al-Nihāyah fī gharīb al-ḥadīth wa-al-athar.

In the margin: Suyūṭī's compendium, entitled: al-Durr al-nathīr.

Ludendorff's own story, August 1914-November 1918; th great war from the siege of Liege to the signing of the armistice as viewed from the Grand headquarters of the German army,

Mode of access: Internet.

Late Quaternary uplift and subsidence of the west coast of Tanna, south Vanuatu, southwest Pacific: U-Th ages of raised coral reefs in the Median Sedimentary Basin

Twelve Late Quaternary TIMS U-Th ages are reported here from 10 coral samples collected in situ from five transgressive coral/algal raised reefs (height: max. 113 m, min. 8 m) and two raised lagoonal deposits (height: max. 18 m, min. 8 m) along and near the west coast of Tanna, which lies in the Median Sedimentary Basin of South Vanuatu, southwest Pacific. These reefs and raised lagoonal deposits represent several age groups: (i) 215 ka (marine oxygen-isotope stage 7) penultimate interglacial (highest elevation and oldest); (ii) one lagoonal deposit of ca 127 ka (marine oxygen-isotope stage 5e); (iii) three last interglacial reefs with ages 102, 89 and 81 ka (representing marine oxygen-isotope stages 5c, 5b and 5a, respectively, of the latter part of the last interglacial); (iv) a lagoonal deposit with a 92 ka age (5b); and (v) a Holocene reef (age >5.7-5.0 ka) (lowest elevation and youngest). A ca 4.9 ka regressive reef (at elevation of 1.5 m above sea-level) is consistent with an island-wide 6.5 m uplift (probably largely coseismic), and a probable further island-wide uplift occurred in the late Holocene. The U-series ages taken together with the heights of transgressive reefs show that uplift since 215 ka was, on average, at similar to0.52 mm/y; although since 5 ka the uplift rate was, on average, similar to1.6 mm/y (the assumption being that a 1.5 m above sea-level reef has a coseismic origin). Elevation of transgressive reefs 5a, 5b and 5c and their ages indicates an island-wide subsidence during the period ?124-89 ka (i.e. Late Quaternary uplift/subsidence was jerky). Late Quaternary uplift/subsidence on the northwest coast of Tanna is considered to be due to irregular thicknesses of crust being subducted beneath Tanna.

Weathering geochronology by (U-Th)/He dating of goethite

Nine samples of supergene goethite (FeOOH) from Brazil and Australia were selected to rest the suitability of this mineral for (U-Th)/He dating. Measured He ages ranged from 61 to 8 Ma and were reproducible to better than a few percent despite very large Variations in [U] and [Th]. In all Samples with internal stratigraphy or independent age constraints, the He ages corroborated the expected relationship's. These data demonstrate that internally consistent He ages can be obtained on goethite. but do not prove quantitative 4 He retention. To assess possible diffusive He loss, stepped-heating experiments were performed on two goethite samples that were subjected to proton irradiation to produce a homogeneous distribution of spallogenic He-3. The He-3 release pattern indicates the presence of at least two diffusion domains, one with high helium retentivity and the other with very low retentivity at Earth surface conditions. The low retentivity domain, which accounts for similar to 5% of He-3, contains no natural He-4 and may represent poorly crystalline or intergranular material which has lost all radiogenic He-4 by diffusion in nature. Diffusive loss of He-3 from the high retentivity domain is independent of the macroscopic dimensions of the analyzed polycrystalline aggregate, so probably represents diffusion from individual micrometer-size goethite crystals. The He-2/He-3 evolution during the incremental heating experiments shows that the high retentivity domain has retained 90%-95% of its radiogenic helium. This degree of retentivity is in excellent agreement with that independently predicted from the helium diffusion coefficients extrapolated to Earth surface temperature and held for the appropriate duration. Considering both the high and low retentivity domains, these data indicate that one of the samples retained 90% of its radiogenic He-4 over 47.5 Ma and the other retained 86% over 12.3 Ma. Thus while diffusive-loss corrections to supergene goethite He ages are required. these initial results indicate that the corrections are not extremely large and can be rigorously quantified using the proton-irradiation He-4/He-3 method. Copyright (C) 2005 Elsevier Ltd.

Dating paleochannel iron ore by (U-Th)/He analysis of supergene goethite, Hamersley province, Australia

(U-Th)/He dating of late-stage authigenic goethite, combined with corrections for diffusive loss of He-4 by the He-4/He-3 methodology, reveals strong correlation between a sample's age and its depth in ferruginized channel sediments from the Yandicoogina deposit, Western Australia. Corrected ages, ranging from ca. 18 Ma near the surface to ca. 5 Ma at the bottom of the profile, indicate that ferruginization of the aggraded channels becomes progressively younger with depth. This trend is consistent with goethite precipitation at the groundwater-atmosphere interface during water table drawdown driven by the aridification of Western Australia during the Neogene. The results demonstrate that the (U-Th)/He system is ideal for dating goethite if diffusive loss corrections are applied. The approach is suitable for dating weathering reactions on Earth and should also be suitable for dating Fe oxyhydroxides in the Martian regolith.

Weathering Geochronology by (U-Th)/He Dating of Geothite

Ten samples of supergene goethite (FeOOH) from Brazil and Australia were selected to test the suitability of this mineral for (U-Th)/He dating. Measured He ages ranged from 8 to 61 Ma, and were reproducible to better than a few percent despite very large variations in [U] and [Th]. In all samples with internal stratigraphy or independent age constraints, the He ages honored the expected relationships. These data demonstrate that internally consistent He ages can be obtained on goethite, but do not prove quantitative 4He retention. To assess possible diffusive He loss, stepped-heating experiments were performed on two goethite samples that were subjected to proton irradiation to produce a homogeneous distribution of spallogenic 3He. The 3He release pattern indicates the presence of at least two diffusion domains, one with high helium retentivity and the other with very low retentivity at Earth surface conditions. The low retentivity domain, which accounts for ~ 5% of 3He, contains no natural 4He, and may represent poorly crystalline or intergranular material which has lost all radiogenic 4He by diffusion in nature. Diffusive loss of 3He from the high retentivity domain is independent of the macroscopic dimensions of the analyzed polycrystalline aggregate, so probably represents diffusion from individual micrometer-size goethite crystals. The 4He/3He evolution during the step heating experiments shows that the high retentivity domain has retained 90-95% of its radiogenic helium. This degree of retentivity is in excellent agreement with that independently predicted from the helium diffusion coefficients extrapolated to Earth surface temperature and held for the appropriate duration. These data indicate that one of the samples retained 90% of its radiogenic 4He over 46.8 Ma and the other retained 86% over 11.9 Ma. Thus while diffusive-loss corrections to supergene goethite He ages are required, these initial results indicate that the corrections are not extremely large and can be rigorously quantified using the proton-irradiation 4He/3He method.

(U-Th)/He and 40Ar/39Ar Geochronology of Weathering, Hamersley Province, Australia: Implications for weathering history and landscape Evolution

(U–Th)/He dating of goethite, when combined with quantification of diffusive 4He loss by the 4He/3He methodology, provides reliable corrected ages for minerals precipitated in weathering profiles. We have combined (U–Th)/He dating of supergene goethite with 40Ar/39Ar dating of supergene manganese oxides to study the weathering history and landscape evolution in the Hamersley Province, northwestern Australia. Incremental heating 40Ar/39Ar analysis of 187 grains of Mn oxides from 65 samples (44 hand specimens) collected from weathering profiles at seven field sites across the Hamersley Province yield precipitation ages ranging from 63.4 ± 0.9 to 1.5 ± 0.2 Ma. These results, combined with previous results of 40Ar/39Ar dating of Mn oxides (Vasconcelos, 1998 Vasconcelos, P.V., 1998. Unpub. report, pp. 1–278.Vasconcelos, 1998 and Cochrane, 2003), reveal a protracted and episodic history of weathering and landscape evolution, which was already ongoing in Late Cretaceous and spans the Palaeogene and Neogene. Seventy-three grains of goethite from 39 samples extracted from 21 hand specimens, collected from the same field sites where the Mn oxides originated, were dated by the (U–Th)/He method. Internally consistent (U–Th)/He ages, which range from 84.3 ± 12.2 to 3.3 ± 0.5 Ma, have been obtained for most samples when corrections are applied for 10% helium diffusive loss. The geochronological results obtained show remarkable similarity in the distribution of ages associated with supergene mineral precipitation. The widespread occurrence of iron oxides such as goethite in soils and weathering profiles and the successful application of (U–Th)/He dating of goethite offers great opportunities for extracting the wealth of palaeoclimatic and palaeoenvironmental information recorded by these profiles on the surface of terrestrial planets such as Earth and Mars.

Do the lichens Xanthoparmelia conspersa (Ach.) Hale and Rhizocarpon Ram. Em. Th. Fr. subgenus Rhizocarpon utilise exogenous carbohydrates for radial growth?

To field test the hypothesis that lichen thalli can use environmental sources of carbon, solutions of ribitol, arabitol and mannitol were added to intact thalli of Xanthoparmelia conspersa (Ach.) Hale and a yellow species of Rhizocarpon (Rhizocarpon Ram. Em. Th. Fr. subgenus Rhizocarpon). In addition, ribitol and an arabitol/mannitol mixture were added to the marginal hypothalli of Rhizocarpon thalli after removal of the areolae. Carbohydrates were added at the beginning of 2- or 3-month growth periods for up to 15 months at concentrations approximately three times the levels estimated to be in the thalli. Addition of carbohydrates to intact thalli of both species had no effect on total radial growth but addition of mannitol significantly increased growth of X. conspersa thalli in the September/October growth period in one experiment. However, this effect was not repeated in a subsequent experiment in which different concentrations of mannitol were added to intact thalli. Addition of ribitol to hypothalli of Rhizocarpon resulted in significantly increased growth in the first few months of the experiment, growth then declining to levels below that of untreated thalli. The data suggest that although hypothalli of Rhizocarpon may have the ability to utilise exogenous carbohydrates for growth, there was little evidence that intact thalli of either species utilise environmental sources of carbon in the field.

Analog of Favard's Theorem for Polynomials Connected with Difference Equation of 4-th Order

Orthonormal polynomials on the real line {pn (λ)} n=0 ... ∞ satisfy the recurrent relation of the form: λn−1 pn−1 (λ) + αn pn (λ) + λn pn+1 (λ) = λpn (λ), n = 0, 1, 2, . . . , where λn > 0, αn ∈ R, n = 0, 1, . . . ; λ−1 = p−1 = 0, λ ∈ C. In this paper we study systems of polynomials {pn (λ)} n=0 ... ∞ which satisfy the equation: αn−2 pn−2 (λ) + βn−1 pn−1 (λ) + γn pn (λ) + βn pn+1 (λ) + αn pn+2 (λ) = λ2 pn (λ), n = 0, 1, 2, . . . , where αn > 0, βn ∈ C, γn ∈ R, n = 0, 1, 2, . . ., α−1 = α−2 = β−1 = 0, p−1 = p−2 = 0, p0 (λ) = 1, p1 (λ) = cλ + b, c > 0, b ∈ C, λ ∈ C. It is shown that they are orthonormal on the real and the imaginary axes in the complex plane ...

An Iterative Method for the Matrix Principal n-th Root

In this paper we give an iterative method to compute the principal n-th root and the principal inverse n-th root of a given matrix. As we shall show this method is locally convergent. This method is analyzed and its numerical stability is investigated.

(Table S1) Uranium and Thorium isotopes and U/Th ages of IODP Exp310 cores from offshore Tahiti

The timing of sea-level change provides important constraints on the mechanisms driving Earth's climate between glacial and interglacial states. Fossil corals constrain the timing of past sea level by their suitability for dating and their growth position close to sea level. The coral-derived age for the last deglaciation is consistent with climate change forced by Northern Hemisphere summer insolation (NHI), but the timing of the penultimate deglaciation is more controversial. We found, by means of uranium/thorium dating of fossil corals, that sea level during the penultimate deglaciation had risen to ~85 meters below the present sea level by 137,000 years ago, and that it fluctuated on a millennial time scale during deglaciation. This indicates that the penultimate deglaciation occurred earlier with respect to NHI than the last deglacial, beginning when NHI was at a minimum.

Activity of isotopes of U, Th and Pa versus depth in bottom sediments from Core ML1_66

A sediment core from the European Basin with alternation of biogenic calcareous oozes and terrigenous sediments is studied by several methods. Isotopic age is determined by 230Th-ex and 231Pa-ex and by the radiocarbon method. Surface water paleotemperatures are reconstructed from complexes of planktic foraminifera and oxygen isotope ratios in their shells, and the ratio of biogenic and terrigenous components are investigated. Stages 1-8 of the oxygen-isotope scale are identified. Fluctuations in paleooceanic conditions in the area of coring are discussed.