Dimensions of projections of sets on Riemannian surfaces of constant curvature

We apply the theory of Peres and Schlag to obtain generic lower bounds for Hausdorff dimension of images of sets by orthogonal projections on simply connected two-dimensional Riemannian manifolds of constant curvature. As a conclusion we obtain appropriate versions of Marstrand's theorem, Kaufman's theorem, and Falconer's theorem in the above geometrical settings.

THE EQUILIBRIUM CONSTANT FOR THE GLYCINE SYNTHASE REACTION (ONE-CARBON, METABOLISM, FOLATE)

The equilibrium constant (K(,c)) under physiological conditions (38(DEGREES)C, 0.25 M ionic strength (I), pH 7.0) for the glycine synthase (GS) reaction (E C 2.1.2.1.0) (Equation 1) has been determined. (UNFORMATTED TABLE FOLLOWS)^ 5,10-CH(,2)-H(,4)Folate NADH NH (,4)+ CO(,2) ^ K(,c) = Eq. 1^ H(,4)Folate NAD('+) GLY ^(TABLE ENDS)^ The enzymatic instability of the GS enzyme complex itself has made it necessary to determine the overall K(,c) from the product of constants for the partial reactions of GS determined separately under the same conditions. The partial reactions are the H(,4)Folate-formaldehyde (CH(,2)(OH)(,2)) condensation reaction (Reaction 1) the K(,c) for which has been reported by this laboratory (3.0 x 10('4)), the lipoate (LipS(,2)) dehydrogenase reaction (LipDH) (Reaction 2) and the Gly-Lip^ decarboxylase reaction (Reaction 3) forming reduced lipoate (Lip(SH)(,2)), NH(,4)('+), CO(,2) and CH(,2)(OH)(,2.) (UNFORMATTED TABLE FOLLOWS)(,)^ H(,4)Fote + CH(,2)(OH)(,2) 5,10-CH(,2)-H(,4)Folate (1)^ Lip(SH)(,2) + NAD('+) LipS(,2) + NADH + H('+) (2)^ H('+) + Gly + LipS(,2) Lip(SH)(,2) + NH(,4)('+) CO(,2) + CH(,2)(OH)(,2) (3)^(TABLE ENDS)^ In this work the K(,c) for Reactions 2 and 3 are reported.^ The K(,c)' for the LipDH reaction described by other authors was reported with unexplainable conclusions regarding the pH depend- ence for the reaction. These conclusions would imply otherwise unexpected acid dissociation constants for reduced and oxidized lipoate. The pK(,a)',s for these compounds have been determined to resolve discrepancy. The conclusions are as follows: (1) The K(,c) for the LipDH reaction is 2.08 x 10('-8); (2) The pK(,a)',s for Lip(SH)(,2) are 4.77(-COOH), 9.91(-SH), 11.59(-SH); for LipS(,2) the carboxyl pK(,a)' is 4.77; (3) Contrary to previous literature, the log K(,c)' for the LipDH reaction is a linear function of the pH, a conclusion supported by the values for the dissociation constants.^ The K(,c) for Reaction 3 is the product of constants for Reactions 4-7. (UNFORMATTED TABLE FOLLOWS)^ LipSHSCH(,2)OH + H(,2)O Lip(SH)(,2) + CH(,2)(OH)(,2) (4)^ H(,2)O + LipSHSCH(,2)NH(,3)('+) LipSHSCH(,2)OH + NH(,4)('+) (5)^ LipSHSCH(,2)NH(,2) + H('+) LipSHSCH(,2)NH(,3)('+) (6)^ Gly + LipS(,2) LipSHSCH(,2)NH(,2) + CO(,2) (7)^(TABLE ENDS)^ Reactions 4-6 are non-enzymatic reactions whose constants were determined spectrophotometrically. Reaction 7 was catalyzed by the partially purified P-protein of GS with equilibrium approached from both directions. The value for K(,c) for this reaction is 8.15 x 10('-3). The combined K(,c) for Reactions 4-7 or Reaction 3 is 2.4 M.^ The overall K(,c) for the GS reaction determined by combination of values for Reactions 1-3 is 1.56 x 10('-3). ^

The Three Body Problem and the Runge-Lenz Equivalent Constant of the Motion

The Runge-Lenz equivalent for the Hydrogen Molecular Cation (and the Earth, Moon and Sun) problem is obtained

Benoit-Constant Coquelin, Brustbild

Signatur des Originals: S 36/F08408

Trace element geochemistry of zircons frim in situ ocean lithoshere

We characterize the textural and geochemical features of ocean crustal zircon recovered from plagiogranite, evolved gabbro, and metamorphosed ultramafic host-rocks collected along present-day slow and ultraslow spreading mid-ocean ridges (MORs). The geochemistry of 267 zircon grains was measured by sensitive high-resolution ion microprobe-reverse geometry at the USGS-Stanford Ion Microprobe facility. Three types of zircon are recognized based on texture and geochemistry. Most ocean crustal zircons resemble young magmatic zircon from other crustal settings, occurring as pristine, colorless euhedral (Type 1) or subhedral to anhedral (Type 2) grains. In these grains, Hf and most trace elements vary systematically with Ti, typically becoming enriched with falling Ti-in-zircon temperature. Ti-in-zircon temperatures range from 1,040 to 660°C (corrected for a TiO2 ~ 0.7, a SiO2 ~ 1.0, pressure ~ 2 kbar); intra-sample variation is typically ~60-15°C. Decreasing Ti correlates with enrichment in Hf to ~2 wt%, while additional Hf-enrichment occurs at relatively constant temperature. Trends between Ti and U, Y, REE, and Eu/Eu* exhibit a similar inflection, which may denote the onset of eutectic crystallization; the inflection is well-defined by zircons from plagiogranite and implies solidus temperatures of ~680-740°C. A third type of zircon is defined as being porous and colored with chaotic CL zoning, and occurs in ~25% of rock samples studied. These features, along with high measured La, Cl, S, Ca, and Fe, and low (Sm/La)N ratios are suggestive of interaction with aqueous fluids. Non-porous, luminescent CL overgrowth rims on porous grains record uniform temperatures averaging 615 ± 26°C (2SD, n = 7), implying zircon formation below the wet-granite solidus and under water-saturated conditions. Zircon geochemistry reflects, in part, source region; elevated HREE coupled with low U concentrations allow effective discrimination of ~80% of zircon formed at modern MORs from zircon in continental crust. The geochemistry and textural observations reported here serve as an important database for comparison with detrital, xenocrystic, and metamorphosed mafic rock-hosted zircon populations to evaluate provenance.

Ocean acidification decreases the light-use efficiency in an Antarctic diatom under dynamic but not constant light, link to supplementary data

There is increasing evidence that different light intensities strongly modulate the effects of ocean acidification (OA) on marine phytoplankton. The aim of the present study was to investigate interactive effects of OA and dynamic light, mimicking natural mixing regimes. The Antarctic diatom Chaetoceros debilis was grown under two pCO2 (390 and 1000 latm) and light conditions (constant and dynamic), the latter yielding the same integrated irradiance over the day. To characterize interactive effects between treatments, growth, elemental composition, primary production and photophysiology were investigated. Dynamic light reduced growth and strongly altered the effects of OA on primary production, being unaffected by elevated pCO2 under constant light, yet significantly reduced under dynamic light. Interactive effects between OA and light were also observed for Chl production and particulate organic carbon (POC) quotas. Response patterns can be explained by changes in the cellular energetic balance. While the energy transfer efficiency from photochemistry to biomass production (Phi_e,C) was not affected by OA under constant light, it was drastically reduced under dynamic light. Contrasting responses under different light conditions need to be considered when making predictions regarding a more stratified and acidified future ocean.

Asymptotic solution for the two-body problem with constant tangencial acceleration

An analytical solution of the two body problem perturbed by a constant tangential acceleration is derived with the aid of perturbation theory. The solution, which is valid for circular and elliptic orbits with generic eccentricity, describes the instantaneous time variation of all orbital elements. A comparison with high-accuracy numerical results shows that the analytical method can be effectively applied to multiple-revolution low-thrust orbit transfer around planets and in interplanetary space with negligible error.

Ab initio Methodology for Calculating Elastic Constant and Sound Velocity for Hydrogen and Deuterium in Molecular Solid Phase

Hydrogen isotopes play a critical role both in inertial and magnetic confinement Nuclear Fusion. Since the preferent fuel needed for this technology is a mixture of deuterium and tritium. The study of these isotopes particularly at very low temperatures carries a technological interest in other applications. The present line promotes a deep study on the structural configuration that hydrogen and deuterium adopt at cryogenic temperatures and at high pressures. Typical conditions occurring in present Inertial Fusion target designs. Our approach is aims to determine the crystal structure characteristics, phase transitions and other parameters strongly correlated to variations of temperature and pressure. With this results is possible calculated the elastic constant and sound velocity for hydrogen and deuterium in molecular solid phase.

A critical force constant of the structural phase transition in quartz

Long wavelength optical phonons of quartz were analyzed by a Born-Von Karman model not previously used. It was found that only one force constant associated with the turning of the Si-O bonds has a critical effect on the soft-mode frequency and the α-β transition in quartz. The square of the soft-mode frequency was found to depend linearly on this force constant which has the temperature dependence K(T)= -5.33+225.3x10-4(851-T)2/3 in units of 104 dyn/cm2.