Rudolph method

A better alternative approach is what will be called the Rudolph method [476], after the person who introduced it into electrochemical simulation. It was known before 1991 under various names, notably block-tridiagonal [280,412,470,471,528,570]. This comes from the fact that if one lumps the large matrix into a matrix of smaller matrices and vectors, the result is a tridiagonal system that is amenable to more efficient methods of solution. In the present context, we define some vectors... 

To illustrate the Rudolph method, we take the relatively simple two-species catalytic or EC/ mechanism... 

The coupled system arising from the EC7 or catalytic system, described in Chap. 8, was programmed using CN and the Rudolph method. That is, the two concentration vectors were gathered into a vector of two-element vectors, and the usual coefficients in the discrete system of equations become a number... 

Rudolph, F. B., Product inhibition and abortive complex formation. Methods Enzymol, 1979. 63 pp. 411-436. 

Frahm SO, Rudolph P, Dworeck C, et al. Immunoenzymatic detection of the new proliferation associated protein plOO by means of a cellular ELISA specific detection of cells in cell cycle phases S, G2 and M. J. Immunol. Methods 1999 223 147-153. 

JOL C N, NEIESS T G, PENNINKHOF B, RUDOLPH B and DE RUITER G A (1999), A novel high-performance anion-exchange chromatographic method for the... 

Rudolph, M., in Physical Chemistry Principles, Methods and Applications, Rubinstein, I. (Ed.), Marcel Dekker, New York, p. 81. 

Gasteiger J, Rudolph C, Sadowski J. 1990. Automatic generation of 3D-atomic coordinates for organic molecules. Tetrahedron Comp Method 3 537... 

Phillips WT, Rudolph AS, Goins B, et al. A simple method for producing a technetium-99m-labeled liposome which is stable in vivo. Nucl Med Biol 1992 19 539. 

Ralph Rudolph made major contributions to our understanding of the structure and bonding of polyhedral cluster compounds and he had an abiding interest in developing a rationale which would enable the structure of individual compounds to be systematized and related to each other. He independently arrived at a method of counting skeletal electrons which is now generally referred to as Wade s Rules, and this has had a decisive influence on our general perceptions of polyhedral cluster compounds. Related to this was his preoccupation with the problem of heteroatoms such as sulfur, and the number of electrons which such atoms contribute to the heteroborane clusters. 

Gasteiger, J., Rudolph, C., and Sadowski, J. Automatic generation of ID-atomic coordinates for organic molecules. Tetrahedron Comput. Methods 1990, 3, 537-547. 

Rudolph Christian Bottger (1806-1881) found in 1866 that the flue dust which condensed in the chimneys of the zdncworks near Goslar contained about one part of indium oxide in one thousand (79). He perfected methods of preparing the rare metals indium, thallium, and cesium (80). 

Moroder, L. Lutz, J. Grams, F. Rudolph-Bohner, S. Osapay, G. Goodman, M. Kolbeck, W. A New Efficient Method for the Synthesis of 1,4-Ben-zodiazepine-2,5-dione Diversomers, Biopolymers 1996, 38, 295. 

J. Gasteiger, C. Rudolph and J. Sadowski, Tetrahedron Comp. Method. 3 (1990) 537-547 CORINA program Molecular Networks GmbH, Erlangen, Germany. 

A method apparently fundamentally related to the above is illustrated by the fractional catalytic dehydration of di-2-butanol observed by Schwab and Rudolph.91 The alcohol recovered after partial thermal dehydration upon a film of copper supported on powdered d- or 1-quartz was faintly active in the same sense as the quartz. Similar results were noted after partial catalytic oxidation on the same surfaces. These results have not been explained fully it is possible that each of the two active forms of the alcohol is adsorbed momentarily on the quartz-copper interface the two diastereoisomeric combinations thus formed then react at different rates. The method is not practical in its present form. 

Moroder L, Lutz J, Grams F, Rudolph-Bohner S, Osapay G, Goodman M, Kolbeck W, A new efficient method for the synthesis of 1,4-benzodiazepine-2, 5-dione diversomers, Biopolymers, 38 295-300, 1996. 

Heymann MA, Payne BD, Hoffmann JIE, Rudolph AM (1977) Blood flow measurements with radionuclide-labeled particles. Prog Cardiovasc Dis 20 55-79 Hof RP, Wyler F, Stalder G (1980) Validation studies for the use of the microsphere method in cats and young minipigs. Basic Res Cardiol 75 747-756... 

---