Concavity factor

Concavity factor n. The entire stress-strain curves of rubbers and elastomers that have no elastic limit are typically concave toward the stress axis (and convex to the strain axis). The concavity factor is the ratio (less than 1) between the energy beneath the extension curve to that beneath the straight line to the same final point. 

The two homologous repeats, each of 88 amino acids, at both ends of the TBP DNA-binding domain form two stmcturally very similar motifs. The two motifs each comprise an antiparallel p sheet of five strands and two helices (Figure 9.4). These two motifs are joined together by a short loop to make a 10-stranded p sheet which forms a saddle-shaped molecule. The loops that connect p strands 2 and 3 of each motif can be visualized as the stirmps of this molecular saddle. The underside of the saddle forms a concave surface built up by the central eight strands of the p sheet (see Figure 9.4a). Side chains from this side of the P sheet, as well as residues from the stirrups, form the DNA-binding site. No a helices are involved in the interaction area, in contrast to the situation in most other eucaryotic transcription factors (see below). 

If surface 1 is convex or planar, all the incoming radiation is from surface 2, and F]2 while the visibility factor expresses that part of radiation coming from this surface. If surface 2 is concave, a part of the radiation is also from this surface. 

In the previous Sections, the properties of acids and bases in macrocycles and other concave structures have been compared. A number of factors have been recognized which influence the acidity or basicity of an acid or base (i) hydrogen bonds, (ii) hindered solvation (exclusion of solvent), (iii) formation of tight ion pairs (high microacidity but low overall acidity), and (iv) Coulomb forces when poly anions are formed. A fifth influence, (v) steric hindrance, still has to be discussed. 

However, for most acids and bases of this review, the dominating influence of the concave environment on the acid-base properties is the formation of stabilizing intramolecular hydrogen bonds. The other factors have been found only in a few cases [microacidity for [45] (van Eerden et al.,... 

In many cases, the dynamic amplification factor or the ratio of static load to dynamic load capacity will exceed two. This is because of the concave up shape of the resistance function and the mobilization of membrane resistance at large deflection to thickness ratios. Because of this phenomenon, it is unconservative to assume the blast capacity of polycarbonate glazing to be no less than one half of its static pressure load capacity. 

The out-of-plane stress intensification factor (SIF) for a reducing branch connection with branch-to-run diameter ratio of 0.5 < dlT) < 1.0 may be nonconservative. A smooth concave weld contour has been shown to reduce the SIF. Selection of the appropriate SIF is the designers responsibility. 

A variety of concave pyridines 3 (Table 1) and open-chain analogues have been tested in the addition of ethanol to diphenylketene (59a). Pseudo-first-order rate constants in dichloromethane have been determined photometrically at 25 °C by recording the disappearance of the ketene absorption [47]. In comparison to the uncatalyzed addition of ethanol to the ketene 59a, accelerations of 3 to 25(X) were found under the reaction conditions chosen. Two factors determine the effectiveness of a catalyst basicity and sterical shielding. Using a Bronsted plot, these two influences could be separated from one another. Figure 4 shows a Bronsted plot for some selected concave pyridines 3 and pyridine itself (50). 

As expected, axial OH groups were easier to differentiate from equatorial ones than equatorial OH groups from one another. In the case of methyl cholate 66a, a standard reagent (pyridine, 50) does a good job. But in the glucose derivative 67a, the two equatorial OH groups are much more similar to one another. Therefore it is not surprising that they react with almost the same rate in the uncatalyzed reaction. When pyridine (50) was used as catalyst, the acylation of the 2-position (67c) was preferred by a factor of 4 but also a bis-acylated product 67d was formed. Concave pyridine 3r showed the best results. With a selectivity of 9 1, the 2-acylated product 67c was formed and no diacylated product 67d could be determined. 

The Kelvin effect is not limited to spheres. For example, the neck of liquid between two supports is described by a paraboloid of revolution. In this case the radius of curvature of the concave surface is outside the liquid and therefore introduces a minus sign into Equation (40). In addition, the factor of 2 is not required to describe the Kelvin effect for this geometry. Example 6.2 illustrates a test of the Kelvin equation based on this kind of liquid neck. 

The interdiffusivity, D, which measures the interdiffusion between Cu and Zn in the laboratory frame, is a strong function of the concentration of Zn. The curve describing D(czn) is concave upward and roughly parabolic in shape, and D(czn) increases by a factor of about 20 when the Zn content increases from 0 to 30 at. % [8]. Describe how the shape of the diffusion-penetration curve for a diffusion couple made of Cu/Cu-30 at. % Zn is expected to deviate from the symmetric form of the constant diffusivity error-function solution. 

Only a constant strain method is specified with a standard strain of 25% for rubbers up to 80 IRHD, 15% for those 80 - 89, and 10% for those over 90. The compression is made between very smooth platens which are lubricated and, hence, the compression is made with some attempt at perfect slippage. Fairly obviously, the degree of slip and the test piece shape factor can affect the measured values of set. At one time it was standard to use glass-paper between the test piece and the platens to prevent slip but this produces greater concavity of the ends after release. 

CA 45 7792(1951) [Combustion profiles of lamelae of a double-base proplnt consisting of NC 69.1, DEGDN 20.6 St EtCentr 6.9% were detd in air and inert gases, with or w/o wrappings of different thermal conductivity. An interpretation of the various profiles obtd(inverted V, rectilinear, concave or parabolic) was proposed. The factor which mainly detd the geometry of the combustion profile is heat transfer from the flame front to the solid lamelae, thru the ambient media) 8)P. Tavernier St P.Prache, MP 34, 255-75(1952) Sc CA 48, 11060(1954)(Rate of combustion of proplnts in an inert atm under pressure) 9)H. Muraour 8t G. Aunis, MP 35, 287-301(1953) CA 49, 13651(1955) Ger translation by Dr. A. Schmidt in Explosivst 1954, 154-7 1955 6-9(Laws of combustion of colloidal proplnts. A survey of French research between WWI St WWII) 10)C. A. Heller A.S, Gordon, JPhysChem 59, 773-77(1955)... 

The formation of liquid depends on pore diameter, surface tension and the contact angle between the solid, liquid and gas phases. The last factor is difficult to estimate in general but is likely to be close to zero between water, humid air and a surface consisting of adsorbed water. It can be deduced that, when the contact angle is zero, the vapour pressure p in equilibrium with a concave liquid meniscus relative to the vapour pressure p0 in equilibrium with a flat surface is given by... 

Other cyclic or bicyclic ketones do not have a convex side but only a less concave and a more concave side. Thus, a hydride donor can add to such a carbonyl group only from a concave side. Because of the steric hindrance, this normally results in a decrease in the reactivity. However, the addition of this hydride donor is still less disfavored when it takes place from the less concave (i.e., the less hindered) side. As shown in Figure 10.10 (top) by means of the comparison of two reductions of norbomanone, this effect is more noticeable for a bulky hydride donor such as L-Selectride than for a small hydride donor such as NaBH4. As can be seen from Figure 10.10 (bottom), the additions of all hydride donors to the norbomanone derivative B (camphor) take place with the opposite diastereoselectivity. As indicated for each substrate, the common selectivity-determining factor remains the principle that the reaction with hydride takes place preferentially from the less hindered side of the molecule. 

The combination of these two factors determines the required shape of an LSS gradient. Linear gradients were shown to result for RPLC in section 5.4, whereas a concave gradient was found to be optimal for LSC in section 6.2.2. 

The heat-conductivity data obtained by Patten were by no means uniform in character. This may be attributed to a number of factors, but particularly to the nature of the packings used. Conductivity when plotted against moisture content as illustrated in Figure 58 was linear, concave upward or concave downward, depending upon the material used. 

---