Cohens method

These normal equations can be found by the same methods as were used for the straight-line case, i.e., successive multiplication of the n observational equations by the coefficients of a, b, and c, followed by addition of the equations in each set. 

It should be noted that the least-squares method is not a way of finding the best curve to fit a given set of observations. The investigator must know at the outset, from his understanding of the phenomenon involved, the kind of relation (linear, parabolic, exponential, etc.) the two quantities x and y are supposed to obey. All the least-squares method can do is give him the best values of the constants in the equation he selects, but it does this in a quite objective and unbiased manner. 

Suppose a cubic substance is being examined in a Debye-Scherrer camera. Then Eq. (11-11), namely. 

By substituting this into Eq. (11-11) we find how the error in sin 0 varies with 6  

The experimental values of sin 9, a, and S are now substituted into Eq. (11-22) for each of the n back-reflection lines used in the determination. This gives n equations in the unknown constants C and A, and these equations can be solved for the most probable values of C and A by the method of least squares. Once C is found, can be calculated directly from the relation given above the constant A is related to the amount of systematic error involved and is constant for any one film, but varies slightly from one film to another. The two normal equations we need to find C and A are found from Eq. (11 -22) and the rules previously given. They are 

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The next problem for H. Umezawa was to use his findings to design new kanamycin derivatives effective against resistant bacteria. The synthetic work was undertaken in cooperation with his brother. Prof Sumio Umezawa of Keio University, and one of the writers (T. Tsuchiya). The first useful derivatives active against resistant bacteria, namely, 3, 4 -dideoxy-kanamycin B (dibekacin) and 3 -deoxykanamycin A, were prepared in 1971. These were also found active against Pseudomonas known to have intrinsic resistance. These results supported the truth of H. Umezawa s theory. In the synthesis of dibekacin, the Tipson-Cohen method for introducing unsaturation, developed by one of the writers (D. Horton, 1966) for pyranoside... 

The di-O-tosylates (prepared by action of tosyl chloride in pyridine) are reduced with zinc (Nal/Zn route e Tipson-Cohen reaction) [13]. Cyclic ortho-esters (prepared by reaction of the diol with ethyl orthoformate) are transformed into olefins by simple heating in the presence of acids (Eastwood reaction, route b) [14]. Cyclic thiocarbonates (obtained by reaction of a diol with thiophosgene or (V,(V -thiocarbonyl-di-imidazole) are reduced to olefin with trimethyl phosphite (Corey-Winter method, route c) [15]. Finally, reduction of vicinal di-xanthates with tri- -butyltin hydride according to the Barton procedure [16] affords olefins via a reductive elimination process route a). The Corey-Winter, Garegg, and Tipson-Cohen methods are most commonly applied for deoxygenation of sugar diols. 

Syntheses of 2, 3 -dideoxykanamycin A, 2, 3 -dideoxyamikacin, and their related derivatives have been described [22]. 2, 3 -Dideoxykanamycin A was prepared by two different methods. In one, a 2, 3 -unsaturated intermediate was obtained by a modified version of the Tipson and Cohen method, which proceeds via triflylation... 

B. I. Cohen, S. R. Presnell, and E E. Cohen, Methods Enzymol. J. J. Langone, Ed. Academic Press, New York, 1991, Pattern Based Approaches to Protein Structure Prediction. 

L. Shapiro, R. Glicklis, and S. Cohen, Method of forming polysaccharide sponges for cell culture and transplantation, US Patent 6 334 968, assigned to Ben Gurion University of the Negev (Beer-Sheva, IL), January 1, 2002. 

Venkatesh P K, Dean A M, Cohen M H and Carr R W 1999 Master equation analysis of intermolecular energy transfer in multiple-well, multiple-channel unimolecular reactions. II. Numerical methods and application to the mechanism of the C. + O2 reaction J. Chem. Phys. Ill 8313... 

Cohen R E, Mehi M J and Papaconstantopouios D A 1994 Tight-binding totai-energy method for transition and nobie metais Phys. Rev. B 50 14 694-7... 

A. P. Cohen, "Test Methods for the CompatibiHty of Desiccants with Alternative Refrigerants," yiSHEAE Transactions Vol. 99, Part 1, American... 

Diphenylmethane has been prepared with aluminum chloride as a catalyst from methylene chloride and benzene, from chloroform and benzene as a by-product in the preparation of triphenylmethane, and from benzyl chloride and benzene. It has been prepared by the reduction of benzophenone with hydriodic acid and phosphorus, or with sodium and alcohol. It has also been made by heating a solution of benzyl chloride in benzene with zinc dust, or with zinc chloride. The above method is only a slight modification of the original method of Hirst and Cohen. ... 

M. Cohen and P.C. Jenning, Silent Boundary Methods for Transient Analysis, Computational Methods for Transient Analysis (edited by J.D. Achenbach), North-Holland, Amsterdam, 1983. 

Oxalic Acid.—The jurciiaration of ovalic acid by the action ol nitric aiid on sugar was introduced bySchccle, and was used for some time as a technical process. I hc vanadium pent-o. ide aits as carrier of o ygen, being alternately leduccd to tctro. ide and re-o. idised. The picscnt commercial method is to heat sawdust with a mi. cturc of caustic potash and soda on Cohen s adv. p. o. c. ... 

The method has been applied by Cohen (1894) to the determination of transition temperatures. Thus the electromotive force of the cell ... 

Cohen et al. (1977) recommend a new method for hydroxy-de-diazoniation. It is based upon an earlier observation (Lewin and Cohen, 1967) that aryl radicals, pro-... 

It is likely that Cohen s method is a homolytic reaction (Sec. 8.6). The catalysis can be represented by Schemes 10-7 to 10-9. The last step of this mechanism is based on competitive hydroxy-/halo-de-diazoniations investigated by Hanson et al. (1991) and discussed in Section 10.5. 

Kirk and Cohen (1969, 1971, 1973 Kirk et al., 1973) successfully applied the photo-fluoro-de-diazoniation method for the introduction of fluorine into imidazole and its derivatives with various substituents (e.g., histidine) 2- and 4-fluoroimi-dazole had not previously been synthesized by other methods. 2-Fluoroimidazole, in contrast to the 4-isomer, is easily hydrolyzed in water (Kirk et al., 1973). 

Cohen, L., Manion, L., Morrison, K. (2000). Research methods in education (5th ed.). London and New York RoutledgePalmer. 

The exchange reaction between Np(VI) and Np(V) has been investigated using the isotopic method ( Np) and an extraction separation (Np(VI) with tri-butylphosphate or thenoyltrifluoroacetone in toluene) Cohen et al. have found, for the exchange in perchlorate media, a rate law... 

Cohen, E. and Saguy, L, A rapid method of determination of betanin and vulgaxanthin 1 in beet powder using a general purpose tristimulus colorimeter, Ztschr. Lebensm. Unters. Forsch., 175, 31, 1982. 

The variational theorem which has been initially proved in 1907 (24), before the birthday of the Quantum Mechanics, has given rise to a method widely employed in Qnantnm calculations. The finite-field method, developed by Cohen andRoothan (25), is coimected to this method. The Stark Hamiltonian —fi.S explicitly appears in the Fock monoelectronic operator. The polarizability is derived from the second derivative of the energy with respect to the electric field. The finite-field method has been developed at the SCF and Cl levels but the difficulty of such a method is the well known loss in the numerical precision in the limit of small or strong fields. The latter case poses several interconnected problems in the calculation of polarizability at a given order, n ... 

Cohen A, Hertz HS, Mandel J, Paule RC, Schaffer R, Sniegoski LT, Sun T, Welch MJ, and White E V (1980) Total serum cholesterol by isotope dilution mass spectrometry A candidate definitive method. Chn Chem 26 854-860. 

Ellerbe P, Cohen A, Welch MJ, and White V E (1990) Determination of serum uric acid by isotope dilution mass spectrometry as a candidate definitive method. Anal. Chem 62 2173-2177. 

White V E, Welch MJ, Sun T, Sniegoski LT, Schaffer R, Hertz HS, and Cohen A (1982) The accurate determination of serum glucose by isotope dilution/mass spectrometry - two methods. Biomed Mass Spectrom 9 395-405. 

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