Numerical algebraic intersection using regeneration

In numerical algebraic geometry, algebraic sets are represented by witness sets. This paper presents an algorithm, based on the regeneration technique, that solves the following problem: given a witness set for a pure-dimensional algebraic set Z, along with a system of polynomial equations f: Z�C n, compute a numerical irreducible decomposition of V�Z�V f. An important special case is when Z�A B for irreducible sets A and B and f x,y�x y for x A, y B, in which case V is isomorphic to A�B. In this way, the current contribution is a generalization of existing diagonal intersection techniques. Another important special case is when Z�A C k, so that the projection of V dropping the last k coordinates consists of the points x A where there exists some y in a new set of variables such that f x,y�0. This arises in many contexts, such as finding the singularities of A, in which case f x,y can be a set of singularity conditions that involve new variables associated to the tangent space of A. The combining of multiple intersection scenarios into one common scheme brings new capabilities and organizational simplification to numerical algebraic geometry

Extracting the depolarization coefficient D_NN from data measured with a full acceptance detector

The spin transfer from vertically polarized beam protons to Lambda or Sigma hyperons of the associated strangeness production pp -> pK Lambda (Sigma) is described with the depolarization coefficient D_NN. As the polarization of the hyperons is determined by their weak decays, detectors, which have a large acceptance for the decay particles, are needed. In this paper a formula is derived, which describes the depolarization coefficient D_NN by count rates of a 4 pi detector. It is shown, that formulas, which are given in publications for detectors with restricted acceptance, are specific cases of this formula for a 4 pi detector.Comment: Accepted for publication by Nuclear Instruments and Methods in Physics Research Section

Accommodation of lattice mismatch in Ge_(x)Si_(1−x)/Si superlattices

We present evidence that the critical thickness for the appearance of misfit defects in a given material and heteroepitaxial structure is not simply a function of lattice mismatch. We report substantial differences in the relaxation of mismatch stress in Ge_(0.5)Si_(0.5)/Si superlattices grown at different temperatures on (100) Si substrates. Samples have been analyzed by x‐ray diffraction, channeled Rutherford backscattering, and transmission electron microscopy. While a superlattice grown at 365 °C demonstrates a high degree of elastic strain, with a dislocation density <10^5 cm^(−2) , structures grown at higher temperatures show increasing numbers of structural defects, with densities reaching 2×10^(10) cm^(−2) at a growth temperature of 530 °C. Our results suggest that it is possible to freeze a lattice‐mismatched structure in a highly strained metastable state. Thus it is not surprising that experimentally observed critical thicknesses are rarely in agreement with those predicted by equilibrium theories

Bupivacaine concentrations in lumbar cerebrospinal fluid in patients with failed spinal anaesthesia

Background Spinal anaesthesia (SA) has high success rates. However, inadequate block after SA has been reported even in the absence of technical problems. Various mechanisms for failed SA (FSA) have been proposed, but reports of cerebrospinal fluid (CSF) concentrations of local anaesthetics (LA) after FSA are scarce. We report lumbar CSF concentrations of bupivacaine in 20 patients in whom adequate block after subarachnoid injection failed to develop. Methods All patients with inadequate block after subarachnoid injection of plain bupivacaine 0.5% and in whom a second subarachnoid injection of LA was to be performed as a rescue technique were eligible for entry into this study. A CSF sample was withdrawn immediately before injection of the second dose of LA. Patients in whom failure was obviously due to technical problems or inadequate dosage were excluded. Bupivacaine concentrations were assessed with high-performance liquid chromatography. Results During the study period of 15 months, 2600 spinal anaesthetics were performed. The failure rate was 2.7% (71 patients). In 20 patients (0.77%), CSF concentrations of bupivacaine were determined, which ranged from 3.36 to 1020 µg ml−1. Conclusions Inadequate CSF concentration of LA is a common reason for FSA. However, in 12 of our 20 patients, concentrations were above 73 µg ml−1, a concentration that should lead to an adequate block. In these patients, maldistribution of bupivacaine could be responsible for FSA. In view of the absence of sufficient block, despite adequate lumbar CSF concentrations of bupivacaine, concerns about neurotoxicity with repeat injections may be warrante

Bupivacaine concentrations in the lumbar cerebrospinal fluid of patients during spinal anaesthesia

Background Data on bupivacaine concentrations in the cerebral spinal fluid (CSF) during spinal anaesthesia are scarce. The purpose of this study was to determine the concentration of bupivacaine in the lumbar CSF of patients with an adequate level of spinal anaesthesia after injection of plain bupivacaine 0.5%. Methods Sixty patients with an adequate level of spinal block after standardized administration of plain bupivacaine 20 mg in men and of 17.5 mg in women were studied. To measure the CSF bupivacaine concentration, we performed a second lumbar spinal puncture and obtained a CSF sample at a randomized time point 5-45 min after the bupivacaine injection. In addition, we calculated the half-life of bupivacaine in the CSF and tested the hypothesis that the level of spinal block is related to the lumbar CSF bupivacaine concentration. Results Men and women had CSF bupivacaine concentrations ranging from 95.4 to 773.0 µg ml−1 (median 242.4 µg ml−1) and from 25.9 to 781.0 µg ml−1 (median 187.6 µg ml−1), respectively. The large variability of bupivacaine concentrations obtained at similar times after subarachnoid administration made calculation of a meaningful half-life of bupivacaine in CSF impossible. There was no association between CSF bupivacaine concentration and spinal block level, and CSF bupivacaine concentrations for the same spinal block level differed between patients by six-fold. Conclusions There is a large variability of CSF bupivacaine concentrations in patients with an adequate level of spinal anaesthesi

Accurate Determination of the Neutron Skin Thickness of \u3csup\u3e208\u3c/sup\u3ePb

We report a precision measurement of the parity-violating asymmetry Apv in the elastic scattering of longitudinally polarized electrons from 208Pb. We measure Apv = 550 ± 16(stat) ± 8(syst) parts per billion, leading to an extraction of the neutral weak form factor Fw (Q2 = 0.00616 GeV2) = 0.368 ± 0.013. Combined with our previous measurement, the extracted neutron skin thickness is Rn - Rp = 0.283 ± 0.071 fm. The result also yields the first significant direct measurement of the interior weak density of 208Pb: ρ0w = -0.0796 ± 0.0036(exp) ± 0.0013(theo) fm-3) leading to the interior baryon density ρ0b)= 0.1480 ± 0.0036(exp) ± 0.0013(theo) fm-3. The measurement accurately constrains the density dependence of the symmetry energy of nuclear matter near saturation density, with implications for the size and composition of neutron stars

High precision measurement of the associated strangeness production in proton proton interactions

A new high precision measurement of the reaction pp -> pK+Lambda at a beam momentum of 2.95 GeV/c with more than 200,000 analyzed events allows a detailed analysis of differential observables and their inter-dependencies. Correlations of the angular distributions with momenta are examined. The invariant mass distributions are compared for different regions in the Dalitz plots. The cusp structure at the N Sigma threshold is described with the Flatt\'e formalism and its variation in the Dalitz plot is analyzed.Comment: accepted for publication in Eur. Phys. J.

First Model-Independent Measurement of the Spin Triplet pΛp\Lambda Scattering Length from Final State Interaction in the p⃗p→pK+Λ\vec{p}p \rightarrow pK^{+}\Lambda Reaction

The $\vec{p}p \rightarrow pK^{+}\Lambda$ reaction has been measured with the COSY-TOF detector at a beam momentum of $2.7\,\mathrm{GeV}/c$. The polarized proton beam enables the measurement of the beam analyzing power by the asymmetry of the produced kaon ($A_N^{K}$). This observable allows the $p\Lambda$ spin triplet scattering length to be extracted for the first time model independently from the final-state interaction in the reaction. The obtained value is $a_{t} = (-2.55 ^{+0.72}_{-1.39} {}_{\textrm{stat.}} \pm 0.6_{\textrm{syst.}} \pm 0.3_{\textrm{theo.}})\mathrm{fm}$. This value is compatible with theoretical predictions and results from model-dependent analyses.Comment: Revised version as accepted for publication in PR

Numerical elimination and moduli space of vacua

We propose a new computational method to understand the vacuum moduli space of (supersymmetric) field theories. By combining numerical algebraic geometry (NAG) and elimination theory, we develop a powerful, efficient, and parallelizable algorithm toextract important information such as the dimension, branch structure, Hilbert series and subsequent operator counting, as well as variation according to coupling constants and mass parameters. We illustrate this method on a host of examples from gauge theory, string theory, and algebraic geometry