On the number of Fourier coefficients that determine a Hilbert modular form

We estimate the number of Fourier coefficients that determine a Hilbert modular cusp form of arbitrary weight and level. The method is spectral (Rayleigh quotient) and avoids the use of the maximum principle.

     

Interfacial thermodynamics of gallic acid adsorption on a chargeable hydrophobic surface

The thermodynamics of adsorption of gallic acid (GA, 3,4,5-trihydroxylbenzoic acid) on the hanging mercury drop electrode (HMDE) surface was studied by temperature-dependent stripping voltammetry (TD-SV), at physiological pH 7.4. The thermodynamic parameters, e.g., Gibbs free energy, ΔG(ADS), enthalpy, ΔΗ(ADS) and entropy, ΔS(ADS), of adsorption have been determined at physiological temperatures 2-40 °C. Chemisorption of the radical species ≡[GA(OH)(2)(O(-))]* is the energetically important reaction. The thermodynamic data show a complex mechanism of adsorption of GA on the electrode surface, which is strongly dependent on temperature. At low-temperatures T<12 °C, adsorption is controlled by enthalpy, while at T>22 °C, adsorption is entropy driven. In the temperature range 12 °C and 22 °C, a combined enthalpy-entropy stabilization occurs. A mechanism is proposed which analyses the implication of thermodynamics to the interfacial adsorption of polyphenols with cell membranes under physiological conditions.     

Regions of exact convergence of the USSOR method applied on generalized consistently ordered matrices

Summary. Using the theory of nonnegative matrices and regular splittings, exact convergence and divergence domains of the Unsymmetric Successive Overrelaxation (USSOR) method, as it pertains to the class of Generalized Consistently Ordered (GCO) matrices, are determined. Our recently derived upper bounds, for the convergence of the USSOR method, re also used as effective tools. Received October 17, 1993 / Revised version received December 19, 1994     

Two theorems about projective sets

In this paper we prove two (rather unrelated) theorems about projective sets. The first one asserts that subsets of ℵ₁ which are in the codes are constructible; thus it extends the familiar theorem of Shoenfield that subsets of ω are constructible. The second is concerned with largest countable sets and establishes their existence under the hypothesis of Projective Determinacy and the assumption that there exist only countably many ordinal definable reals. Y. N. Moschovakis is a Sloan Foundation Fellow. During the preparation of this paper, both authors were partially supported by NSF Grant GP-27964.     

Pressure dependence of zone-boundary phonons in AlSb

Abstract

We have investigated the effect of hydrostatic pressure on zone-boundary and other critical-point phonon frequencies of AlSb by second-order Raman scattering. A softening of the TA(X), TA(L) and (L/T)A([Sgrave]) modes has been observed for pressures up to the first phase transition at 7.7 GPa. The LA(L) as well as the optical TO at X-, L-, and LO at [Sgrave]-, X-points harden with increasing pressure. Mode Griineisen parameters of all the resolved modes were calculated. Reflectivity measurements indicate that the high pressure phase above 7.7 GPa is metallic.     

Local remeshing for large amplitude grid deformations

Fluid-structure interaction (FSI) modelling can involve large deformations in the fluid domain, which could lead to degenerating mesh quality and numerical inaccuracies or instabilities, if allowed to amplify unchecked. Complete remeshing of the entire domain during the solution process is computationally expensive, and can require interpolation of solution variables between meshes. As an alternative, we investigate a local remeshing algorithm, with two emphases: (a) the identification and remedy of flat, degenerate tetrahedra, and (b) the avoidance of node motion, and hence associated interpolation errors.Initially, possible topological changes are examined using a dynamic programming algorithm to maximise the minimum local element quality through edge reconnection. In the 3D situation it was found that reconnection improvements tend to be limited to long edges, and those with few (three or four) element neighbours. The remaining degenerate elements are classified into one of four types using three proposed metrics – the minimum edge-to-edge distance (EE), the minimum node-to-edge distance (NE), and the shortest edge length (SE) – and removed according to the best manner for their type. Optimised thresholds for identifying and classifying elements for removal were found to be EE < 0.18, NE < 0.21, SE < 0.2.     

Ion-pair single-drop microextraction versus phase-transfer catalytic extraction for the gas chromatographic determination of phenols as tosylated derivatives

A sensitive ultra-performance liquid chromatography-electrospray tandem mass spectrometry method, combined with solid-phase extraction and silica cartridge cleanup, was established for nine androgens (androstenedione, 19-nor-4-androstene-3,17-diol, androsterone, epiandrosterone, testosterone, methyltestosterone, trenbolone, nandrolone, stanozolol) and nine progestogens (progesterone, 17alpha-hydroxyprogesterone, 21alpha-hydroxyprogesterone, 6alpha-methyl-hydroxyprogesterone, 17alpha,20beta-dihydroxy-4-pregnene-3-one, megestrol acetate, norethindrone, norgestrel, medroxyprogesterone acetate) in environmental waters. For the various water matrices considered, the overall method recoveries were from 78 to 100%, and no apparent signal suppression was found. The method detection limits for the eighteen analytes in the influent, effluent and surface water samples were 0.20-50, 0.04-20 and 0.01-12 ng/L, respectively. This method was used to analyze the residual androgens and progestogens in the wastewater and surface water samples from Japan, and ten analytes (0.03 (medroxyprogesterone acetate)-1441 ng/L (androsterone)) were detected in the wastewater samples, and four analytes (0.06 (progesterone)-0.46 ng/L (androstenedione)) were detected in the surface water samples.     

Gas chromatographic determination of carbonyl compounds in biological and oil samples by headspace single-drop microextraction with in-drop derivatisation

A suitable method for the gas chromatographic determination of 10 characteristic carbonyls in biological and oil samples based on the in-drop formation of hydrazones by using 2,4,6-trichlorophenylhydrazine (TCPH), has been developed. The derivatisation-extraction procedure was optimized separately for aqueous and oil samples with respect to the appropriate organic drop solvent, drop volume, in-drop TCPH concentration, sample stirring rate, temperature during single-drop microextraction (SDME), reaction time and headspace-to-sample volume ratio. The optimization showed differentiation of optimum values between the studied matrices. The limits of detection were found to range from 0.001 to 0.003 μg mL⁻¹ for the aqueous biological samples and from 0.06 to 0.20 μg mL⁻¹ for the oil samples. The limits of quantification were in the range of 0.003-0.010 μg mL⁻¹ and 0.020-0.059 μg mL⁻¹ for aqueous and oil samples, respectively. The overall relative standard deviations of the within-day repeatability and between-day reproducibility were <4.4% and <8.2% for the aqueous biological samples and <3.9% and <7.4% for the oxidized oil samples.     

Metalloradical complexes of manganese and chromium featuring an oxidatively rearranged ligand

Redox events involving both metal and ligand sites are receiving increased attention since a number of biological processes direct redox equivalents toward functional residues. Metalloradical synthetic analogues remain scarce and require better definition of their mode of formation and subsequent operation. The trisamido-amine ligand [(RNC6H4)3N]3-, where R is the electron-rich 4-t-Bu Ph, is employed in this study to generate redox active residues in manganese and chromium complexes. Solutions of [(L1)Mn(II)-THF]- in THF are oxidized by dioxygen to afford [(L1re-1)Mn(III)-(O)2-Mn(III)(L1 re-1)]2-as the major product. The rare dinuclear manganese (III,III) core is stabilized by a rearranged ligand that has undergone an one-electron oxidative transformation, followed by retention of the oxidation equivalent as a pi radical in ano-diiminobenzosemiquinonate moiety. Magnetic studies indicate that the ligand-centered radical is stabilized by means of extended antiferromagnetic coupling between the S ) 1/2 radical and the adjacent S ) 2 Mn(III) site, as well as between the two Mn(III) centers via the dioxo bridge. Electrochemical and EPR data suggest that this system can store higher levels of oxidation potency. Entry to the corresponding Cr(III) chemistry is achieved by employing CrCl3 to access both[(L1)Cr(III)-THF] and [(L1re-1)Cr(III)-THF(Cl)], featuring the intact and the oxidatively rearranged ligands, respectively. The latter is generated by ligand-centered oxidation of the former compound. The rearranged ligand is perceived to be the product of an one-electron oxidation of the intact ligand to afford a metal-bound aminyl radical that subsequently mediates a radical 1,4-(N-to-N) aryl migration.