A Dedekind Criterion over Valued Fields

Siberian Mathematical Journal - Let $ (K,nu) $ be an arbitrary-rank valued field, let  $ R_{nu} $ be the valuation ring of  $ (K,nu) $ , and let  $ K(alpha)/K $ be...     

Distribution and cycle of arsenic compounds in the ocean

In order to understand the distribution and the cycle of arsenic compounds in the marine environment, the horizontal distributions of arsenic(V) [As(V)], arsenic(III) [As(III)], monomethylarsonic acid (MMAA) and dimethylarsinic acid (DMAA) in the Indian Pacific Oceanic surface waters have been investigated. This took place during cruises of the boat Shirase from Tokyo to the Syowa Station (15 November–19 December 1990), of the tanker Japan Violet from Sakai to Fujayrah (28 July–17 August 1991) and of the boat Hakuho-maru from Tokyo to Auckland (19 September–27 October 1992). Vertical distributions of arsenic in the west Pacific Ocean have also been investigated. The concentration of As(V) was found to be relatively higher in the Antarctic than in the other areas. Its concentration varied from 340 ng dm^?3 (China Sea) to 1045 ng dm^?3 (Antarctic). On the other hand, the concentrations of the biologically produced species, MMAA and DMAA, were extremely low in the Antarctic and southwest Pacific waters. Their concentrations in Antarctic waters were 8 ng dm^?3 and 22 ng dm^?3 and those in the southwest Pacific were 12 ng dm^?3 and 25 ng dm^?3. In the other regions the concentration varied from 16 ng dm^?3 (China Sea) to 36 ng dm^?3 (north Indian Ocean) for MMAA and from 50 ng dm^?3 (east Indian Ocean) to 172 ng dm^?3 (north Indian Ocean) for DMAA. As a result, with the exception of Antarctic and southwest Pacific waters, the percentages of each arsenic species in the surface waters were very similar and varied from 52% (east Indian Ocean) to 63% (northwest Pacific Ocean) for As(V), from 22% (northwest Pacific Ocean) to 27% (east Indian Ocean) for As(III) and from 15% (northwest Pacific Ocean) to 21% (north and east Indian Oceans) for the methylated arsenics (MMAA+DMAA). These percentages in Antarctic waters were 97%, 0.2% and 2.8%, respectively, and those in the southwest Pacific Ocean were 97% for As(V)+As(III) and 3% for MMAA+DMAA. The very low concentrations of the biologically produced species in Antarctic waters and that of methylated arsenic in southwest Pacific waters indicated that the microorganism communities in these oceans was dominated by microorganisms having a low affinity towards arsenic. Furthermore, microorganism activity in the Antarctic was also limited due to the much lower temperature of the seawater there. The vertical profile of inorganic arsenic was 1350 ng dm^?3 in surface waters, 1500 ng dm^?3 in bottom waters with a maximum value of 1700 ng dm^?3 at a depth of about 2000 m in west Pacific waters. This fact suggested the uptake of arsenic by microorganisms in the surface waters and the co-precipitation of arsenic with hydrated heavy-metal oxides in bottom waters. The suggested uptake of inorganic arsenic and subsequent methylation was also supported by the profile of DMAA, with a high concentration of about 26 ng dm^?3 in surface water and a significant decrease to a value of 9 ng dm^?3 at a depth of 1000 m.     

Method of micro-sampling human dentine collagen for stable isotope analysis

Rationale

Sampling of dentine for stable carbon (δ¹³C) and nitrogen (δ¹⁵N) isotope ratios in the direction of tooth growth allows the study of temporal changes to the diet and physiological stress of an individual during tooth formation. Current methods of sampling permanent teeth using 1 mm increments provide temporal resolution of 6–9 months at best depending on the tooth chosen. Although this gives sufficient sample sizes for reliable analysis by mass spectrometry, sectioning the dentine across the incremental structures results in a rolling average of the isotope ratios. A novel method of incremental dentine collagen sampling has been developed to decrease the collagen increment size to 0.35 mm along the incremental structures, thus reducing averaging and improving the temporal resolution of short-term changes within the δ¹³C and δ¹⁵N values.

Methods

This study presents data for a MicroMill-assisted sampling method that allows for sampling at 0.35 mm width × 1 mm depth increments following the incremental growth pattern of dentine. A NewWave MicroMill was used to sample the demineralised dentine section of modern donated human third molars from Sudan and compared to data from the same teeth using the 1 mm incremental sectioning method 2 established by Beaumont et al.

Results

The δ¹³C and δ¹⁵N isotopic data showed an increased temporal resolution, with each increment providing data for 2–4 months of dentine formation.

Conclusions

The data show the potential of this method for studying dietary reconstruction, nutritional stress, and physiological change with greater temporal resolution potentially to seasonal level and with less attenuation of the δ¹³C and δ¹⁵N values than was previously possible from human dentine.

     

An inverse problem in reaction kinetics

In this paper we investigate the problem of extracting information about chemical reactions involving multiple species from the time history of the concentration of each species. The mathematical model of the kinetic system leads to a system of ordinary differential equations. Our focus is to examine whether the species’ concentrations as functions of time are sufficient to determine what chemical reactions, and at what reaction rates, have occurred. We show that within the limitation of our model, there may be many candidate reaction systems that could explain the data. Using the notion of sparsity, we provide a quantitative assessment of the question of distinguishability. We further demonstrate that sparsity enforcing approaches, such as minimizing the ℓ ₁ or the ℓ ₀ norms are not reliable. Our conclusion is that additional knowledge about the kinetic system will be necessary to reliably solve this inverse problem.     

Hybrid of chitin and humic acid as high performance sorbent for Ni(II)

Hybrid of humic acid (HA) and chitin has been synthesized and the hybrid material (chitin-HA) was then applied as sorbent to adsorb Ni(II). The HA was extracted from peat soil of Gambut District, South Kalimantan, Indonesia, according to the procedure recommended by IHSS (International Humic Substances Society). The chitin was isolated from crab shell waste of sea food restaurants through deproteination using NaOH 3.5% (w/v) and followed by removal of inorganic impurities using HCl 1 M. The synthesis of chitin-HA was performed by reacting gelatinous chitin solution in HCl 0.5 M and HA solution in NaOH 0.5 M. Parameters investigated in this work consists of effect of medium acidity on the sorption, sorption rate (k_s) and desorption rate (k_d) constants, Langmuir (monolayer) and Freundlich (multilayer) sorption capacities, and energy (E) of sorption. The k_s and k_d were determined according to a kinetic model of first order sorption reaching equilibrium, monolayer sorption capacity (b) and energy (E) were determined according to the Langmuir isotherm model, and multilayer sorption capacity (B) was determined based on the Freundlich isotherm model.Sorption of Ni(II) on both chitin and chitin-HA was maximum at pH 8.0. The kinetic expression resulted from the proposed kinetic model has been shown to be more applicable than the commonly known Lagergren equation obtained from the pseudo-first order sorption model. The application of the proposed model revealed that the presence of HA increased the k_s from 0.018 min⁻¹ for chitin to 0.031 min⁻¹ for chitin-HA. As for k_s, the value of b was also bigger in the presence of HA, i.e. 7.42 × 10⁻⁵ mol/g for chitin and 9.93 × 10⁻⁵ mol/g for the chitin-HA. Unlike k_s and b, the value of E slightly decreased from 23.23 to 21.51 kJ/mol for the absence and presence of HA, respectively. It can also be deduced that the presence of HA on chitin contributed more to the additional layer of Ni(II) sorbed on sorbent. Without HA, B for chitin was only 6.17 times higher than b, while with the presence of HA, the enhancement of the sorption capacity from the multilayer (B) to the monolayer (b) was 19.40. The increase of k_s, b, B, and the decrease of E would be very benefit in the real application of chitin-HA for the recovery of Ni(II) from aqueous samples.     

Scattering techniques for a one dimensional inverse problem in geophysics

A one dimensional problem for SH waves in an elastic medium is treated which can be written as v_tt = A^?1 (Av_y)_y, A = (?μ)^1/2, ? = density, and μ = shear modulus. Assume A ? C¹ and A′/A ? L¹; from an input v_y(t, 0) = ?(t) let the response v(t, 0) = g(t) be measured (v(t, y) = 0 for t < 0). Inverse scattering techniques are generalized to recover A(y) for y > 0 in terms of the solution K of a Gelfand-Levitan type equation, .     

Synthesis and utilization of Mg/Al hydrotalcite for removing dissolved humic acid

It has been synthesized Mg/Al layered double hydroxide anionic clay (Mg/Al hydrotalcite) through direct precipitation by adding 0.5 M NaOH solution into a mixed solution containing Mg(NO₃)₂ and Al(NO₃)₃ with molar ratio of 0.1:0.05 until the medium acidity reached pH 10.1. The synthesized Mg/Al hydrotalcite was then utilized to remove dissolved humic acid in aqueous medium. The humic acid was isolated from peat soil taken in Gambut District, South Kalimantan, Indonesia using the recommended procedure of IHSS (International Humic Substances Society). The removal of humic acid was mostly occurred through simple sorption process without accompanied by significant intercalation. The sorption was optimum at pH 9.0, with the first order rate constant, capacity and energy of sorption were 5.50 × 10⁻³ min⁻¹, 0.12 mmol g⁻¹ (69 mg g⁻¹), and 28.32 kJ mol⁻¹, respectively.     

On complete recovery of geophysical data

One considers an elastic halfspace with depth (x₁) dependent density Q and Lamé moduli (λ,m?). Impulsive stresses τli = δ(x₂, x₃)δ(t) for x₁ = 0 are applied with displacement responses u_i = g_i(t, x₂, x₃) at x₁ = 0 (i = 1, 2, 3). Let v_i(t, x₁) = ∫∫u_idx₂dx₃ (i = 1, 2 is enough) and set w(t, x₁) = ∫∫x₂u₁dx₂dx₃. One obtains a system of 3 differential equations for v₁, v₂, and w to which the spectral techniques of inverse scattering theory are applied as in [25]. The inverse problems for the uncoupled v_i can then be solved to produce 2 functions A₁ and A₂ involving (Q, λ, μ) as functions of “bound” variables y₁ and y₂ containing (Q, λ, μ), between which a relation then is determined. Analysis of the coupled equation for w then leads to a Fredholm integral equation whose solution provides an additional relation between (Q, λ, μ) from which (Q, λ, μ) can be determined as functions of x₁. The integral equation is reduced to a Volterra type equation by results and techniques of transmutation and then solved by a modification of standard techniques. A number of features and results of independent mathematical interest arise from the transmutation theory.     

On the Measurement of two Independent Viscoelastic Functions with Instrumented Indentation Tests

In the present paper, a methodology for complete characterization of linear isotropic viscoelastic material with spherical instrumented indentation test is proposed. The developed method allows for measuring two independent viscoelastic functions, shear relaxation modulus and time-dependent Poisson’s ratio, from the indentation test data obtained at non-decreasing loading, but otherwise arbitrary. Finite element modelling (FEM) is relied upon for validating the proposed methodology and for quantifying the influence of experimental variables on the measurements accuracy. Spherical indentation experiments are performed on several viscoelastic materials: polyoxymethylene, bitumen and bitumen-filler mastics. The viscoelastic material functions obtained with the indentation tests are compared with the corresponding results from the standard mechanical tests. Numerical and experimental results presented indicate that the methodology proposed allows mitigating the machine compliance and loading rate effects on the accuracy of the viscoelastic indentation tests.