Intrinsic relaxation rates of polarized Cs vapor in miniaturized cells

The intrinsic relaxation rates of the vector magnetization of cesium vapor enclosed in microfabricated atomic magnetometer cells are investigated. Two methods—the optically detected magnetic resonance and the ground-state Hanle effect—are used to carry out automated measurements in dependence on cell temperature and nitrogen buffer gas pressure. The experimental results are compared with expected contributions of the different relaxation processes and in this way allow the discrimination between them to help further optimization of cell design. The methods are compared in terms of basic features, data quality, and practical applicability.     

On Conformal Invariants Built from Spinor Fields

By means of a conformal covariant differentiation process we construct generating systems for conformally invariant symmetric (r, s)–spinors in an arbitrary curved space–time. Extending this method to conformally invariant linear differential operators acting on symmetric spinor fields some classes of such operators are derived.     

K3Cr2(PS4)3: A New Chromium Thiophosphate with a One‐Dimensional [Cr2(PS4)]3— Anion Chain

A new chromium thiophosphate, K₃Cr₂(PS₄)₃ has been prepared and characterized by single‐crystal diffraction, temperature dependent magnetic susceptibility measurements and optical spectroscopy. K₃Cr₂(PS₄)₃ crystallizes in the monoclinic space group P2₁/n (No. 14) with a = 9.731(2) Å, b = 11.986(2) Å, c = 17.727(4) Å, β = 96.52(2)°, V = 2054.2(2) ų, Z = 4, and R = 0.044. The anionic part of the structure consists of dimeric Cr₂(μ₃‐S₃PS)₂ units which are linked by bidentate PS₄ groups to form infinite one‐dimensional [S₂P_S2Cr₂(μ₃S₃P_S)₂]^3— chains separated by K⁺ cations. The Cr^III centers of the Cr₂(μ₃‐S₃PS)₂ units are antiferromagnetically coupled. The magnetic susceptibility data may be fitted using a D‐Heisenberg model for S = 3/2 with g = 2.02 and J/k = 10K. K₃Cr₂(PS₄)₃ is semiconducting with an optical band gap of 1.35 eV.     

Simultaneous Credible Regions for Multiple Changepoint Locations

Within a Bayesian retrospective framework, we present a way of examining the distribution of changepoints through a novel set estimator. For a given level, α, we aim at smallest sets that cover all changepoints with a probability of at least 1 ? α. These so-called smallest simultaneous credible regions, computed for certain values of α, provide parsimonious representations of the possible changepoint locations. In addition, combining them for a range of different α’s enables very informative yet condensed visualizations. Therewith we allow for the evaluation of model choices and the analysis of changepoint data to an unprecedented degree. This approach exhibits superior sensitivity, specificity, and interpretability in comparison with highest density regions, marginal inclusion probabilities, and confidence intervals inferred by stepR. While their direct construction is usually intractable, asymptotically correct solutions can be derived from posterior samples. This leads to a novel NP-complete problem. Through reformulations into an Integer Linear Program we show empirically that a fast greedy heuristic computes virtually exact solutions. Supplementary material for this article is available online.     

Combinatorics & Topology of Stratifications of The Space of Monic Polynomials With Real Coefficients

We study the stratification of the space of monic polynomials with real coefficients according to the number and multiplicities of real zeros. In the first part, for each of these strata we provide a purely combinatorial chain complex calculating (co)homology of its one-point compactification and describe the homotopy type by order complexes of a class of posets of compositions. In the second part, we determine the homotopy type of the one-point compactification of the space of monic polynomials of fixed degree which have only real roots (i.e., hyperbolic polynomials) and at least one root is of multiplicity k. More generally, we describe the homotopy type of the one-point compactification of strata in the boundary of the set of hyperbolic polynomials, that are defined via certain restrictions on root multiplicities, by order complexes of posets of compositions. In general, the methods are combinatorial and the topological problems are mostly reduced to the study of partially ordered sets.     

Microanalytical flow-through method for assessment of the bioavailability of toxic metals in environmental samples

The application of a recently proposed microanalytical flow-through system for on-line sequential extraction of heavy metals from solid samples of environmental interest is described. Using various extraction schemes (a nitric acid scheme, a two-stage extraction scheme using two reagents applied in the BCR procedure) and comparison with the common batch sequential BCR procedure, the suitability of the system for fast screening of solid environmental samples is demonstrated. By pumping leaching agents sequentially through the sample held in a micro cartridge, the different metal fractions present can be assessed in less than an hour. Method evaluation was performed using SRM 1648 urban particulate matter and BCR 701 lake sediment reference material certified for extractable metals. The need for and design of laboratory internal reference material suitable for simulating the natural (dynamic) processes of metal release into the environment is also discussed. For the first time correlation is sought between fractionation techniques and physiologically based methods for assessment of the bioaccessibility of metals in biomatrices.