Lucas number

The case a = 1 is also interesting, especially because Fibonacci numbers and Lucas numbers turn up (Bergan, Cyvin BN and Cyvin 1987 Cyvin SJ 1990) ... 

Here the Fibonacci and Lucas numbers are defined by and Lq = 1, = 3, respectively. 

Cyvin SJ (1990) The Lucas Numbers and Kekule Structures of Some Coronoid and Coronoid—Like—Hydrocarbons. Acta Chim Hung 127 849... 

The coefficients for given bond order increase like a Fibonacci series with increasing n. This is immediately obvious for the coefficients of bond orders 4 and 0, which correspond, in both cases, to the familiar Lucas numbers. This correspondence is interpreted to define a closed, and hence periodic, system. 

In the numerous studies of the IR-spectra of the matrix-isolated reactants (see, e.g., Frei and Pimentele [1983]) there have been found a number of chemical conversions. Among them, from the point of view of the present review, the reaction NO with O3 [Lucas and Pimentele 1979],... 

A study by Kontogiannis and Lucas (1990) has reviewed these approaches and developed a classification of cognitive phenomena which occur under high stress. This is presented in Figure 3.5. The classification was developed by examining a number of incidents from various industrial sectors. The cognitive phenomena illustrate in a practical manner the psychological mechanisms which can precipitate errors under stress. 

The idea that the properties of many organic compounds, especially the aromatic compounds, cannot be simply correlated with a single valence-bond structure, but require the assignment of a somewhat more complex electronic structure, was developed during the period 1923 to 1926 by a number of chemists, including Lowry, Lapworth, Robinson, and Ingold in England, Lucas... 

These ideas have arisen through the combined efforts of a large number of different workers, among whom may be mentioned Fry, Stieglitz, Lapworth, Lewis, Lucas, Lowry, Robinson, and especially Ingold. For details the reader is referred to the excellent review articles of the last named author.2... 

Holz, M Lucas, O Muller, C, NMR in the Presence of an Electric Current, Simultaneous Measurements of Ionic Mobilities, Transference Numbers, and Self-Diffusion Coefficients Using an NMR Pulsed-Gradient Experiment, Journal of Magnetic Resonance 58, 294, 1984. Hooper, HH Baker, JP Blanch, HW Prausnitz, JM, Swelling Equilibria for Positively Ionized Polyacrylamide Hydrogels, Macromolecules 23, 1096, 1990. 

Je ryl was probably not used in Egypt before Ptolemaic times (87). A. Lucas stated that the mines in the Red Sea hills, which were mentioned by Strabo and Pliny the Elder, were probably the only source of beryl in ancient times (87). In 1817 F. Cailliaud discovered the emerald mines near Mt. Zabara nearly in the same state in which they had been left by the engineers of the Ptolemies. He penetrated into a vast number of excavations and subterraneous canals, some of which are so deep that four hundred men may work in them at once.. .. M. C. himself set about working the mines, and he has presented six pounds of emeralds to Mahommed Ali Pashaw (88). 

It appears that a number of complications await the recovering bipolar patient after an episode of mania. For example, Lucas et al. ( 44) reported on a retrospective linear discriminant analysis of 100 manic episodes (1981 to 1985) during the recovery phase and found that the incidence of subsequent depression was 30% in the first month. Many episodes were transient, however, and did not necessarily require treatment. This phenomenon could be successfully predicted in 81% of cases in which there is a premorbid history of cyclothymia with either a personal or a family history of depression. The highly significant association between family history and postmanic depression again supports the hypothesis of a genetic basis for bipolar disorder. 

Allyl Ethers of Carbohydrate. A number of compds, such as allyl glycerol, allylglycol, allyl mannitol, allylsorbitol, all yl pent a-erythritol, etc were prepd during and after WWII by Nichols Yanovsky. They also discussed previous work on this subject and listed several refs. According to them the first compd of this type was triallyl-glycerol prepd in 1856 by M.Berthelot S. de Luca... 

Disiloxanediols are sometimes obtained inadvertantly when the silanediol is desired, or appear as by-products of the latter. Synthesis of the lower members is often quite difficult, and careful control of pn and temperature was found necessary by Lucas and Martin (38) to prepare tetramethyldisiloxanediol. Frisch, Goodwin and Scott (19) obtained a number of divinyl- and diallyldisiloxanediols under conditions similar to those used for the preparation of the related silanediols. Robinson and Kipping (57) early obtained relatively stable disiloxanediols from silanediols by means of heat or acids. 

After World War II, mechanization became virtually essential for weed control and resulted in dramatic adoption of tractors in sugarcane. In Louisiana, the number of tractors on sugarcane farms doubled between 1940 and 1947. During this same period, sugarcane acreage in Louisiana increased 20% while farm labor decreased 40%. Much of this change was due to cultivation with tractors and the introduction of 2,4-D for broadleaf weed control (Conrad and Lucas, 1995). 

The effects of gaseous pollutants on both crops and trees has been reviewed by Mansfield and Lucas (1990), and a number of books have appeared on the topic, for example Unsworth and Ormrod (1982) Koziol and Whatley (1984) Treshaw (1984) Winner et al. (1985) Hutchinson and Meema (1987) Mathy (1988) Schulte-Hostede et al. (1988). 

Lucas JB, Kramkowski RS. 1975. Health hazard evaluation determination report number 74-87-221. Cincinnati, OH U.S. Department of Health, Education, and Welfare, Center for Disease Control, National Institute for Occupational Safety and Health. 

THE HISTORICAL ROOTS OF ELEMENTARY MATHEMATICS, Lucas N.H. Bunt, Phillip S. Jones, and Jack D. Bedient. Fundamental underpinnings of modem arithmetic, algebra, geometry and number systems derived from ancient civilizations. 320pp. 5H x 8b. 25563-8 Pa. 7.95... 

Dysbindin-2B has been identified as both stem cell factor apoptosis response protein 1 (SCF ARP1) by Lucas et al. (2005) and as a casein kinase 1 binding partner (CK1BP) by Yin et al. (2006). SCF ARP1 is expressed in bone marrow-derived myelomonocytic stem cells upon induction of apoptosis by withdrawal of stem cell growth factor SCF (Lucas et al., 2005). Programmed cell death via apoptosis controls stem cell numbers during hematopoietic cell development (Domen 2001). Since apoptosis is similarly important in development of neurons (Kuan et al., 2000 Buss and Oppenheim, 2004), dysbindin-2B may play a role in nervous system development (see also Section 2.2.33.1). 

A number of workers have studied the epitaxial relationships of ZnO on Zn (57-61). The earlier reports of pseudomorphism (58) have not been confirmed by later workers. The most careful study with attention to the surface preparation of the metal was that of Lucas (57) and his results for room temperature oxidation are included in Table IL This work emphasized the importance of surface preparation, and showed conclusively that different orientations could occur on a surface as a result of facet formation. At higher temperatures Raether (59) reported an orientation in which the (0001) planes of the ZnO were normal to the surface rather than parallel as in the case of room temperature oxidation. Yang (61), however, reported the usual parallel orientation at 350°C. 

Moreno-Arribas and Lonvaud-Funel (1999). Moreno-Arribas et al. (2000) isolated and identified a number of tyramine-producing lactic acid bacteria in wine that had undergone malolactic fermentation all belonging to the lactobacilli. Tyrosine decarboxylase was then purified (Moreno-Arribas and Lonvaud-Funel 2001) and the corresponding gene was purified and sequenced (Lucas and Lonvaud-Funel 2002 Lucas et al. 2003). As far as the literature suggests, no tyramine-producing 0. oeni strain has yet been reported, with the exception of one strain (O. oeni DSM 2025) that was shown to be able to produce tyramine in a laboratory medium (Choudhury etal. 1990). 

In the Southern Ocean, a number of temporal and spatial correlation studies have shown lowerJ rarios with elevated NH concentrations where the reduction in the J-rario may be due to increased NH uptake rates and/or reduced NOj" uptake rates (e.g., Goeyens et al., 1995 1998 Lucas et al., 2007 Owens et al., 1991). However, there have been few inhibition (suppression) studies in the Southern Ocean where either single or multiple NHj concentrations are experimentally increased to evaluate the effects on NOj" uptake rates. The first such study was conducted at two stations in the Scotia Sea by Glibert et al. (1982), and an inhibitory effect was... 

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