A B S T R A C TLet a circular flat punch penetrate a finitely thick slab resting on a rigid foundation. Lebedev and Ufliand showed that the determination of the stresses and displacements can be reduced to solving the Fredholm integral equationWe show how to reduce this integral equation to a Cauchy system in which ,~. plays the role of the time-like variable. Numerical experiments show the computational efficacy;
Z U S A M M E N F A S S U N GMan lasse einen flachen, kreisrunden Durchschlag in eine auf einer steifen Unterlage ruhenden Platte yon endlicher Dicke eindringen. Lebedeff und Ufliand haben gezeigt wie das Bestimmen der Drticke und Verschiebungen zuriickgefiihrt werden kann auf die Losung der Integralgleichung yon Fredholm, u(t) = 0 ( t ) + 2 k(t, y, 2)u(y)dy, 0 <. t.<~ 1.Wir zeigen, wie man dieses Problem auf ein Cauchysystem reduziert, worin der Parameter t die Rolle der Zeit spielt. Ein numerisches Beispiel illustriert die digitale L6sbarkeit.
SUMMARY
Specifically stained features in microscopic images rarely have a unique range of grey levels which would permit selection of the features by simple thresholding. The spaces between features and immediately surrounding them are often as dark or darker than the more lightly stained features. An algorithm for minima equalization which facilitates the extraction and segmentation of such features was designed and is explained in intuitive terms. It is applied to the analysis of cross‐sections of peripheral myelinated nerve fibres. It is shown that the binary image obtained can be combined with a gradient image to give a binary image which accurately reflects the thickness of the myelin in the original image. Using silver‐impregnated nerve endings and bile canaliculi stained for thiamine pyrophosphatase, binary images like those prepared manually from thick specimens using a camera lucida can be obtained using the minima equalization procedure. The image processor is used to develop a composite image by combining images at various focal planes through the thick specimen. This image is then processed to obtain the binary image.
A conical punch presses into an elastic layer resting on a rigid foundation. Precision numerical results for the radius of the circle of contact, the force required, and the displacement of the center of the punch are presented.
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