Four angles

A quadrilateral is a four-sided polygon determined by four coplanar points (three of which are noncollinear), if the line segments thus formed intersect each other only at their end points, forming four angles. 

P. A. Bottomley, R. Quwerkerk, R. F. Lee and R. G. Weiss, Four-angle saturation transfer (FAST) method for measuring creatine kinase reaction rates in vivo. Magn. Reson. Med., 2002,47,850-863. 

Mean values of the short and long bonds of the four asymmetrically bound ligands. K Mean values of the four angles in the two interpenetrating trapezoids. 

Sweet potato starch (Plate IV, Fig. 27). This consists of granules of irregular form and size. The typical shape is rounded with four angles, somewhat like an egg or a kettle, and some granules are striated and exhibit a well-marked eccentric hilum. The mean size is 30 fx, but the largest granules may attain 65 fx. 

This is a four-fold differential cross section, because it depends on four continuous variables two energies and two directions in space. (This is often also called a six-fold differential cross section because the two directions in space are fixed by four angles.) The expression given contains the following dependences ... 

The wavefunction depends on R and on the four angles Or, Schrodinger equation, we expand h in terms of parity adapted angular wavefunctions of the form (Launay 1976)... 

In the starting material there are four angles of about 109°. In the transition state (enclosed in square brackets and marked as usual) there are three angles of 120° and six angles of 90°, a significant increase in crowding. The larger the substituents R, the more serious this is. We can easily see the effects of steric hindrance if we compare these three structural types ... 

The opposite is true of the S l reaction. The slow step is simply the loss of the leaving group. The starting material is again tetrahedral (four angles of about 109°) and in the intermediate cation there are just three angles of 120°—fewer and less serious interactions. The transition state will be on the way towards the cation, rather closer to it than to the starting material. 

Fig. 12a, b a The structure of C4-acetone. b Possible orientation of the acetone molecule with respect to C6 in pinched cone conformation. T is ca. 120° and is equally divided into four angles of 30°. The angles between the twofold axes of calixarene and the CD3 vector averaged about the twofold axis of acetone are a, pi and p2 for the A, and B2 orientations. (Adopted from [48] by permission of the PCCP Owner Societies)... 

Figure S shows in rough schematic form a conventional four-circle x-ray diffractometer, in which the four angles 20,0, x, and co can be independently set. The integration, to obtain the integrated intensity, may be obtained by scanning over 20, with cj set equal to 0 (the 0-20 scan ), or by scanning over co with 20 fixed (the co scan ), or in other ways. At one end or the other of the scan, more often both, the counter is held steady to obtain background counts. The integrated intensity is given by...

The four angles of the chart the Ascendant, Midheaven, Descendant, and I.C. 

Chlorine tank car manway, four angle valves, safety relief valve, packing gland leaks, installing valve hoods and outlet valve nuts, yoke assemblies, and checking tank car pressure. 

The beta (P) phase of uranium occurs at elevated temperatures. This phase has a tetragonal (having four angles and four sides) lattice structure and is quite complex. 

The spectroscopic constants corresponding to the equilibrium distance (/ ), the well depth (De). and the harmonicity frequency (ft>e) of all potential energy surfaces without and with the three-body interactions are collected in Table 16.2. The analysis of these data shows that the equilibrium distance, the depth of the well, and the harmonicity frequency depend on the angle y showing the strong anisotropy of the Li2" (X Sg+)-Xe system. In fact, we remark that the well depth and the harmonicity frequency decrease when y increases. The same remark is observed for the equilibrium distance for the lowest four angles y, then it increases for y = 68.5°... 

The 3D site correlation functions of acetonitrile solvent around the DMA+ and AN solutes obtained from the 3D-RISM/KH theory have been used to calculate the PMF between the solutes by using the HNC approximation (4.32) with the correction (4.35). The PMF profiles were calculated at the six relative orientations of the DMA" " and AN molecules corresponding to the parallel arrangements of their symmetry planes. They are denoted by four angles between the molecular planes Pj3MA - AN> molecular axes dma an-... 

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