Curvature Centre

The aminolysis of Y-phenyl X-benzoates by piperidine in 20 mol% DMS0-H20 at 25 °C proceeded, on the basis of a curved Brpnsted-type plot, via a zwitterionic tetrahedral intermediate with a change in the RDS the curvature centre of the plots was at p Ka = 6.4 regardless of the electronic nature of the substituent X in thebenzoyl moiety 27 The rates of aminolysis of a series of Y-phenyl benzoates by acylic secondary amines were compared with new results for similar reactions with Y-phenyl diphenylphosphi-nates (discussed further in the section Phosphates and Phosphinates). The results showed that the C=0 compounds were more reactive than the P=0 compounds 28... 

In studies of the reactions of S-(4-nitrophenyl) 4-methylthiobenzoate with a series of six secondary alicyclic amines and a series of eight pyridines in 44 wt% ethanol-water at 25 °C, the Brpnsted-type plots were non-linear with the curvature centre defined as pK(j located at pK.d 9.7 and 9.4 for the reactions of secondary alicyclic amines and pyridines, respectively. The plots are consistent with a zwitterionic tetrahedral intermediate on the reaction path and, as the basicity of the amine increases, a change in rate-determining step from its breakdown to its formation.47... 

FbwO) is the Fourier transformation of effective beam width as a function of spatial frequency / Fuff) is the MTF of the XRll. Because of the XRll windows curvature, projection data must be transformed to obtain uniform pixel spacing, described by Errors in object centre... 

Close to the wall of a pipe, the effect of the curvature of the wall has been neglected and the shear stress in the fluid has been taken to be independent of the distance from the wall. However, this assumption is not justified near the centre of the pipe. 

On an image with a scale factor of 500 to 800 this additional component leads to significant shift of the reflection position (6 to 9 pixels). The shift of the reflection centre caused by the Ewald sphere curvature is seen easily while analyzing the positions of reflections lying on the minor... 

This difference in j-coordinate can be explained by the shift of the centre in y-direction caused by the curvature of the Ewald sphere. The curvature of the Ewald sphere does not affect the position of the centre in the four-clicks method, but leads to a shift of the ellipse centre when calculating this centre from a single ellipse. Thus the four-clicks method is better for the centre calculation. 

In a flame, as the concentration of atoms increases, the possibility increases that photons emitted by excited atoms in the hot region in the centre will collide with atoms in the cooler outer region of the flame, and thus be absorbed. This self-absorption effect contributes to the characteristic curvature of atomic emission calibration curves towards the concentration axis, as illustrated in Fig. 4.4. The inductively coupled plasma (ICP) tends to be hotter in the outer regions compared with the centre—a property known as optical thinness—so very little self-absorption occurs, even at high atom concentrations. For this reason, curvature of the calibration curve does not occur until very high atom concentrations are reached, which results in a much greater linear dynamic range. 

E. Winkler, F. Grashof, H. Hertz,8 etc., have studied the stresses which are set up when two elastic isotropic bodies are in contact over a portion of their surface, when the surfaces of contact are perfectly smooth, and when the press, exerted between the surfaces is normal to the plane of contact. H. Hertz showed that there is a definite point in such a surface representing the hardness defined as the strength of a body relative to the kind of deformation which corresponds to contact with a circular surface of press. and that the hardness of a body may be measured by the normal press, per unit area which must act at the centre of a circular surface of press, in order that in some point of the body the stress may first reach the limit consistent with perfect elasticity. If H be the hardness of a body in contact with another body of a greater hardness than H, then for a circular surface of pressure of diameter d press. p radius of curvature of the line p and the modulus of penetration E,... 

In field emission spectroscopy (FEM), a refactory metal, such as tungsten, is fabricated to give a very fine hemispherical tip of radius of curvature about 1CT7 m. The tip is located at the centre of curvature of a hemispherical fluorescent screen and a potential difference of about 10 kV is applied, with the fluorescent screen as... 

When the radius of the tube is appreciable, equation (2) requires correction, because the meniscus is no longer spherical. In Fig. 57, let b be the radius of curvature of the lowest point O of the meniscus (the two radii will be equal at this point, since the tube is cylindrical and the point is on the axis of revolution). The pressure immediately under the centre of the... 

---