On the Density of Coprime m-tuples over Holomorphy Rings

Let $\mathbb F_q$ be a finite field, $F/\mathbb F_q$ be a function field of genus $g$ having full constant field $\mathbb F_q$, $\mathcal S$ a set of places of $F$ and $H$ the holomorphy ring of $\mathcal S$. In this paper we compute the density of coprime $m$-tuples of elements of $H$. As a side result, we obtain that whenever the complement of $\mathcal S$ is finite, the computation of the density can be reduced to the computation of the $L$-polynomial of the function field. In the rational function field case, classical results for the density of coprime $m$-tuples of polynomials are obtained as corollaries.Comment: To appear in International Journal of Number Theor

Influence of higher d-wave gap harmonics on the dynamical magnetic susceptibility of high-temperature superconductors

Using a fermiology approach to the computation of the magnetic susceptibility measured by neutron scattering in hole-doped high-Tc superconductors, we estimate the effects on the incommensurate peaks caused by higher d-wave harmonics of the superconducting order parameter induced by underdoping. The input parameters for the Fermi surface and d-wave gap are taken directly from angle resolved photoemission (ARPES) experiments on Bi{2}Sr{2}CaCu{2}O{8+x} (Bi2212). We find that higher d-wave harmonics lower the momentum dependent spin gap at the incommensurate peaks as measured by the lowest spectral edge of the imaginary part in the frequency dependence of the magnetic susceptibility of Bi2212. This effect is robust whenever the fermiology approach captures the physics of high-Tc superconductors. At energies above the resonance we observe diagonal incommensurate peaks. We show that the crossover from parallel incommensuration below the resonance energy to diagonal incommensuration above it is connected to the values and the degeneracies of the minima of the 2-particle energy continuum.Comment: 13 pages, 7 figure

Influence of Inorganic Phosphate on Photosynthesis of Wheat Chloroplasts: I. PHOTOSYNTHESIS AND ASSIMILATE EXPORT AT 5 °C AND 25 °C

Chloroplasts were isolated from 10 d old wheat seedlings and illuminated at 5 °C or 25 °C in various concentrations of PO43-. Photosynthetic oxygen evolution, ATP content, and export of triose phosphates and 3-phosphoglycerate were measured. Incorporation of 14C from NaH14CO3 into pentose monophosphates, fructose monophosphate, and glucose monophosphates was determined. The ATP content in illuminated chloroplasts decreased when the PO43- concentration in the medium was low. The ATP content increased when the PO43- concentration was increased. A higher PO43-. concentration in the medium was needed to increase the ATP at 5 °C than at 25 °C. This would suggest that PO43- deficiency occurs more readily at low than at high temperatures. More 14C was incorporated into photosynthetic metabolites within the chloroplasts at 5 °C than at 25 °C, indicating decreased assimilate export when the temperature was low. Dihydroxyacetone phosphate was preferentially exported when the PO43- concentration enabled a high rate of photosynthesis at 25 °C. However, under conditions of PO43- deficiency, either due to low PO43- concentration in the medium or due to low temperature, 3-phosphoglycerate was preferred for export. The results suggest that the relatively high photosynthetic rates at low temperature are due to increased concentrations of photosynthetic metabolites. The assimilate export at low temperature seems to be decreased due to decreased concentrations of dihydroxyacetone phosphate in the stroma. Preferential export of 3-phosphoglycerate at low temperature or at low PO43- concentration in the medium may be a consequence of high stromal concentrations of this metabolite. On the other hand, it could also be due to decreased stromal p

Regeneration of Ribulose 1,5-bisphosphate and Ribulose 1,5-bisphosphate carboxylase/oxygenase Activity Associated with Lack of Oxygen Inhibition of Photosynthesis at Low Temperature

The nature of the lack of oxygen inhibition of C3-photosynthesis at low temperature was investigated in white clover (Trifolium repens L.). Detached leaves were brought to steady-state photosynthesis in air (34 Pa p(CO2), 21 kPa p(O2), balance N2) at temperatures of 20°C and 8°C, respectively. Net photosynthesis, ribulose 1,5-bisphosphate (RuBP) and ATP contents, and ribulose 1,5-bisphosphate carboxylase/oxygenase (RuBPCO) activities were followed before and after changing to 2·0 kPa p(O2). At 20°C, lowering p(O2) increased net photosynthesis by 37%. This increase corresponded closely with the increase expected from the effect on the kinetic properties of RuBPCO. Conversely, at 8°C net photosynthesis rapidly decreased following a decrease in p(O2) and then increased again reaching a steady-state level which was only 7% higher than at 21 kPa p(O2). The steady-state rates of RuBP and associated ATP consumption were both estimated to have decreased. ATP and RuBP contents decreased by 18% and 33% respectively, immediately after the change in p(O2) suggesting that RuBP regeneration was reduced at low p(O2) due to reduced photophosphorylation. Subsequently, RuBP content increased again. Steady-state RuBP content at 2·0 kPa p(O2) was 24% higher than at 21 kPa p(O2). RuBPCO activity decreased by 22%, indicating control of steady-state RuBP consumption by RuBPCO activity. It is suggested that lack of oxygen inhibition of photosynthesis at low temperature is due to decreased photophosphorylation at low temperature and low p(O2). This may be due to assimilate accumulation within the chloroplasts. Decreased photophosphorylation seems to decrease RuBP synthesis and RuBPCO activity, possibly due to an acidification of the chloroplast strom

Influence of Temperature and O2 Concentration on Photosynthesis and Light Activation of Ribulosebisphosphate Carboxylase Oxygenase in Intact Leaves of White Clover (Trifolium repens L.)

Detached leaves of white clover (Trifolium repens L.) were kept for 1 h under various conditions of temperature, oxygen concentration and light intensity. Rates of photosynthesis were measured where appropriate and then ribulosebisphosphate carboxylase oxygenase (RuBPCO) was extracted rapidly and its initial activity measured immediately. The extracted activity increased with increased intensity of illumination of the leaves. Where leaves were pretreated at low light intensity, the lower the temperature of the leaves the higher the extracted activity of RuBPCO. At high light intensity temperature did not affect the activity of subsequently extracted RuBPCO but the light intensity which was necessary for maximum activity increased with temperature. Activity of RuBPCO from leaves pretreated in the dark was least when CO2 was low and temperature high. Leaves, pretreated at low temperatures and high light intensity in 20% O2, yielded higher activity in extracts than leaves pretreated under similar conditions but in 2% O2. A relatively weak temperature response of photosynthesis at low irradiances was associated with a decrease in extractable RuBPCO activity with increasing temperature. A strong temperature dependence of the oxygen inhibition of photosynthesis was associated with lower extractable RuBPCO activity in leaves pretreated at low oxygen concentration at low temperatures. With leaves from plants grown at low temperatures prior to treatment of leaves, oxygen inhibition of photosynthesis was less temperature dependent and activity of RuBPCO in extracts was not decreased by low O2 at low temperatures. Differences in the activation of RuBPCO appear to influence photosynthesis and account for an absence of oxygen inhibition of photosynthesis at low temperatures in plants grown in warm condition