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.     

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.     

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.     

Search for Superconductivity in Ultra-dense Deuterium D(?1) at Room Temperature: Depletion of D(?1) at Field Strength >0.05 T

Ultra-dense deuterium D(?1) is expected to be both a superfluid and a superconductor as shown by recent theoretical research. Condensed D(?1) can be deposited on surfaces by a source which produces a stream of clusters. A magnetic field strongly influences the type of material formed. Very little of D(?1) and of the form D(1), which is strongly coupled to D(?1), exists on the magnet surface or within several mm from the magnet surface. Even the formation of D(?1) on the source emitter is strongly influenced by a magnetic field, with a critical field strength in the range 0.03?C0.07 T. Higher excitation levels D(2) and D(3) dominate in a magnetic field. The excitation level D(2) is now observed for the first time. The removal of D(?1) and D(1) in strong magnetic fields is proposed to be due to a Meissner effect in long D(?1) clusters by large-orbit electron motion. The lifting of long D(?1) clusters above the magnet surface is slightly larger than expected, possibly due to the coupling to D(1). The previously reported oscillation between D(?1) and D(1) in an electric field is proposed to be due to destruction of D(?1).     

Correcting for contact geometry in Seebeck coefficient measurements of thin film devices

Driven by promising recent results, there has been a revived interest in the thermoelectric properties of organic (semi)conductors. Concomitantly, there is a need to probe the Seebeck coefficient S of modestly conducting materials in thin film geometry. Here we show that geometries that seem desirable from a signal-to-noise perspective may induce systematic errors in the measured value of S, S_m, by a factor 3 or more. The enhancement of S_m by the device geometry is related to competing conduction paths outside the region between the electrodes. We derive a universal scaling curve that allows correcting for this and show that structuring the semiconductor is not needed for the optimal electrode configuration, being a set of narrow, parallel strips.