A mixed boundary-value problem of elasticity with parabolic boundary

Summary The mixed boundary-values problem of elasticity with parabolic boundary when the prescribed displacement is parabolic has been reduced to the solution of the non-homogeneous Hilbert problem following the method of complex variable. The result has been compared with that obtained byParia [5] for parabolic boundary with prescribed constant displacement as a particular case.

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Zusammenfassung Das gemischte Randwertproblem der Elastizitätstheorie wird für parabolische Berandung auf die Lösung des inhomogenen Hilbert-Problems unter Benützung der komplexen Methode zurückgeführt. Die Randverschiebung wird durch ein Polynom zweiten Grades dargestellt. Das Ergebnis wird mit dem vonParia [5] verglichen, das als Sonderfall konstante Verschiebungen am parabolischen Rand vorschreibt.

     

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.

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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.

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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.

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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.

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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.     

释放你的内在潜能

技术工人在当今的制造环境中是必不可少的。通过运用你的IT知识,可以消除时间和精力上的浪费。     

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.

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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.