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## Groupoids

### Exploring Abstract Algebra With Mathematica® (1999-01-01): 252-320 , January 01, 1999

As we saw in chapter 1, there are several means by which Groupoids can be formed. Here we consider these methods in detail and consider all the available options.

## A Practical Estimation Technique for Spatial Distribution of Groundwater Contaminant

### Control of Distributed Parameter and Stochastic Systems (1999-01-01) 13: 55-62 , January 01, 1999

To predict the fate of groundwater contaminants, accurate spatially continuous information is needed. Because most field sampling of groundwater contaminants are not conducted spatially continuous manner, a special estimation technique is required to interpolate/extrapolate concentration distributions at unmeasured locations. A practical three-dimensional estimation method for *in situ* groundwater contaminant concentrations is introduced.

## Back Matter - Linear Optimization and Extensions

### Linear Optimization and Extensions (1999-01-01): 12 , January 01, 1999

## Against “Paradoxes”: A New Quantum Philosophy for Quantum Mechanics

### Quantum Structures and the Nature of Reality (1999-01-01) 7: 103-140 , January 01, 1999

It is a commonplace that XXth century physics has produced powerful new theories, such as Relativity and quantum mechanics, that upset the world view provided by XIXth century physics. But every physicist knows how difficult it may be to explain the basic aspects of these theories to people having a non-physical professional training. The main reason of this is that both Relativity and quantum mechanics are based on fundamental ideas that are not hard to grasp in themselves, but deeply contrast the primary categories on which our everyday thinking is based, so that it is impossible to place relativistic and quantum results within the framework suggested by ordinary intuition and common sense. Yet, despite this similarity, there are some relevant differences between the difficulties arising in Relativity and in quantum mechanics. In order to understand this point better, let us focus our attention on Special Relativity first (analogous arguments can be forwarded by considering General Relativity). Here, the strange links between space and time following from the even more strange assumption that the velocity of light is independent of the motion of the observer conflict with the very simple conception of space and time implicit in our daily practice (and explicitly stated in classical Physics, think of Newton’s “absolute space” and “absolute time”): but this conflict regards geometrical space-time models, not the very roots of our language, hence our thought. Then, let us consider quantum mechanics. Here it is a basic notion that properties of physical systems are *nonobjective*, in the sense that a property cannot be thought of as existing if a measurement of it is not performed. As Mermin [30] writes,

“it is a fundamental quantum doctrine that a measurement does not, in general, reveal a preexisting value of the measured property”.

## On certain exact relations for sojourn probabilities of a wiener process

### Ukrainian Mathematical Journal (1999-06-01) 51: 942-947 , June 01, 1999

New exact relations are proved for the sojourn probability of a Wiener process between two time-de-pendent boundaries. The proof is based on the investigation of the heat-conduction equation in the domain determined by these functions-boundaries. The relations are given in the form of series.

## On the Dido Problem and Plane Isoperimetric Problems

### Acta Applicandae Mathematica (1999-07-01) 57: 287-338 , July 01, 1999

This paper is a continuation of a series of papers, dealing with contact sub-Riemannian metrics on R^{3}. We study the special case of contact metrics that correspond to isoperimetric problems on the plane. The purpose is to understand the nature of the corresponding optimal synthesis, at least locally. It is equivalent to studying the associated sub-Riemannian spheres of small radius. It appears that the case of generic isoperimetric problems falls down in the category of generic sub-Riemannian metrics that we studied in our previous papers (although, there is a certain symmetry). Thanks to the classification of spheres, conjugate-loci and cut-loci, done in those papers, we conclude immediately. On the contrary, for the Dido problem on a 2-d Riemannian manifold (i.e. the problem of minimizing length, for a prescribed area), these results do not apply. Therefore, we study in details this special case, for which we solve the problem generically (again, for generic cases, we compute the conjugate loci, cut loci, and the shape of small sub-Riemannian spheres, with their singularities). In an addendum, we say a few words about: (1) the singularities that can appear in general for the Dido problem, and (2) the motion of particles in a nonvanishing constant magnetic field.

## A Cellular Triangle Containing a Specified Point

### Graphs and Combinatorics (1999-06-01) 15: 239-247 , June 01, 1999

### Abstract.

Let *P* be a set of finite points in the plane in general position, and let *x* be a point which is not contained in any of the lines passing through at least two points of *P*. A line *l* is said to be a *k-bisector* if both of the two closed half-planes determined by *l* contain at least *k* points of *P*. We show that if any line passing through *x* is a
-bisector and does not contain two or more points of *P*, then there exist three points *P*_{1}, *P*_{2}, *P*_{3} of *P* such that Δ*P*_{1}*P*_{2}*P*_{3} contains *x* and does not contain points of *P* in its interior, and such that each of the lines passing through two of them is a
-bisector.

## Integration im ℝ n

### Analysis mit Mathematica und Maple (1999-01-01): 294-331 , January 01, 1999

### Zusammenfassung

Bei der Einführung des Riemannschen Integrals im ℝ^{n} müssen wir zuerst die Begriffe Intervall, Partition und Feinheit übertragen.

## Der Vergleich unabhängiger Stichproben gemessener Werte

### Angewandte Statistik (1999-01-01): 326-402 , January 01, 1999

### Zusammenfassung

Wissen wir einiges über die zu erwartende Heterogenität innerhalb der Grundgesamtheit, die wir untersuchen wollen, dann gibt es wirksamere Verfahren als die Auswahl zufälliger Stichproben (vgl. [132]). Wichtig ist die Verwendung *geschichteter* oder stratifizierter Stichproben; hier wird die Grundgesamtheit in relativ homogene Teilgrundgesamtheiten, *Schichten oder Strata* unterteilt, und zwar jeweils nach den Gesichtspunkten, die für das Studium der zu untersuchenden Variablen von Bedeutung sind. Geht es um die Voraussage von Wahlergebnissen, dann wird man die Stichprobe so wählen, daß sie ein verkleinertes Modell der Gesamtbevölkerung darstellt. Dabei werden in erster Linie Altersschichtung, das Verhältnis zwischen Männern und Frauen und die Einkommensgliederung berücksichtigt. So gliedern sich die Erwerbstätigen in der BRD im April 1990 (Statistisches Jahrbuch 1992, S. 114) nach der Stellung im Beruf etwa in 37% Arbeiter, 43% Angestellte, 9% Selbständige und 9% Beamte sowie 2% Mithelfende Familienangehörige*. Stratifizierung verteuert meist die Stichprobenerhebung, ist jedoch ein wichtiges Hilfsmittel. Der Stichprobenumfang pro Schicht ist um so kleiner, je kleiner die Schicht, je kleiner die Varianz und je teurer die Erhebung in der betreffenden Schicht ist. Einige Formeln sind in Übersicht 61 zusammengestellt.

## Hurst’s analysis to detect fluctuation of the jet in a two-dimensional fluidized bed

### Wuhan University Journal of Natural Sciences (1999-06-01) 4: 233-236 , June 01, 1999

The experimental study of vertical jet in a two-dimensional fluidized bed is presented. The time series of vertical jet penetration depth are acquired by image processing. The fluctuation of jet which is studied by means of Hurst’s analysis becomes weaker with increase in jet velocity, fluidization number, particle diameter and static bed height. They are found that the signal is persistent and the fractal dimensional of vertical jet is between 1. 19 and 1. 64.