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1

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Solving linear equations using residue arithmetic — Algorithm II (1970)

Howell, Jo Ann ; Gregory, Robert T.

Springer

BIT 10 (1970), S. 23-37

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ISSN: 1572-9125

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract In a previous paper, which appeared in two parts, Algorithm I was described. (See [1] and [2] for details). Algorithm II differs from Algorithm I in that the Chinese Remainder Theorem is not used whenever it is necessary to reconstruct a unique integer from its residue representation. Instead, the residue representation is converted to asymmetric residue representation and then the symmetric residue representation is converted to its associatedsymmetric mixed-radix representation, from which the unique integer can be reconstructed in an easy manner. This procedure has advantages over the procedure using the Chinese Remainder Theorem.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01940889

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2

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An algorithm for solving linear algebraic equations using residue arithmetic I (1969)

Howell, Jo Ann ; Gregory, Robert T.

Springer

BIT 9 (1969), S. 200-224

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ISSN: 1572-9125

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract This paper is in two parts. Part I contains a survey of the elementary theory of residue arithmetic and a description of an algorithm for solvingAx=b using single-modulus residue arithmetic. In Part II there is a description of the algorithm using more than one modulus. Part II also contains a discussion of how to select the moduli along with some numerical results. There is a sketch of this procedure in Newman [1]. However, the treatment here is complete and uses the notation of Szabó and Tanaka [2]. It lays the foundation for a subsequent paper which will extend these results.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01946813

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3

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An algorithm for solving linear algebraic equations using residue arithmetic II (1969)

Howell, Jo Ann ; Gregory, Robert T.

Springer

BIT 9 (1969), S. 324-337

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ISSN: 1572-9125

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Part I contained an algorithm for solvingAx=b using single-modulus residue arithmetic. Part II contains a description of the algorithm when more than one modulus is used. There is a discussion of how to select the moduli along with some numerical results. There is a sketch of this procedure in Newman [1]. However, the treatment here is complete and uses the notation of Szabó and Tanaka [2]. It lays the foundation for a subsequent paper which will extend these results.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF01935864

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4

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Possible non-equilibrium oxygen isotope effects in mantle nodules, an alternative to the Kyser-O'Neil-Carmichael18O/16O geothermometer (1986)

Gregory, Robert T. ; Taylor, Hugh P. ; Kyser, T. Kurtis ; [et al.]

Springer

Contributions to mineralogy and petrology 93 (1986), S. 114-119

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ISSN: 1432-0967

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences

Notes: Abstract Kyser, O'Neil, and Carmichael (1981, 1982) measured theδ 18O values of coexisting minerals from peridotite nodules in alkali basalts and kimberlites, interpreting the nodules as equilibrium assemblages. Using Ca-Mg-Fe element-partition geothermometric data, they proposed an empirical18O/16O geothermometer: T(°C)=1,151−173Δ−68Δ 2, whereΔ is the per mil pyroxene-olivine fractionation. However, this geothermometer has an unusual “crossover” at 1,150 °C, and in contrast to what might be expected during closed-system equilibrium exchange, the most abundant mineral in the nodules (olivine) shows a much greater range inδ 18O (+4.4 to +7.5) than the much less abundant pyroxene (all 50 pyroxene analyses from spinel peridotites lie within the interval +5.3 to +6.5). Onδ 18O-olivinevs. δ 18O-pyroxene diagrams, the mantle nodules exhibit data arrays that cut across theΔ 18O=zero line. These arrays strongly resemble the non-equilibrium quartzfeldspar and feldspar-pyroxeneδ 18O arrays that we now know are diagnostic of hydrothermally altered plutonic igneous rocks. Thus, we have re-interpreted the Kyser et al. data as non-equilibrium phenomena, casting doubt on their empirical geothermometer. The peridotite nodules appear to have been open systems that underwent metasomatic exchange with an external, oxygen-bearing fluid (CO2, magma, H2O, etc.); during this event, the relatively inert pyroxenes exchanged at a much slower rate than did the coexisting olivines and spinels, in agreement with available exchange-rate and diffusion measurements on these minerals. This accounts for the correlation betweenΔ 18O pyroxene-olivine and the whole-rockδ 18O of the peridotites, which is a major difficulty with the equilibrium interpretation.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00963589

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5

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Implications of the structure of the Wadi Tayin metamorphic sole, the Ibra-Dasir block of the Samail ophiolite, and the Saih Hatat window for late stage extensional ophiolite emplacement, Oman (2000)

Gray, David R. ; Gregory, Robert T.

Springer

Marine geophysical researches 21 (2000), S. 211-227

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ISSN: 1573-0581

Keywords: extensional faulting ; obduction ; ophiolite ; Oman

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences , Physics

Notes: Abstract Late stage extensional character of the Samail Ophiolite, as inferred from structure within the Ibra-Dasir blocks, supports gravity-driven final emplacement for the ophiolite. This however, is not related to ‘collapse’ off ramp-related domal culminations as speculated in Late Cretaceous thrusting scenarios. Domal structures of the Oman Mountains are Tertiary structures as originally inferred by Glennie et al. (1974). Gravity-driven emplacement of the ophiolite is related to the rising NE-directed Saih Hatat fold-nappe, now preserved within the Saih Hatat window and offshore along the Batinah coast as the Saih Hatat axis. Ar-Ar geochronology indicates that the Saih Hatat antiformal fold-nappe development (76–70 Ma) was occurring at the time the ophiolite was being emplaced onto the margin between 70–80 Ma. Evidence for extension is shown by: (1) the truncation of fold structures in the ophiolite pseudostratigraphy by the approximately planar, late stage basal fault (previously referred to as the ‘Samail thrust’ and now as the Samail detachment fault), (2) faults within the ophiolite cutting down section (e.g., Jabal Dimh fault), and (3) by the presence of both high angle and low angle normal faults, particularly in the metamorphic sole rocks at Wadi Tayin. Kinematic analysis of the high angle fault pairs in the metamorphic sole at Wadi Tayin indicates N–S pull-apart. These features of the Samail Ophiolite, along with similar features in the Bay of Islands Ophiolite in New Foundland, suggest that final stages of ophiolite obduction onto continental margins must involve extensional emplacement as a thin (〈 5 km) sheet. This emplacement is accompanied by further thinning of the ophiolite sheet with internal development of both low and high angle normal faults.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1023/A:1026772717865

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6

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Hydrogen and oxygen isotopic compositions of waters from fumaroles at Kilauea summit, Hawaii (1995)

Hinkley, Todd K. ; Quick, James E. ; Gregory, Robert T. ; [et al.]

Springer

Bulletin of volcanology 57 (1995), S. 44-51

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ISSN: 1432-0819

Keywords: Key words Isotopic compositions ; Fumaroles ; Kilauea ; Hawaii

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences

Notes: Abstract Condensate samples were collected in 1992 from a high-temperature (300° C) fumarole on the floor of the Halemaumau Pit Crater at Kilauea. The emergence about two years earlier of such a hot fumarole was unprecedented at such a central location at Kilauea. The condensates have hydrogen and oxygen isotopic compositions which indicate that the waters emitted by the fumarole are composed largely of meteoric water, that any magmatic water component must be minor, and that the precipitation that was the original source to the fumarole fell on a recharge area on the slopes of Mauna Loa Volcano to the west. However, the fumarole has no tritium, indicating that it taps a source of water that has been isolated from atmospheric water for at least 40 years. It is noteworthy, considering the unstable tectonic environment and abundant local rainfall of the Kilauea and Mauna Loa regions, that waters which are sources to the hot fumarole remain uncontaminated from atmospheric sources over such long times and long transport distances. As for the common, boiling point fumaroles of the Kilauea summit region, their 18O, D and tritium concentrations indicate that they are dominated by recycling of present day meteoric water. Though the waters of both hot and boiling point fumaroles have dominantly meteoric sources, they seem to be from separate hydrological regimes. Large concentrations of halogens and sulfur species in the condensates, together with the location at the center of the Kilauea summit region and the high temperature, initially suggested that much of the total mass of the emissions of the hot fumarole, including the H2O, might have come directly from a magma body. The results of the present study indicate that it is unreliable to infer a magmatic origin of volcanic waters based solely on halogen or sulfur contents, or other aspects of chemical composition of total condensates.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00298706

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7

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Non-equilibrium, metasomatic18O/16O effects in upper mantle mineral assemblages (1986)

Gregory, Robert T. ; Taylor, Hugh P.

Springer

Contributions to mineralogy and petrology 93 (1986), S. 124-135

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ISSN: 1432-0967

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences

Notes: Abstract Kyser, O'Neil, and Carmichael (1981, 1982) measured theδ 18O values of coexisting minerals from peridotite nodules in alkali basalts and kimberlites, interpreting the nodules as equilibrium assemblages. Based mainly on the systematics revealed inδ 18O-olivinevs. δ 18O-pyroxene diagrams, we have re-interpreted the Kyser et al. data as non-equilibrium phenomena. On suchδ-δ diagrams, the mantle nodules exhibit data arrays that cut across theΔ 18O=zero line; these arrays strongly resemble the non-equilibrium quartz-feldspar and feldspar-pyroxeneδ 18O arrays that we now know arediagnostic of hydrothermally altered plutonic igneous rocks. Thus, the peridotites appear to have been open systems that underwent metasomatic exchange with an external, oxygen-bearing fluid (CO2 magma, H2O, etc.); during this event, the relatively inert pyroxenes exchanged at a much slower rate than did the coexisting olivines and spinels. This accounts for the correlation betweenΔ 18O pyroxene-olivine and the whole-rockδ 18O of the peridotites, which is a major difficulty with the equilibrium interpretation. The metasomatic18O-enrichments of the peridotites can be related to metasomatic enrichments in LIL elements and the development of amphibole and phlogopite. This type of precursor metasomatic activity can explain the development of alkali basalt magmas, as well as leucitites and nephelinites (all of which tend to be slightly18O-rich relative to MORB, withδ 18O=+6 to +7.5). Fluids with appropriateδ 18O values to explain the open-system metasomatic effects can be produced by exchange with ancient subducted oceanic crust (eclogite). However, fluid/rock ratios of about 0.4 to 2.5 are required, indicating that this cannot be a mantle-wide phenomenon. Also, these non-equilibrium effects are apparently transient phenomena, probably associated with the eruptive events that brought the nodules to the surface; at characteristic mantle temperatures, the effects would likely disappear in a few tens of millions of years, or less, implying that the ultramafic nodules are not typical samples of the upper mantle.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00963591

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8

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Contrasting stable isotope behavior between calcite and dolomite marbles, Lone Mountain, Nevada (1996)

Richards, I. J. ; Labotka, Theodore C. ; Gregory, Robert T.

Springer

Contributions to mineralogy and petrology 123 (1996), S. 202-221

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ISSN: 1432-0967

Source: Springer Online Journal Archives 1860-2000

Topics: Geosciences

Notes: Abstract Late Proterozoic to Cambrian carbonate rocks from Lone Mountain, west central Nevada, record multiple post-depositional events including: (1) diagenesis, (2) Mesozoic regional metamorphism, (3) Late Cretaceous contact metamorphism, related to the emplacement of the Lone Mountain granitic pluton and (4) Tertiary hydrothermal alteration associated with extension, uplift and intrusion of silicic porphyry and lamprophyre dikes. Essentially pure calcite and dolomite marbles have stable isotopic compositions that can be divided into two groups, one with positive δ13C values from+3.1 to +1.4 ‰ (PDB) and high δ18O values from +21.5 to +15.8 ‰ (SMOW), and the other with negative δ13C values from –3.3 to –3.6‰ and low δ18O values from +16.9 to +11.1‰. Marbles also contain minor amounts of quartz, muscovite and phlogopite. Brown and blue luminescent, clear, smooth textured quartz grains from orange luminescent calcite marbles have high δ18O values from +23.9 to +18.1‰, while brown luminescent, opaque, rough textured quartz grains from red luminescent dolomite marbles typically have low δ18O values from +2.0 to +9.3‰. The δ18O values of muscovite and phlogopite from marbles are typical of micas in metamorphic rocks, with values between +10.4 and +14.4‰, whereas mica δD values are very depleted, varying from −102 to −156‰. No significant lowering of the δ18O values of Lone Mountain carbonates is inferred to have occurred during metamorphism as a result of devolatilization reactions because of the essentially pure nature of the marbles. Bright luminescence along the edges of fractures, quartz cements and quartz overgrowths in dolomite marbles, low δD values of micas, negative δ13C values and low δ18O values of calcite and dolomite, and depleted δ18O values of quartz from dolomite marbles all indicate that meteoric fluids interacted with Lone Mountain marbles during the Tertiary. Partial oxygen isotopic exchange between calcite and low 18O meteoric fluids lowered the δ18O values of calcite, resulting in uniform quartz-calcite fractionations that define an apparent pseudoisotherm. These quartz-calcite fractionations significantly underestimate both the temperature of metamorphism and the temperature of post-metamorphic alteration. Partial oxygen isotopic exchange between quartz and meteoric fluids also resulted in 18O depletion of quartz from dolomite marbles. This partial exchange was facilitated by an increase in the surface area of the quartz as a result of its dissolution by meteoric fluids. The negative δ13C values in carbonates result from the oxidation of organic material by meteoric fluids following metamorphism. Stable isotopic data from Lone Mountain marbles are consistent with the extensive circulation of meteoric hydrothermal fluids throughout western Nevada in Tertiary time.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/s004100050151

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