Howison

D. L. Morse, N. Raghunand, P. Sadarangani, S. Murthi, C. Job, S. Day, C. Howison and R. J. Gillies, Response of choline metabolites to docetaxel therapy is quantified in vivo by localized P MRS of human breast cancer xenografts and in vitro by high-resolution P NMR spectroscopy of cell extracts. Magn. Reson. Med., 2007, 58, 270-280. 

For a CaO/Si02 ratio of 1.5, the pseudocell of the modified Taylor-Howison hypothesis contains 3.30 molecules of CaO, 2.20 molecules of Si02, and 2.20 molecules of H20. Thus, the cell is 10% heavier than the one in the model discussed before, which results in a 10% smaller specific surface area. The specific surface area for the two-layer tobermorite is 343 sq. meters per gram for the three-layer tobermorite, 229 sq. meters per grams. The corresponding CaO/Si02 ratios, from... 

In the model described earlier, the addition of two molecules of lime results in the disappearance of a unit surface. A similar calculation, based on the modified Taylor-Howison hypothesis, leads to the conclusion that the substitution of 0.78 molecule of CaO for Si02 causes the disappearance of a unit surface. This substitution is equivalent to the replacement by CaO of one molecule of Si02 out of 8.58 molecules. 

Considering everything, the model proposed is more consistent with the data presented in this paper than the Taylor-Howison model. Nevertheless, the latter model does not lead to absurd results. There is some evidence (4) for the constancy of the weight of the pseudocell with changing CaO/Si02 ratio, and further work is contemplated to ascertain this. 

The Taylor-Howison hypothesis gives an almost identical structure for the three-layer tobermorite with the one shown in Figure 8 the pseudocell surface contains one molecule of Si02 and 0.75 molecule of CaO, and the CaO content of the layers between the pseudocells is 1.50 molecules. The two-layer structure, however, shows greater differences. The surface is not very different it contains... 

K. F. Riley, M. P. Hobson, and S. I. Bence, Mathematical Methods for Physics and Engineering A Comprehensive Guide (Cambridge University Press, Cambridge, 1998) I. R. Ockendon, S. Howison, J. Ockendon, A. Lacey, and A. Movchan, Applied Parital Differential Equations (Oxford University Press, Oxford, 2003) H. F. Weinberger, First Course in Partial Differential Equations with Complex Variables and Transform Methods (Dover, Dover edition New York, 1995). 

N. Raghunand, C. Howison, A.D. Sherry, S. Zhang, and R.J. Gillies, Magn. Reson. 

Howison, Sam. Practical Applied Mathematics Modelling, Analysis, Apprordmation. New Ysrk Cambridge University Press, 2005. Provides a basic introduction to several practical aspects of applied mathematics, supported by in-depth case studies that demonstrate the applications of mathematics to actual physical phenomena and operations. Kurzweil, Ray. The Age of Spiritual Machines When Computers Exceed Human Intelligence. New York Penguin Books, 2000. Presents a thought-provoking view of the nature of artificial intelligence that may arise as a direct result of applied mathematics. 

R. C. Howison and C. K. McCord, Equilibria of Spherical Charge Distributions, preprint, 1994. 

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