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Hertz (1882, 1895) established the state of stress and strain between two contacting elastic bodies. In this section we present two cases: (a) two crowned rollers and (b) two cylindrical rollers. Figure 9.1 shows two crowned rollers of different sizes in elastic contact. A plane tangent to each body at the touching point forms the tangent plane. If the bodies are now pressed together so that the collinear force is normal to the tangent plane, deformation takes place and a small contact area will replace the contact point O of the unloaded state. First, we will nd the size and shape of this contact area and distribution of normal pressure. Then we can calculate the stresses and strains that the interfacial pressure induces in the contacting members. Hertz assumed that (a) the two contacting bodies are isotropic and elastic in accordance with Hookes law, (b) the contact area is quite small compared to the radii of curvature of the undeformed bodies, and (c) only normal pressures that exist during contact are prevalent. Displacements in the xy plane and shearing tractions are neglected. In Fig. 9.1, the pressure distribution between the two contacting bodies form a semiellipsoid, and the surface of contact traced on the tangent plane will have an elliptical boundary. The intensity of pressure over the surface of contact is represented by the coordinates of the semiellipsoid x 2 y2 p = p0 1 - 2 - 2 a b

1 pi +1 2 ( x + y 2 )(3 xy + x y)dp 8 pi 3 pi +1 1 pi +1 = - ( x 2 + y 2 ) xy dp - ( x 2 + y 2 ) x ydp. pi 8 8 pi

from mathematics where a function gives one value. A relationship that has a m a x i m u m cardinality o f one in one direction and more than one (many) in the other direction is called a 1-M (read one-to-many) relationship. Both the

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sort in descending order, reverse the outcome of the comparison. When implementing IComparable<T>, you will usually pass the type name of the implementing class as a type argument. The following example reworks the preceding program so that it uses IComparable<T>. Notice it uses the generic List<T> collection rather than the non-generic ArrayList.

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A less-experienced colleague e-mails you this image and wants to know if you think a biopsy is indicated. A history and clinical image were not supplied. 1. 2. 3. 4. 5. There are annular-granular structures. There is asymmetry of color and structure. There is asymmetrical follicular pigmentation. The borders are poorly defined. The differential diagnosis includes a pigmented actinic keratosis vs lentigo maligna.

ing effects to improve the overall sound. Use effects judiciously, as you can seriously alter the character of the original sound le by going overboard on the effects processing.

A client may use the optional organization specific OAM frame to implement additional OAM functions not specified by the standard. Stations may accumulate performance parameters related to the RPR layer to enable the detection of developing failures before a total outage is detected. RPR error monitoring is based on the fairness frame errors. Performance monitoring counters are accumulated for: errored fairness frames, errored seconds, severely errored seconds, and unavailable seconds.

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