Published derived

A published derivation of the Green-Kubo or fluctuation-dissipation expressions from the combination of the FR and the central limit theorem (CLT) was finally presented in 2005. This issue had been addressed previously and the main arguments presented, but subtleties in taking limits in time and field that lead to breakdown of linear response theory at large fields, despite the fact that both the FR and CLT apply, " were not fully resolved. ... 

The pour point of a cut or petroleum fraction can be derived from the characteristic properties by an expression published by the API ... 

Chu B 1991 Laser Light Scattering, Basic Principies and Practice 2nd edn (New York Academic) (See also the first edition (published in 1974) that contains more mathematical derivations.)... 

The Universal Force Field, UFF, is one of the so-called whole periodic table force fields. It was developed by A. Rappe, W Goddard III, and others. It is a set of simple functional forms and parameters used to model the structure, movement, and interaction of molecules containing any combination of elements in the periodic table. The parameters are defined empirically or by combining atomic parameters based on certain rules. Force constants and geometry parameters depend on hybridization considerations rather than individual values for every combination of atoms in a bond, angle, or dihedral. The equilibrium bond lengths were derived from a combination of atomic radii. The parameters [22, 23], including metal ions [24], were published in several papers. 

They compared the PME method with equivalent simulations based on a 9 A residue-based cutoflF and found that for PME the averaged RMS deviations of the nonhydrogen atoms from the X-ray structure were considerably smaller than in the non-PME case. Also, the atomic fluctuations calculated from the PME dynamics simulation were in close agreement with those derived from the crystallographic temperature factors. In the case of DNA, which is highly charged, the application of PME electrostatics leads to more stable dynamics trajectories with geometries closer to experimental data [30]. A theoretical and numerical comparison of various particle mesh routines has been published by Desemo and Holm [31]. 

Breindl et. al. published a model based on semi-empirical quantum mechanical descriptors and back-propagation neural networks [14]. The training data set consisted of 1085 compounds, and 36 descriptors were derived from AMI and PM3 calculations describing electronic and spatial effects. The best results with a standard deviation of 0.41 were obtained with the AMl-based descriptors and a net architecture 16-25-1, corresponding to 451 adjustable parameters and a ratio of 2.17 to the number of input data. For a test data set a standard deviation of 0.53 was reported, which is quite close to the training model. 

Compounds of class (iii) are either totally synthetic (a few steroids) or derivatives of natural products isolated from plants or microorganisms. They are discussed within the indicated sections. We will briefly describe published syntheses of the most common compounds... 

The controversy seemed then to be closed. In 1890 Hantzsch had already started his work on the structure of oximes, and his synthetic work on heterocycles was practically ended. However, 27 years later, in July 1919, Tcherniac published a new paper entitled TTiiocyanoacetone and its derivatives as isomerides (33), where, after the description of improved and generalized methods for the preparation of thiocyanoacetone he came to the explosive conclusion that the substance which has been known since 1887 as hydroxymethylthiazole is not a thiazole at all. It might be called 2-imino-4-methylthioxole, but for the sake of simplicity, and in view of the now proved existence of two other isomerides of thiocyanoacetone, it seems preferable to adopt the generic... 

Schwartz has published some hypothetical data for the titration of a 1.02 X ICr" M solution of a monoprotic weak acid (pXa = 8.16) with 1.004 X ICr M NaOH. " A 50-mL pipet is used to transfer a portion of the weak acid solution to the titration vessel. Calibration of the pipet, however, shows that it delivers a volume of only 49.94 ml. Prepare normal, first-derivative, second-derivative, and Gran plot titration curves for these data, and determine the equivalence point for each. How do these equivalence points compare with the expected equivalence point Comment on the utility of each titration curve for the analysis of very dilute solutions of very weak acids. 

P. A. S. Smith, Derivatives ofHydra ne and Other My dronitrogens Having N-N Ponds, The Benjamin/Cummings Publishing Co., Reading, Mass., 1983, pp. 80-141. 

P. A. S. Smith, Derivatives ofHjdra ne and Other Djdronitrogens Having N-NBonds, The Benjamin /Cummings Publishing Co., Inc., Reading, Mass., 1983. P. A. S. Smith, The Chemistry of Open-Chain Nitrogen Compounds, Vols. 1 and 2, W. A. Benjamin, Inc., Menlo Park, Calif., 1965—1966. 

R. H. Boundy and R. F. Boyer, eds.. Styrene, Its Toljmers, Copolymers, and Derivatives, Reinhold Publishing Corp., New York, 1952. 

C. Ellis, Chemistry of Petroleum Derivatives, Vol. 11, Reiohold Publishing Corp., New York, 1937. 

The excellent book by the late Professor T. J. Batterham contains all the available information (up to 1973) on pyrazoles and their non-aromatic derivatives (B-73NMR165) and on indazoles (B-73NMR263). The bibliography for pyrazoles and pyrazolones has been updated in (B-76MI40402). It should be emphasized that almost all the principal results about the H NMR spectra of these heterocycles were published at that time, and thus only a summary of the principal conclusions is needed here. 

The same group has published two articles on indazoles [indazole (36), 1-methyl- (106) and 2-methyl-indazole (107)]. The He-I and He-II spectra have been obtained and satisfactorily interpreted by means of ab initio LCGO calculations (78JST(43)33, 78JST(43)203). The PE spectra support the conclusion (Section 4.04.1.5.1) that the 1//-tautomer is by far the more stable. X-Ray photoelectron spectra of some pyrazole and pyrazoline derivatives have been reported (83MI40400). 

In the section dealing with electrophilic attack at carbon some results on indazole homocyclic reactivity were presented nitration at position 5 (Section 4.04.2.1.4(ii)), sulfon-ation at position 7 (Section 4.04.2.1.4(iii)) and bromination at positions 5 and 7 (Section 4.04.2.1.4(v)). The orientation depends on the nature (cationic, neutral or anionic) of the indazole. Protonation, for instance, deactivates the heterocycle and directs the attack towards the fused benzene ring. A careful study of the nitration of indazoles at positions 2, 3, 5 or 7 has been published by Habraken (7UOC3084) who described the synthesis of several dinitroindazoles (5,7 5,6 3,5 3,6 3,4 3,7). The kinetics of the nitration of indazole to form the 5-nitro derivative have been determined (72JCS(P2)632). The rate profile at acidities below 90% sulfuric acid shows that the reaction involves the conjugate acid of indazole. 

The circular dichroism curves for a variety of penicillanic acid derivatives have been published and discussed (B-77MI51100) and have been used to support extended Hiickel MO calculations (77T711). 

The majority of published °Pb reports address the utility of °Pb as a geochronological tool rather than as an element that is involved in complex biogeochemical cycles. Nonetheless, some of these studies do provide insight into the geochemical behavior of °Pb and °Po. Nearly all of the lead in the world s surface oceans is believed to be of anthropogenic origin—derived from combustion... 

Humans can not know the ultimate and detailed true reaction mechanism of any reaaJon, or the kinetics that can be derived from it.. Bodenstein (1906) studied the mechanism of the H2 + Br2 = 2 HBr reaction and after several decades of work and dozens of publications wrote the final paper on the subject. Within a few years one of his students published a correction to Bodenstein s explanations. 

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