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## The Marquis and the Land-Agent; A Tale of the Eighteenth Century

### Pi: A Source Book (2000-01-01): 258-270 , January 01, 2000

*There* is a well-known story about the late Archbishop Temple, that he once had to listen to a sermon by a youthful and inexperienced clergyman, and to dine with him afterwards; the young man, by way of making conversation during the meal, ventured to remark, “ I think, my lord, that I chose a good text for my sermon ”. Instantly there came the grim reply, “ There was nothing wrong with the text ”. It may be that the consequence of my having selected a seductive title which does not possess a very close connection with the actual subject of my address will be that, when we adjourn presently, I may get the impression that my audience has consisted entirely of archbishops.

## Romeo und Julia, spontane Musterbildung und Turings Instabilität

### Alles Mathematik (2000-01-01): 77-95 , January 01, 2000

### Zusammenfassung

Kristalle, Schneeflocken, Seifenblasen, Wasserwellen, Dünen, Gebirgstäler, Tannenzapfen, Embryonalentwicklung, Sonnenblumen, Zebrastreifen, Herzschlag und Nervenzittern: Nahezu überall scheinen geordnete Strukturen und Muster, Regelmäßigkeiten wie „von selbst“ zu entstehen. Dieses „von selbst“: Klingt das nicht nach einer Ausrede, nach Nicht-Wissen oder Nicht-Wissen-Wollen? Also fragen wir erst recht: Wie funktioniert denn dieses „von selbst“, diese „Selbstorganisation“? Wie vermag Gestalt und Form sich hervorzuheben, sich zu bilden und zu entwickeln aus gleichförmigem Einerlei? Wie kann sich solche Bildung behaupten und entfalten gegen die allgegenwärtigen Kräfte des Zerfließens und des Zurücksinkens in entropische Gleichmacherei und homogene Formlosigkeit? Und so könnten wir immer weiter fragen und formulieren, verwundert und ratlos.

## Structural Identification of Nonlinear Coefficient Functions in Transport Processes through Porous Media

### Lectures on Applied Mathematics (2000-01-01): 157-175 , January 01, 2000

Mathematical models provide the starting point for the simulation of complex processes, which arise in the natural and engineering sciences. Characteristic properties of the considered systems are represented by model parameters or coefficients. These have to be determined by experiments. If the coefficients are not measured directly, as direct measurements are not possible or do not lead to satisfying results, numerical identification procedures have to be applied.

## Front Matter - Polytopes — Combinatorics and Computation

### Polytopes — Combinatorics and Computation (2000-01-01): 29 , January 01, 2000

## Integration with respect to local time

### Potential Analysis (2000-12-01) 13: 303-328 , December 01, 2000

Let
$$\left( {L_t^x ;x \in \mathbb{R},t \geqslant 0} \right)$$
be the local time process of a linear Brownian motion *B*. We integrate the Borel functions on
$$\mathbb{R}_ \times \mathbb{R}_ + $$
with respect to
$$\left( {L_t^x ;x \in \mathbb{R},t \geqslant 0} \right)$$
. This allows us to write Itôrs formula for new classes of functions, and to define a local time process of *B* on any borelian curve. Some results are extended from deterministic to random functions.

## Lower Bounds on Strip Discrepancy for Nonatomic Colorings

### Monatshefte für Mathematik (2000-09-01) 130: 311-328 , September 01, 2000

### Abstract.

A method of proof is given for obtaining lower bounds on strip discrepancy when the distributions do not have atoms. Partition the unit square
into an
chessboard of
congruent square pixels, where *n* is even. Color
of the pixels red, and the rest blue. For any convex set *A*, let
be the difference between the amounts of red and blue areas in *A*. Under a technical local balance condition, we prove there must be a strip *S*, of width less than
, for which
, where *c* is a positive constant, independent of *n* and the coloring. The proof extends methods discovered by Alexander and further developed by Chazelle, Matoušek, and Sharir. Integral geometric notions figure prominently.

## An Affordable Approach for Robust Design of Thick Laminated Composite Structure

### Optimization and Engineering (2000-09-01) 1: 305-322 , September 01, 2000

A systematic and affordable approach is proposed for the robust design of thick laminated composite structures. Our approach integrates the principles of the Robust Concept Exploration Method (RCEM) for designing complex engineering systems and the hierarchical multi-level optimization procedure for managing the complexity of composite structure optimization. Foundational to the proposed approach is the use of Design of Experiments (DOE) techniques and the Response Surface Methodology (RSM) for improving computational efficiency in using high fidelity design simulations; and the use of the robust design method for improving the quality of a product that is insensitive to potential variations of design parameters. Our approach is illustrated through the design of a laminated composite femoral component for hip joint arthroplasty. The solution yields the robust design of a composite hip implant, which is applicable for a range of bone stiffness, thereby eliminating the need to design specifically for an individual.

## The vanishing theorems

### Strong Shape and Homology (2000-01-01): 269-283 , January 01, 2000

In general, the computation of higher derived limits lim^{n}*X* of an inverse system of modules is very difficult. Therefore, most applications of these functors depend on the information whether lim^{n}*X* vanishes or not. Consequently, it is very important to have conditions, which imply lim^{n}*X* = 0, as well as conditions, which imply lim^{n}*X* ≠ O. This section is devoted to both cases.

## Simple zeropotent paramedial groupoids are balanced

### Czechoslovak Mathematical Journal (2000-06-01) 50: 397-399 , June 01, 2000

This short note is a continuation of [1] and [2] and its purpose is to show that every simple zeropotent paramedial groupoid containing at least three elements is strongly balanced in the sense of [4].

## A Hierarchy of Modal Event Calculi: Expressiveness and Complexity

### Advances in Temporal Logic (2000-01-01) 16: 1-20 , January 01, 2000

We consider a hierarchy of modal event calculi to represent and reason about partially ordered events. These calculi are based on the model of time and change of Kowalski and Sergot’s Event Calculus (*EC*): given a set of event occurrences, *EC* allows the derivation of the maximal validity intervals (MVIs) over which properties initiated or terminated by those events hold. The formalisms we analyze extend *EC* with operators from modal logic. They range from the basic Modal Event Calculus *(MEC)*, that computes the set of all current MVIs (MVIs computed by *EC)* as well as the sets of MVIs that are true in some/every refinement of the current partial ordering of events (◊-/□;-MVIs), to the Generalized Modal Event Calculus (*GMEC*),that extends *MEC* by allowing a free mix of boolean connectives and modal operators. We analyze and compare the expressive power and the complexity of the proposed calculi, focusing on intermediate systems between *MEC* and *GMEC*. We motivate the discussion by using a fault diagnosis problem as a case study.