. Using graph-theoretic concepts, scientists study properties of real systems by modelling and simulation. The aim of graph-theoretic investigations is, in fact, the simplest topological structure after that of isolated points: The structure of a graph is that of “points” or “vertices”, and “edges” or “lines”.

## Divergence in measure of multiple Fourier series

### Mathematical notes of the Academy of Sciences of the USSR (1988-08-01) 44: 589-592 , August 01, 1988

## Zeros of orthogonal polynomials on harmonic algebraic curves

### Orthogonal Polynomials and their Applications (1988-01-01) 1329: 320-327 , January 01, 1988

Starting with an infinite, complex, positive-definite, hermitian matrix, we build a triangular +1 matrix $$\hat D_n$$ generalising the tridiagonal one of the Hankel case. We apply this construction to moments matrices arising from distributions on curves Im(A(z))=0, A(z) θ C[z]. We study the matrix $$A\left( {\hat D_n } \right)$$ and its relationship with the truncated matrix of the correspondinding symmetric operator and we give conditions for the zeros to be on the curve.