On the intrinsic complexity of the arithmetic Nullstellensatz

We show several arithmetic estimates for Hilbert's Nullstellensatz. This includes an algorithmic procedure computing the polynomials and constants occurring in a Bézout identity, whose complexity is polynomial in the geometric degree of the system. Moreover, we show for the first time height estimates of intrinsic type for the polynomials and constants appearing, again polynomial in the geometric degree and linear in the height of the system. These results are based on a suitable representation of polynomials by straight-line programs and duality techniques using the Trace Formula for Gorenstein algebras. As an application we show more precise upper bounds for the function πS(x) counting the number of primes yielding an inconsistent modular polynomial equation system. We also give a computationally interesting lower bound for the density of small prime numbers of controlled bit length for the reduction to positive characteristic of inconsistent systems. Again, this bound is given in terms of intrinsic parameters.Facultad de Ciencias Exacta

On the intrinsic complexity of the arithmetic Nullstellensatz

We show several arithmetic estimates for Hilbert's Nullstellensatz. This includes an algorithmic procedure computing the polynomials and constants occurring in a Bézout identity, whose complexity is polynomial in the geometric degree of the system. Moreover, we show for the first time height estimates of intrinsic type for the polynomials and constants appearing, again polynomial in the geometric degree and linear in the height of the system. These results are based on a suitable representation of polynomials by straight-line programs and duality techniques using the Trace Formula for Gorenstein algebras. As an application we show more precise upper bounds for the function πS(x) counting the number of primes yielding an inconsistent modular polynomial equation system. We also give a computationally interesting lower bound for the density of small prime numbers of controlled bit length for the reduction to positive characteristic of inconsistent systems. Again, this bound is given in terms of intrinsic parameters.Facultad de Ciencias Exacta

Ultrafast pump-probe dynamics in ZnSe-based semiconductor quantum-wells

Pump-probe experiments are used as a controllable way to investigate the properties of photoexcited semiconductors, in particular, the absorption saturation. We present an experiment-theory comparison for ZnSe quantum wells, investigating the energy renormalization and bleaching of the excitonic resonances. Experiments were performed with spin-selective excitation and above-bandgap pumping. The model, based on the semiconductor Bloch equations in the screened Hartree-Fock approximation, takes various scattering processes into account phenomenologically. Comparing numerical results with available experimental data, we explain the experimental results and find that the electron spin-flip occurs on a time scale of 30 ps.Comment: 10 pages, 9 figures. Key words: nonlinear and ultrafast optics, modeling of femtosecond pump-probe experiments, electron spin-flip tim

On the intrinsic complexity of the arithmetic Nullstellensatz

We show several arithmetic estimates for Hilbert's Nullstellensatz. This includes an algorithmic procedure computing the polynomials and constants occurring in a Bézout identity, whose complexity is polynomial in the geometric degree of the system. Moreover, we show for the first time height estimates of intrinsic type for the polynomials and constants appearing, again polynomial in the geometric degree and linear in the height of the system. These results are based on a suitable representation of polynomials by straight-line programs and duality techniques using the Trace Formula for Gorenstein algebras. As an application we show more precise upper bounds for the function πS(x) counting the number of primes yielding an inconsistent modular polynomial equation system. We also give a computationally interesting lower bound for the density of small prime numbers of controlled bit length for the reduction to positive characteristic of inconsistent systems. Again, this bound is given in terms of intrinsic parameters.Facultad de Ciencias Exacta

Spin injection through the depletion layer: a theory of spin-polarized p-n junctions and solar cells

A drift-diffusion model for spin-charge transport in spin-polarized {\it p-n} junctions is developed and solved numerically for a realistic set of material parameters based on GaAs. It is demonstrated that spin polarization can be injected through the depletion layer by both minority and majority carriers, making all-semiconductor devices such as spin-polarized solar cells and bipolar transistors feasible. Spin-polarized {\it p-n} junctions allow for spin-polarized current generation, spin amplification, voltage control of spin polarization, and a significant extension of spin diffusion range.Comment: 4 pages, 3 figure

On the central abundances of Active Galactic Nuclei and Star-forming Galaxies

We examine the relation between oxygen abundances in the narrow-line regions (NLRs) of active galactic nuclei (AGNs) estimated from the optical emission lines through the strong-line method (the theoretical calibration of Storchi-Bergmann et al. 1998), via the direct Te-method, and the central intersect abundances in the host galax- ies determined from the radial abundance gradients. We found that the Te-method underestimates the oxygen abundances by up to ∼2 dex (with average value of ~0.8 dex) compared to the abundances derived through the strong-line method. This con- firms the existence of the so-called ?temperature problem? in AGNs. We also found that the abundances in the centres of galaxies obtained from their spectra trough the strong-line method are close to or slightly lower than the central intersect abun- dances estimated from the radial abundance gradient both in AGNs and Star-forming galaxies. The oxygen abundance of the NLR is usually lower than the maximum at- tainable abundance in galaxies (~2 times the solar value). This suggests that there is no extraordinary chemical enrichment of the NLRs of AGNs.Fil: Dors Jr., O. L.. Universidade Do Vale Do Paraíba; BrasilFil: Cardaci, Monica Viviana. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico La Plata. Instituto de Astrofísica de La Plata; ArgentinaFil: Hägele, Guillermo Federico. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico la Plata. Instituto de Astrofísica de la Plata; Argentina. Universidad Nacional de la Plata. Facultad de Ciencias Astronómicas y Geofísicas; ArgentinaFil: Rodrigues, I.. Universidade Do Vale Do Paraíba; BrasilFil: Grebel, E. K. . Universität Heidelberg. Astronomisches Rechen-Institut. Zentrum für Astronomie; AlemaniaFil: Pilyugin, L. S. . Universität Heidelberg; Alemania. National Academy of Sciences of Ukraine; Ucrania. Kazan Federal University; RusiaFil: Freitas Lemes, P. . Universidade Do Vale Do Paraíba; BrasilFil: Krabbe, A. C. . Universidade Do Vale Do Paraíba; Brasi

On the central abundances of Active Galactic Nuclei and Star-forming Galaxies

We examine the relation between oxygen abundances in the narrow-line regions (NLRs) of active galactic nuclei (AGNs) estimated from the optical emission lines through the strong-line method (the theoretical calibration of Storchi-Bergmann et al. 1998), via the direct Te-method, and the central intersect abundances in the host galaxies determined from the radial abundance gradients. We found that the Te-method underestimates the oxygen abundances by up to ∼2 dex (with average value of ~0.8 dex) compared to the abundances derived through the strong-line method. This con- firms the existence of the so-called ?temperature problem? in AGNs. We also found that the abundances in the centres of galaxies obtained from their spectra trough the strong-line method are close to or slightly lower than the central intersect abun- dances estimated from the radial abundance gradient both in AGNs and Star-forming galaxies. The oxygen abundance of the NLR is usually lower than the maximum at- tainable abundance in galaxies (~2 times the solar value). This suggests that there is no extraordinary chemical enrichment of the NLRs of AGNs.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

On the central abundances of Active Galactic Nuclei and Star-forming Galaxies

We examine the relation between oxygen abundances in the narrow-line regions (NLRs) of active galactic nuclei (AGNs) estimated from the optical emission lines through the strong-line method (the theoretical calibration of Storchi-Bergmann et al. 1998), via the direct Te-method, and the central intersect abundances in the host galaxies determined from the radial abundance gradients. We found that the Te-method underestimates the oxygen abundances by up to ∼2 dex (with average value of ~0.8 dex) compared to the abundances derived through the strong-line method. This con- firms the existence of the so-called ?temperature problem? in AGNs. We also found that the abundances in the centres of galaxies obtained from their spectra trough the strong-line method are close to or slightly lower than the central intersect abun- dances estimated from the radial abundance gradient both in AGNs and Star-forming galaxies. The oxygen abundance of the NLR is usually lower than the maximum at- tainable abundance in galaxies (~2 times the solar value). This suggests that there is no extraordinary chemical enrichment of the NLRs of AGNs.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

Basic obstacle for electrical spin-injection from a ferromagnetic metal into a diffusive semiconductor

We have calculated the spin-polarization effects of a current in a two dimensional electron gas which is contacted by two ferromagnetic metals. In the purely diffusive regime, the current may indeed be spin-polarized. However, for a typical device geometry the degree of spin-polarization of the current is limited to less than 0.1%, only. The change in device resistance for parallel and antiparallel magnetization of the contacts is up to quadratically smaller, and will thus be difficult to detect.Comment: Revtex, 4 pages, 3 figures (eps), Definition of spin pilarization changed to standard definition in GMR, some straight forward algebra removed. To appear as PRB Rap. Comm. August 15t