Fourier methods for quasi‐periodic oscillations

Quasi‐periodic oscillations and invariant tori play an important role in the study of forced or coupled oscillators. This paper presents two new numerical methods for the investigation of quasi‐periodic oscillations. Both algorithms can be regarded as generalizations of the averaging and the harmonic (spectral) balance methods. The algorithms are easy to implement and require only minimal a priori knowledge of the system. Most importantly, the methods do not depend on an a priori co‐ordinate transformation. The methods are applied to a number of illustrative examples from non‐linear electrical engineering and the results show that the methods are efficient and reliable. In addition, these examples show that the presented algorithms can also continue through regions of sub‐harmonic (phase‐locked) resonance even though they are designed only for the quasi‐periodic case. Copyright © 2006 John Wiley & Sons, Ltd.     

Teaching meshes, subdivision and multiresolution techniques

In recent years, geometry processing algorithms that directly operate on polygonal meshes have become an indispensable tool in computer graphics, CAD/CAM applications, numerical simulations, and medical imaging. Because the demand for people that are specialized in these techniques increases steadily the topic is finding its way into the standard curricula of related lectures on computer graphics and geometric modeling and is often the subject of seminars and presentations. In this article we suggest a toolbox to educators who are planning to set up a lecture or talk about geometry processing for a specific audience. For this we propose a set of teaching blocks, each of which covers a specific subtopic. These teaching blocks can be assembled so as to fit different occasions like lectures, courses, seminars and talks and different audiences like students and industrial practitioners. We also provide examples that can be used to deepen the subject matter and give references to the most relevant work.     

Generalized notions of mind change complexity

Gold introduced the notion of learning in the limit where a class S is learnable iff there is a recursive machine M which reads the course of values of a function f and converges to a program for f whenever f is in S. An important measure for the speed of convergence in this model is the quantity of mind changes before the onset of convergence. The oldest model is to consider a constant bound on the number of mind changes M makes on any input function; such a bound is referred here as type 1. Later this was generalized to a bound of type 2 where a counter ranges over constructive ordinals and is counted down at every mind change. Although ordinal bounds permit the inference of richer concept classes than constant bounds, they still are a severe restriction. Therefore the present work introduces two more general approaches to bounding mind changes. These are based on counting by going down in a linearly ordered set (type 3) and on counting by going down in a partially ordered set (type 4). In both cases the set must not contain infinite descending recursive sequences. These four types of mind changes yield a hierarchy and there are identifiable classes that cannot be learned with the most general mind change bound of type 4. It is shown that existence of type 2 bound is equivalent to the existence of a learning algorithm which converges on every (also nonrecursive) input function and the existence of type 4 is shown to be equivalent to the existence of a learning algorithm which converges on every recursive function. A partial characterization of type 3 yields a result of independent interest in recursion theory. The interplay between mind change complexity and choice of hypothesis space is investigated. It is established that for certain concept classes, a more expressive hypothesis space can sometimes reduce mind change complexity of learning these classes. The notion of mind change bound for behaviourally correct learning is indirectly addressed by employing the above four types to restrict the number of predictive errors of commission in finite error next value learning (NV′′)—a model equivalent to behaviourally correct learning. Again, natural characterizations for type 2 and type 4 bounds are derived. Their naturalness is further illustrated by characterizing them in terms of branches of uniformly recursive families of binary trees.     

Nanoscale Plasmon‐Enhanced Spectroscopy in Memristive Switches

Resistive switching memories are nonvolatile memory cells based on nano‐ionic redox processes and offer prospects for high scalability, ultrafast write and read access, and low power consumption. In two‐terminal cation based devices a nanoscale filament is formed in a switching material by metal ion migration from the anode to the cathode. However, the filament growth and dissolution mechanisms and the dynamics involved are still open questions, restricting device optimization. Here, a spectroscopic technique to optically characterize in situ the resistive switching effect is presented. Resistive switches arranged in a nanoparticle‐on‐mirror geometry are developed, exploiting the high sensitivity to morphological changes occurring in the tightly confined plasmonic hotspot within the switching material. The focus is on electrochemical metallization and the optical signatures detected over many cycles indicate incomplete removal of metal particles from the filament upon RESET and suggest that the filament can nucleate from different positions from cycle to cycle. The technique here is nondestructive and the measurements can be easily performed in tunable ambient conditions and with realistic cell geometries.     

Transport properties of 1,1,1,2-tetrafluoroethane (R134a)

New equations for the thermal conductivity and the viscosity of R134a that are valid in a wide range of pressures and temperatures are presented. They were obtained through a theoretically based, critical evaluation of the available experimental data, which showed considerable inconsistencies between data sets, in particular in the vapor phase. In the critical region the observed enhancement in the thermal conductivity is well represented by a crossover model for the transport properties of fluids. Since thermodynamic properties enter into the calculation of the critical enhancement of the transport properties, a new fundamental equation for the critical region was developed also.Paper dedicated to Professor Joseph Kestin.     

Probabilistic analysis of the application of the cross ratio to model based vision

The probability density function for the cross ratio is obtained under the hypothesis that the four image points have independent, identical, Gaussian distributions. The density function has six symmetries which are closely linked to the six different values of the cross ratio obtained by permuting the quadruple of points from which the cross ratio is calculated. The density function has logarithmic singularities corresponding to values of the cross ratio for which two of the four points are coincident. The cross ratio forms the basis of a simple system for recognising or classifying quadruples of collinear image points. The performance of the system depends on the choice of rule for deciding whether four image points have a given cross ratio . A rule is stated which is computationally straightforward and which takes into account the effects on the cross ratio of small errors in locating the image points. Two key properties of the rule are the probabilityR of rejection, and the probabilityF of a false alarm. The probabilitiesR andF depend on a thresholdt in the decision rule. There is a trade off betweenR andF obtained by varyingt. It is shown that the trade off is insensitive to the given cross ratio . LetF _w =max _o {F}. ThenR, F _w are related approximately by , provided ^–1 F _w 4. In the equation, is the accuracy with which image points can be located relative to the width of the image, andr _F is a constant known as the normalised false alarm rate. In the range ^–1 F _w 4 the probabilitiesR andF _w are related approximately by . The value ofr _F is 14.37. The consequences of these relations between R and F_w are discussed. It is conjectured that the above general form of the trade off betweenR andF _w holds for a wide class of scalar invariants that could be used for model based object recognition. Invariants with the same type of trade off between the probability of rejection and the probability of false alarm are said to be nondegenerate for model based vision.     

Die Bewertung von Wurstwaren auf Grund des Verh?ltnisses Leimgebende Substanz: Gesamt-Stickstoffsubstanz

Ohne ZusammenfassungMitteilung aus der Nahrungsmittel-Untersuchungsstelle an der Technischen Hochschule in Braunschweig.