Approximation mit Exponentialsummen

Zusammenfassung Für die Approximation mit Exponentialsummen ist die beste Approximation imTschebyscheffschen Sinne eindeutig, abgesehen von bisher nicht erkannten Ausnahmen. Eindeutigkeit liegt dagegen immer bei der Anpassung mit positiven Exponentialsummen vor. Daß diese Familie eine andere Struktur hat als die bekannten Verallgemeinerungen linearer Funktionenfamilien, zeigt sich am Charakter des Alternantenkriteriums.

---

Summary In this paper we investigate the approximation by sums of exponentials in the sense ofChebyshev. The best approximation is shown to be unique apart from exceptions not previously recognized. However, there is always uniqueness, when only sums of positive exponentials are considered. This family has a structure which is different from that of other generalizations of linear families of functions. This feature is reflected in the criterion on the alternations of the error curve.

---

---

Kernforschungszentrum Karlsruhe, Institut für Neutronenphysik und Reaktortechnik     

Some theorems of the eddy-current theory

Contents In the paper, theorems for the electric vector potentialT and magnetic scalar potentialU are discussed, which occur in the boundary-value problems for eddy currents induced in a conducting block by an external magnetic field. Uniqueness of the solution is examined. An integral representation of the scalar potentialU is derived for a nonmagnetic conductor. It is shown that for a thin metallic shell the integrodifferential equation results from general formulas related to the block.

---

Einige Theoreme der Wirbelstromtheorie

Übersicht In der Arbeit werden drei Theoreme für das elektrische VektorpotentialT und das magnetische SkalarpotentialU beschrieben, die in den Randwertaufgaben für in einem metallischen Block durch das äußere magnetische Feld induzierte Wirbelströme auftreten. Es wird bewiesen, daß eine solche Randwertaufgabe eine eindeutige Lösung hat, wenn das Vektorpotential auf dem Rand gleich Null ist. Eine Integralrepräsentation des Skalarpotentials wird abgeleitet. Es wird gezeigt, daß die Integrodifferentialgleichung für eine dünne metallische Hülle aus allgemeinen, den Block betreffenden Formeln hervorgeht.

---

List of principal symbols e coordinate unit vector - H magnetic intensity - J current density - T electric vector potential - U magnetic scalar potential - permeability - conductivity - V boundary of regionV     

Residual encoder-decoder up-sampling for structural preservation in noise removal

Multimedia Tools and Applications - While denoising 3D MRI, structural preservation is a very critical process in the medical region. However, Rician noise in MRI has affected the image quality...     

Korrosion von ölgefeuerten Zentralheizungskesseln

Corrosion of oil-fired domestic boilers Depending on the surface temperature of the flue gas side the corrosion of oil fired domestic boilers proceeds either mainly by acid corrosion or by oxygen corrosion:

• – At surface temperatures of 60°C and higher the corrosion mechanism of acid corrosion prevails and the corrosion rates amount to 0.1–0.3 mm/year (values referred to continuous burner operation). The corrosion products consist of soluble iron(II)- and iron(III)sulfates. Higher corrosion rates can be attributed to an appreciable catalytic formation of sulfur trioxide on the corrosion products formed on the convective heating surfaces.
• – At surface temperatures of 40°C the mechanism of oxygen corrosion already dominates and the corrosion rates are about ten times higher (1.5–3 mm/year, referred to continous burner operation). The high portion of ioron oxide hydrates, especially goethit (α-FeOOH), makes the corrosion products difficult to remove.
• – Distinctly reduced service lives are also expected for the so called reduced temperature boilers (“Niedertemperaturkessel”) and low temperature boiers (“Tieftemperaturkessel”): According to the manufacturers these boilers may be operated at boiler water temperatures well below 60°C, as they are equipped with constructive measures to enhance the surface temperature on the flue gas side. However, these measures are only fully effective under stationary conditions.

Some of the results were obtained from weight loss measurements on test specimen made from St 35.8 and gray cast iron, that were exposed to the flue gases of an oil fired experimental boiler. Other important results come from field measurements of the sulfuric acid content of about 30 boilers that are in practical use.     

A prototype scanning stylus profilometer for rapid measurement of small surface areas

A novel stylus based profiling instrument has been developed for rapid measurement of small surface areas. Outlined in the following paper are some of the key features of the prototype system including the wideband stylus pick-up and the dedicated scanning traverse mechanism. In addition, some preliminary results obtained by scanning the instrument over several different surfaces are presented.     

Hierarchical classification of protein function with ensembles of rules and particle swarm optimisation

This paper focuses on hierarchical classification problems where the classes to be predicted are organized in the form of a tree. The standard top-down divide and conquer approach for hierarchical classification consists of building a hierarchy of classifiers where a classifier is built for each internal (non-leaf) node in the class tree. Each classifier discriminates only between its child classes. After the tree of classifiers is built, the system uses them to classify test examples one class level at a time, so that when the example is assigned a class at a given level, only the child classes need to be considered at the next level. This approach has the drawback that, if a test example is misclassified at a certain class level, it will be misclassified at deeper levels too. In this paper we propose hierarchical classification methods to mitigate this drawback. More precisely, we propose a method called hierarchical ensemble of hierarchical rule sets (HEHRS), where different ensembles are built at different levels in the class tree and each ensemble consists of different rule sets built from training examples at different levels of the class tree. We also use a particle swarm optimisation (PSO) algorithm to optimise the rule weights used by HEHRS to combine the predictions of different rules into a class to be assigned to a given test example. In addition, we propose a variant of a method to mitigate the aforementioned drawback of top-down classification. These three types of methods are compared against the standard top-down hierarchical classification method in six challenging bioinformatics datasets, involving the prediction of protein function. Overall HEHRS with the rule weights optimised by the PSO algorithm obtains the best predictive accuracy out of the four types of hierarchical classification method.     

USE of Railway Analysis Tools from an Australian Perspective

The functions of Australia’s railways are divided between the delivery of suburban passenger railway services, long distance general and intermodal freight services and regional bulk commodity haulage. There is a national interest in the efficient carriage of export freight flows because Australia is a major trading nation. Australia’s railways are expected play their part in hauling export commodities. Unsurprisingly, there are conflicting demands on these railways. Hence, universities, and the industry itself, are directing research and investigation effort into policy, planning, engineering, operational and human factors matters. A question which then arises is what means could be used to analyse the problems identified during this research and investigation. This paper is thus concerned with the inter-relationships between the planning, engineering and operations of railways in Australia. It identifies four areas of analysis associated with the planning and development of railway infrastructure and operations. It then discusses a range of analytical tools which could be applied to different components of these analytical areas and critiques their appropriateness from an Australian perspective. Having made this assessment, the paper uses a recent Australian case study to show how analytical tools could be used and what lessons might be learnt from the process. Figure Use of Railway Analysis Tools from an Australian Perspective

On finite dynamic equations for fluid-saturated porous media

Summary The paper concerns the relations between two principally different approaches to the formulation of momentum balance equations in porous media theories, namely, the dynamic approach similar to Biot's theory and the modern approach as a result of mixture theories extended by the concept of volume fractions. In particular, it is shown that both approaches necessarily lead to the same type of momentum balance equations and furthermore contain, in a certain sense, within the geometrically linear case, the well-known classical equations of Biot's theory.     

Electromagnetic field diffusion, θ-functions,and image solutions

Contents We discuss some initial and boundary value problems of one-dimensional electromagnetic field diffusion. The solutions can be given by infinite series in two essentially different (however equivalent) forms, one being the usual Fourier-expansion and the other one being an infinite series of Gaussian exponentials or related functions (as for instance error-functions). The second form can be obtained by using infinitely many images to fulfill initial and boundary conditions. Finally the mathematical relations between the two equivalent types of solutions are discussed in terms of -functions and their transformation properties. The existence of the solutions in these two different forms is very interesting from a numerical point of view also.

---

Die Diffusion elektromagnetischer Felder, -Funktionen und Spiegelungsmethoden

Übersicht Es werden einige Anfangs- und Randwertprobleme eindimensionaler elektromagnetischer Felddiffusion erörtert. Die Lösungen können in zwei wesentlich verschiedenen (jedoch gleichwertigen) Formen angegeben werden, erstens in Form üblicher Fourier-Reihen und zweitens in Form unendlicher Reihen von Gaußschen Exponentialfunktionen oder damit verwandter Funktionen (z.B. Fehlerfunktionen). Diese zweite Form der Lösungen läßt sich durch die Anwendung unendlich oft wiederholter Spiegelung zur Erfüllung der Rand- und Anfangsbedingung anschaulich interpretieren. Abschließend werden die beiden Lösungstypen mit Hilfe von -Funktionen und deren Transformationseigenschaften erläutert. Die Verfügbarkeit der Lösungen in beiden Formen ist auch numerisch sehr interessant.

     

An Automated Brain Image Analysis System for Brain Cancer using Shearlets

In this paper, an Automated Brain Image Analysis (ABIA) system that classifies the Magnetic Resonance Imaging (MRI) of human brain is presented. The classification of MRI images into normal or low grade or high grade plays a vital role for the early diagnosis. The Non-Subsampled Shearlet Transform (NSST) that captures more visual information than conventional wavelet transforms is employed for feature extraction. As the feature space of NSST is very high, a statistical t-test is applied to select the dominant directional sub-bands at each level of NSST decomposition based on sub-band energies. A combination of features that includes Gray Level Co-occurrence Matrix (GLCM) based features, Histograms of Positive Shearlet Coefficients (HPSC), and Histograms of Negative Shearlet Coefficients (HNSC) are estimated. The combined feature set is utilized in the classification phase where a hybrid approach is designed with three classifiers; k-Nearest Neighbor (kNN), Naive Bayes (NB) and Support Vector Machine (SVM) classifiers. The output of individual trained classifiers for a testing input is hybridized to take a final decision. The quantitative results of ABIA system on Repository of Molecular Brain Neoplasia Data (REMBRANDT) database show the overall improved performance in comparison with a single classifier model with accuracy of 99% for normal/abnormal classification and 98% for low and high risk classification.