Mehrotra method

Method of Mehrotra The Mehrotra method [24] has been derived with 273 heavy (Af > 100 gmol-1) hydrocarbons such as n-paraffins, 1-olefins, branched paraffins and olefins, mono- and polycycloalkanes, and fused and nonfused aromatics. Based on 1300 individual dynamic viscosity-temperature values for these compounds, the following one-parameter equation has been obtained by employing regression analysis ... 

Figure 5. Comparison of viscosity predictions of various Andrade-type models for some alkane hydrocarbons at atmospheric pressure. Data are from the compilation of Viswanath and Natarajan [1], solid lines are predictions by the Orbey-Sandler Method, long-dashed lines are predictions by the Allan-Teja Method, short-dashed lines are predictions by the Reid et al. method, and dotted lines are predictions by the Mehrotra Method.

At atmospheric pressure, hydrocarbon viscosities can be estimated by two methods the ASTM method and that of Mehrotra (1990). 

In Mehrotra s method, the dynamic viscosity is expressed as a function of temperature according to the relation ... 

The Mehrotra and ASTM methods apply with acceptable accuracy only for viscosities between 1 and 1000 mPa s. The average error is about 20%. The largest spreads are obtained at low and very high viscosities. 

Finally, the general algorithm framework of the infeasible primal-dual path-following Mehrotra-type predictor-corrector interior-point method is the following. 

The alcoholysis of sulfites such as dimethyl sulfite offers a convenient method for the preparation of high-boiling dialkyl sulfites [33]. Earlier, Voos and Blanke [8a] reported that dimethyl sulfite is converted to diethyl sulfite in 44 % yield. The reaction was shown to be acid-catalyzed and failed when barium carbonate was present. However, a patent refers to the use of lithium hydride in the transalcoholysis of 2,2-(4,4 -dihydroxyphenyl)propane with diphenyl sulfite or di-o-cresyl sulfite [32]. Recently Mehrotra and Mathur [34] reported that the alcoholysis reaction proceeds in the absence of catalysts. Their results are summarized in Eqs. (21)—(23) and Table VII. Tertiary butanol did not... 

See. for example, Martin Gott Goodlett Hasek /. Org. Chem. 1965,30, 4175 Brady O Neal /. Org. Chem. 1967,32, 2704 Huisgen Feiler Otto Tetrahedron Lett. 1968,4491, Chem. Ber. 1969,102, 3475. For indirect methods of the 1,4 addition of the elements of ketene to a diene see Freeman Balls Brown /. Org. Chem. 1968, 33, 2211 Corey Ravindranathan Terashima /. Am. Chem. Soc. 1971, 93, 4326. For a review of ketene equivalents see Ranganathan Ranganathan Mehrotra Synthesis 1977, 289-296. 

An important development of this method has recently been carried out by Mehrotra and Veith. The reaction with the excess of halide was found to provide bimetallic alkoxide halides. Their interaction with the alkoxometallate of the third metal provided access to trimetallic alkoxides ... 

The greatest number of Ti(OR)4homologs was obtained using the alcohol interchange reaction (method 6), the isopropoxide being usually applied as reactant [225, 224, 235]. This reaction has also been reported to lead to numerous T OR OR )., . Application of esters as alkoxylating agents has also been reported Mehrotra [1111, 1800],... 

MC15 with alcohols in the presence of ammonia (method 5) and the alcohol interchange of M(OPr )5 (method 6). Mehrotra proposed later the application of esters in the alcohol interchange reaction for Nb(OEt)5 [223],... 

Classical /3-diketones can be obtained from the acylation of ketones by esters (Claisen condensation), in the presence of alkali-metal hydroxides, ethoxides, hydrides, or amides as condensing agents, to enhance the relatively low reactivity of the ester carbonyl group (Equation (l)).41 5 Other general synthetic methods have been described by Mehrotra.2... 

Stubbs R. and Mehrotra S. 1999. A branch-and-cut method for 0-1 mixed convex programming. Mathematical Programming, 86(3), 515-532. 

Mehrotra DV, Heyse J. 2004. Use of the false discovery rate for evaluating clinical safety data. Statistical Methods in Medical Research 13(3) 227-238. 

Li J, Mehrotra DV, An efficient method for accommodating potentially underpowered primary endpoints. Statistics in Medicine, 27 5377-5391,2008. 

Separation of coal and mineral matter can also be achieved by exploiting differences in the surface properties certain minerals, especially clays, have polar, hydrophilic surfaces although pyrite may exhibit markedly hydrophobic behavior and cause difficulties when present in discrete particles that are selectively floated with coal particles. Froth flotation and oil agglomeration methods (Mehrotra et al., 1983 Franzidis, 1987 Schlesinger and Muter, 1989 Vettor et al., 1989 Xiao et al., 1989 Couch, 1991 Carbini et al., 1992) are examples of how such separations can be achieved and although differences exist in the surface properties of the coal components (macerals Chapters 4 and 9), these are generally small in relation to those of the minerals present. 

The one-fluid approach can be used with some of the models presented earlier. In the method of Mehrotra [II], the one-fluid model can be used to obtain the needed normal boiling temperature, T, from = [ZxjT y ], if the mixture is well defined. This proposal has not been tested in that method. However, Orbey and Sandler [ 13] found this boiling-point estimation method to be suitable for use in their viscosity model as discussed later. 

The lithium alkoxide method has been extensively exploited, by Mehrotra and co-workers for the synthesis of insoluble alkoxides of later transition metals (Eqs 2.68 and 2.69). 

The method was extended by Mehrotra and co-workers for the preparation of tertiary alkoxides of a number of metals lanthanides, " titanium, hafnium, vanadium,niobium, tautalum, " iron, and gallium. ... 

As stated earlier, the method has been extended for the preparation of alkoxides and mixed alkoxides of a large number of metals. However, Mehrotra and Srivastava made the interesting observation that boron alkoxides do not appear to undergo ttans-esterification reactions at all, although they do undergo alcoholysis reactions. 

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