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## Geometrical problem solving — the state of the art c. 1635

### Redefining Geometrical Exactness (2001-01-01): 211-221 , January 01, 2001

The present chapter concludes my discussion of the early modern tradition of geometrical problem solving before Descartes. Problem solving constituted the primary context of Descartes’ geometrical studies to which Part II is devoted. His contributions, however, changed the theory and practice of geometrical problem solving in so fundamental a manner that they eclipsed many of the techniques, concepts, and concerns of the earlier tradition. It is therefore appropriate to conclude Part I by a sketch of the state of the art of geometrical problem solving around 1635, that is, just before Descartes published his innovations (and also before Fermat’s new techniques began to circulate among cognoscenti).

## Composite Embedding

### Holomorphic Q Classes (2001-01-01) 1767: 13-22 , January 01, 2001

This chapter is devoted to study the smooth properties of the *Q*_{p}-functions through characterizing a self-map φ of *D* such that the composition operator *C*_{φ} maps *Q*_{p} into *B*^{α} (the Bloch-type space) and vice versa.

## A Note on Minty Variational Inequalities and Generalized Monotonicity

### Generalized Convexity and Generalized Monotonicity (2001-01-01) 502: 240-246 , January 01, 2001

Some notions of generalized monotonicity for multi-valued mappings are characterized in terms of properties of the associated Minty variational inequalities. In particular, it is shown that the Minty variational inequality problem derived from a map *F* defined on a convex domain is solvable on any nonempty, compact, and convex subdomain if and only if *F* is properly quasimonotone.

## Grundlagen der Polyedertheorie

### Optimierung Operations Research Spieltheorie (2001-01-01): 31-50 , January 01, 2001

### Zusammenfassung

Unser Ziel ist es, die Geometrie von linearen Optimierungsaufgaben vollständig zu verstehen und daraus für die algebraische und arithmetische Lösung die richtigen Konsequenzen zu ziehen. Dementsprechend beschäftigen wir uns zunächst mit einer wichtigen Eigenschaft des Zulässigkeitsbereichs von linearen Optimierungsproblemen, der Konvexität.

## Generalization of the Berezin Formula to the Noncommutative Case

### Mathematical Notes (2001-01-01) 69: 262-268 , January 01, 2001

With the help of functional integrals in Fock space, under some analytical assumptions, we construct representations for exponents of quadratic functions of creation and annihilation operators with noncommuting coefficients.

## Implementation Issues

### Linear Programming (2001-01-01) 37: 125-150 , January 01, 2001

In the previous chapter, we rewrote the simplex method using matrix notation. This is the first step toward our aim of describing the simplex method as one would implement it as a computer program. In this chapter, we shall continue in this direction by addressing some important implementation issues.

## Wavelets

### Praktische Numerik mit Mathematica (2001-01-01): 103-136 , January 01, 2001

### Zusammenfassung

Der Name „Wavelet“bedeutet „kleine Welle“oder „Wellenpaket“. Wavelets können zur Analyse von Zeitsignalen eingesetzt werden, das sind Funktionen f: ℝ→ ℂ bei denen die unabhängige Variable die Bedeutung der Zeit hat. Die Waveletanalyse stellt in gewissem Sinne eine Erweiterung der Fourier-Analyse dar.

## Computational Studies

### Mathematical Programming and Financial Objectives for Scheduling Projects (2001-01-01) 38: 103-116 , January 01, 2001

As mentioned before, only optimal solution procedures for the resource investment problem have been presented so far making use of rather small test sets. Hence, we decided to adapt well established instances for the resource constrained project scheduling problem for our purposes. The project scheduling problem library PSPLIB (see page 51) provides a collection of systematically generated instances. We used the 480 instances with
*n* = 30
non-dummy activities and*K*= 4
resources. The resource limits of these instances have no meaning in our context, so we simply ignored them. The ProGen instances have different network complexities
*NC* ∈ 1.5, 1.8, 2.1
and different resource factors
*RF* ∈ 0.25, 0.5, 0.75, 1.0.

## Neighborhoods of an Ordinary Linear Differential Equation

### Computer Algebra in Scientific Computing CASC 2001 (2001-01-01): 107-121 , January 01, 2001

In this paper the notion of neighborhood of a linear ordinary differential equation with constant coefficients is introduced. The general concept of neighborhood is often used in Scientific Computation where involved data have limited accuracy. In this context we introduce the notion of pseudo-integral of a differential equation. Furthermore we use the notion of differential resultant in order to know the relations between the integrals of a linear ordinary differential equation with constant coefficients and the integrals of a linear ordinary differential equation in its neighborhood.