Lucas fraction

Alternatively, Fn = 5(Ln i + Ln+1), with L0 = 2. The simplest formulation of the converging Lucas fractions is therefore given by... 

The derived Ford circles define the same periodicity as 4. An alternative convergence through Lucas fractions ... 

Siddiqi-Lucas suggested that component volume fractions might be used to correlate the effects of concentration dependence. They found an average absolute deviation of 4.5 percent for nonpolar-nonpolar mixtures, 16.5 percent for polar-nonpolar mixtures, and 10.8 percent for polar-polar mixtures. 

Seiber JN, Glotfelty DW, Lucas AD, et al. 1990. A multiresidue method by high performance liquid chromatography-based fractionation and gas chromatographic determination of trace levels of pesticides in air and water. Arch Environ Contam Toxicol 19 583-592. 

It was claimed by Henry(Ref 2) that 0. de Battice prepd nitroacetone in 1895 in Belgium by oxidation of nitroisopropanol with chromic mixture. Henry described the compd as a coi, mobile liq with a sharp odor, a 1.070 at 14°, bp 152° at 767 mm and insol in w. Lucas c]aimed(Ref 3) that the compd described by Henry was not nitroacetone, but this statement was disputed by Henry(Ref 4). Harries also claimed(Ref 5) that the compd described by Henry is not nitroacetone More recently, Hass Hudgin(Ref 7) claimed that they had isolated some nitroacetone from the high-boiling fraction of the vapor-phase nitration of acetone but it is not clear from their paper whether the substance was liq or solid. Hurd NilsonfRef 8) prepd nitroacetone as pale-green crysts, mp 47°, by oxidizing 1—nitro—2—propanol with sodium dichromate and sulfuric acid. The yield was (5% of theoretical. The explosifcility of this compd was not mentioned... 

Stott, G.H. and Lucas, D.O. 1989. Immunologically active whey fraction and recovery process. US Patent No. 4,834,974. 

Sharkey T. D. and Berry J. A. (1985) Carbon isotope fractionation of algal as influenced by an inducible CO2 concentrating mechanism. In Inorganic Carbon Uptake by Aquatic Photosynthetic Organisms (eds. W. J. Lucas and J. A. Berry). American Society of Plant Physiologists, pp. 389-401. 

Lucas, A. Lepage, F. Cardot, Ph. Field Flow Fractionation Flandbook Shimpf, M.E., Caldwell, K., Giddings, J.C., Eds. Wiley-Interscience New York, 2000 471. 

The identification of primary factors is not a simple matter. Complex statistical designs (generally known as the Lucas tests) have been developed and applied in classifying chemical components of forages (35, 59). It is on the basis of such analyses that detergent-fiber methods were developed to provide a more ideal chemical fractionation of forages (61). 

Figure 9.2. A. Localization of the coding sequences used in hybridisation experiments on the DNA fractions from Ciona. B. GC and GCj levels of the coding sequences are listed. (From De Luca et al., 2002).

Lucas, F., Shaw.J.T.B. and Smith, S.G. (1958) Ainino-acid sequence in a fraction of Bombyx silk fibroin. 

The calculation of the excess Rn activity of the sample must include (1) a decay correction from the time the sample was collected until the mid-point of the counting time, (2) the fraction of equilibrium attained with the Rn daughters ( Po, Pb, Bi) before counting, (3) the efficiency of the detector, (4) the background of the detector and (5) the blank associated with the sample container and extraction system. These calculations and the errors associated with the measurements have been discussed by Lucas and Woodward (1964), Sar-miento et al. (1976) and Key et al. (1979). The best precision (2o) obtained for the scintillation counting procedures is approximately 13 %. Schlosser et al. (1984) claimed a precision of 11 % for the proportional counting technique. 

Taxine is the name used for the amorphous basic fraction extracted from the leaves of Taxus baccata L. and related species such material, which is responsible for the poisonous nature of the plants, was first obtained in 1856 by Lucas (1). In the past it has been uncertain whether taxine is a single substance or a mixture, and whether the taxine fractions from related species are the same or different. The earlier chemical studies (2), not surprisingly, made little progress. The most significant results, due to Winterstein (3) and his colleagues, indicated that taxine was an ester of a nitrogen-free polyhydroxylic compound with acetic acid and j8-dimethylamino- -phenylpropionic acid (Winterstein s acid). 

As (he solids and liquid phase were pumped around the flow rig, two weighing hoppers were used to delermine the amount of solids and liquid collected in a given time. This determines the overall flow rate. To determine the overall volume fraction at the test pipe section, a gradiomanometer was used. Details regarding the workings of the gradiomanometer are documented in the literature (Loh [3] and Lucas et al.[12]). 

Lucas GP, Cory J, Waterfall RC, Loh WW, Dickin FJ (1999) Measurement of the solids volume fraction and velocity distributions in solids-Uquid flows using dual-plane electrical resistance tomography. Flow Meas Instrum 10 249-258... 

Kunamaneni, S., Buzza, D. M. A., De Luca, D., Richards, R. W. Rheology of fractionated and unfractionated hyperbranched polyesters. MacromoL (2004) 37, pp. 9295-9297 Hsieh, H. L., Quirk, R. R, Anionic Polymerization (1996) Marcel Dekker, New York Morton, M., Anionic Polymerization Principles and Practice (1983) Academic Press, New York... 

The Lucas rules are based on corresponding states methods. This approach estimates pseudocritical and other mixture properties fiom pure component properties, the composition of tte mixture, and mixing and combining rules defined by Lucas. The Lucas approach is the first of the correlations considered that is not interpolative, it will not result in the pnre component viscosity if the mole fraction of one component is 1 and the mole fraction of the other component is 0. The methods utilizing corresponding states are not as accurate as those based on the kinetic theory, but provide an advantage in the lack of necessity of having pure component data. 

The empirical data obtained by INL for HeXe gas tnixmre viscosity are provided for a temperature range of approximately 300 K to 800 K at various mole fractions. The correlation methods described above were all computed using the DIPPR pure component equations, with the exception of the Lucas Rules, which do not utilize pure component values. This allows a consistent comparison of methods. The methods used for the comparison in Figure 5 and labeled as such are as follows ... 

---