Numerical aspects of computing the Moore-Penrose inverse of full column rank matrices

This paper presents a comparison of certain direct algorithms for computing the Moore-Penrose inverse, for matrices of full column rank, from the point of view of numerical stability. It is proved that the algorithm using Householder QR decomposition, implemented in floating point arithmetic, is forward stable but only conditionally mixed forward-backward stable. A similar result holds also for the Classical Gram-Schmidt algorithm with reorthogonalization (CGS2). This algorithm was developed and analyzed by Abdelmalek (BIT, 11(4):354–367, 1971) and its detailed error analysis was given in Giraud et al. (Numer. Math. 101(1):87–100, 2005).     

Signals of neutropenia in human breath?

Children undergoing systemic chemotherapy often suffer from severe immunosuppression usually associated to severe neutropenia (neutrophils <?0.5 x 10⁹/l). Clinical courses during those periods range from asymptomatic to septic general conditions. Development of septic symptoms can be very fast and life-threatening. Swift detection of risk factors in those patients is therefore needed. So far no early, rapid and reliable marker or tool exists. Ion-Mobility-Spectrometry coupled with a Multi-Capillary-Column (IMS-MCC) can analyze more than 600 volatile components from exhaled air within a few minutes and hence is a potential, rapid detection-tool. As a proof of concept we measured the exhaled breath of 11 patients with neutropenia and 10 healthy controls ranging from 3 to 18 years of age at the time of measurement. Ten milliliters breath samples were taken at the outpatient clinic and analyzed with an onsite IMS-MCC (BreathDiscovery, B&S Analytik, Dortmund, Germany). Dead-space-volume was adapted to two groups (small 250 ml, large 500 ml). Interestingly 59 differing peaks were measured. Eleven were significantly different (p?≤?0.05), three of which highly significant (p?≤?0.01) in Mann-Whitney-Rank-Sum-testing. The corresponding analytes used in the decision tree are 2-Propanol, D-Limonene and Acetone. The analytes with the lowest rank sum identified are 2-Hexanone, Iso-Propylamine and 1-Butanol. Eventually we were able to show a three-step-decision-tree, which discerns the 21 samples except one from each group. Sensitivity was 90 % and specificity was 91 %. Naturally these findings need further confirmation within a bigger population. Our pilot-study proves that Ion-Mobility-Spectrometry coupled with a Multi-Capillary-Column is a feasible rapid diagnostic tool in the setting of a pediatric oncology out-patient clinic for patients 3 years and older. Our first results furthermore encourage additional analysis as to whether patients at risk for septic events during immunosuppression can be diagnosed in advance by rapidly assessing risk factors such as Neutropenia in exhaled breath.     

Splitting kernels into small summands

Let λ be a regular cardinal. An epimorphism between abelian groups is λ -pure if it is projective with respect to abelian groups of size less than λ. We show that cotorsion groups A have λ-pure projective dimension greater than 1 for all uncountable λ ≤ |A/tA|, where tA denotes the torsion subgroup of A. For λ > |A/tA|, cotorsion groups A are λ-pure projective.     

Controlled Synthesis of Thorium and Uranium Oxide Nanocrystals

Very little is known about the size and shape effects on the properties of actinide compounds. As a consequence, the controlled synthesis of well‐defined actinide‐based nanocrystals constitutes a fundamental step before studying their corresponding properties. In this paper, we report on the non‐aqueous surfactant‐assisted synthesis of thorium and uranium oxide nanocrystals. The final characteristics of thorium and uranium oxide nanocrystals can be easily tuned by controlling a few experimental parameters such as the nature of the actinide precursor and the composition of the organic system (e.g., the chemical nature of the surfactants and their relative concentrations). Additionally, the influence of these parameters on the outcome of the synthesis is highly dependent on the nature of the actinide element (thorium versus uranium). By using optimised experimental conditions, monodisperse isotropic uranium oxide nanocrystals with different sizes (4.5 and 10.7 nm) as well as branched nanocrystals (overall size ca. 5 nm), nanodots (ca. 4 nm) and nanorods (with ultra‐small diameters of 1 nm) of thorium oxide were synthesised.     

Electronic structure,novel synthesis,and O—H...O and C—H...O interactions in two 6‐oxopiperidine‐2‐carboxylic acid derivatives

Molecules of (S)‐6‐oxo‐1‐(thiophen‐2‐ylmethyl)piperidine‐2‐carboxylic acid, C₁₁H₁₃NO₃S, crystallize as single enantiomers in the space group P2₁ and the thiophene ring is disordered over two positions, while (S)‐6‐oxo‐1‐(thiophen‐3‐ylmethyl)piperidine‐2‐carboxylic acid, C₁₁H₁₃NO₃S, crystallizes as a single enantiomer in the space group P2₁2₁2₁. Their absolute configurations were confirmed by anomalous dispersion effects in diffraction measurements on the crystals. The molecules of each compound are linked by a combination of strong O—H...O hydrogen bonds and weak C—H...O interactions, resulting in two‐ and three‐dimensional networks, respectively, in the crystal structures.     

Maleimide Glycidyl Ether: A Bifunctional Monomer for Orthogonal Cationic and Radical Polymerizations

A novel bifunctional monomer, namely maleimide glycidyl ether (MalGE), prepared in a four‐step reaction sequence is introduced. This monomer allows for selective (co)polymerization of the epoxide group via cationic ring‐opening polymerization, preserving the maleimide functionality. On the other hand, the maleimide functionality can be copolymerized via radical techniques, preserving the epoxide moiety. Cationic ring‐opening multibranching copolymerization of MalGE with glycidol was performed, and a MalGE content of up to 24 mol% could be incorporated into the hyperbranched polymer backbone (M_n = 1000–3000 g mol⁻¹). Preservation of the maleimide functionality during cationic copolymerization was verified via NMR spectroscopy. Subsequently, the maleimide moiety was radically crosslinked to generate hydrogels and additionally employed to perform Diels‐Alder (DA) “click” reactions with (functional) dienes after the polymerization process. Radical copolymerization of MalGE with styrene (M_n = 5000–9000 g mol⁻¹) enabled the synthesis of a styrene copolymer with epoxide functionalities that are useful for versatile crosslinking and grafting reactions.

     

Ultra‐Small Plutonium Oxide Nanocrystals: An Innovative Material in Plutonium Science

Apart from its technological importance, plutonium (Pu) is also one of the most intriguing elements because of its non‐conventional physical properties and fascinating chemistry. Those fundamental aspects are particularly interesting when dealing with the challenging study of plutonium‐based nanomaterials. Here we show that ultra‐small (3.2±0.9 nm) and highly crystalline plutonium oxide (PuO₂) nanocrystals (NCs) can be synthesized by the thermal decomposition of plutonyl nitrate ([PuO₂(NO₃)₂] ? 3 H₂O) in a highly coordinating organic medium. This is the first example reporting on the preparation of significant quantities (several tens of milligrams) of PuO₂ NCs, in a controllable and reproducible manner. The structure and magnetic properties of PuO₂ NCs have been characterized by a wide variety of techniques (powder X‐ray diffraction (PXRD), X‐ray absorption fine structure (XAFS), X‐ray absorption near edge structure (XANES), TEM, IR, Raman, UV/Vis spectroscopies, and superconducting quantum interference device (SQUID) magnetometry). The current PuO₂ NCs constitute an innovative material for the study of challenging problems as diverse as the transport behavior of plutonium in the environment or size and shape effects on the physics of transuranium elements.     

A Molecular Approach to Self‐Supported Cobalt‐Substituted ZnO Materials as Remarkably Stable Electrocatalysts for Water Oxidation

In regard to earth‐abundant cobalt water oxidation catalysts, very recent findings show the reorganization of the materials to amorphous active phases under catalytic conditions. To further understand this concept, a unique cobalt‐substituted crystalline zinc oxide (Co:ZnO) precatalyst has been synthesized by low‐temperature solvolysis of molecular heterobimetallic Co_4?xZn_xO₄ (x=1–3) precursors in benzylamine. Its electrophoretic deposition onto fluorinated tin oxide electrodes leads after oxidative conditioning to an amorphous self‐supported water‐oxidation electrocatalyst, which was observed by HR‐TEM on FIB lamellas of the EPD layers. The Co‐rich hydroxide‐oxidic electrocatalyst performs at very low overpotentials (512 mV at pH 7; 330 mV at pH 12), while chronoamperometry shows a stable catalytic current over several hours.     

Nanoparticle directed domain orientation in thin films of asymmetric block copolymers

We investigated the thin film morphology of two different asymmetric block copolymers (BCP), polystyrene-block-poly(4-vinylpyridine) (PS-b-P4VP) and poly(n-pentyl methacrylate)-block-poly(methyl methacrylate) (PPMA-b-bel="PMMA" gaAction="reference-keyword">PMMA), loaded with pre-synthesized iron oxide nanoparticles (NP). The chemical composition of the BCP constituents determines the strength of the interaction between polymer chains and nanoparticles. In the case of NP/PS-b-P4VP system, the nanoparticles interact preferentially with the P4VP block and hence localize selectively in the P4VP cylindrical microdomains. However, for the NP/PPMA-b-bel="PMMA" gaAction="reference-keyword">PMMA system, the nanoparticles have no significant preference for the copolymer blocks and segregate at the polymer/substrate interface. Interestingly, this changes the effective substrate surface energy and hence leads to a remarkable change in domain orientation from parallel to perpendicular with respect to the substrate. These results clearly demonstrate the importance of both enthalpic and entropic factors which determine spatial distribution of NP in BCP films and influence domain orientation.     

Confined Crystallization of Spin‐Crossover Nanoparticles in Block‐Copolymer Micelles

Nanoparticles of the spin‐crossover coordination polymer [FeL(bipy)]_n were synthesized by confined crystallization within the core of polystyrene‐block‐poly(4‐vinylpyridine) (PS‐b‐P4VP) diblock copolymer micelles. The 4VP units in the micellar core act as coordination sites for the Fe complex. In the bulk material, the spin‐crossover nanoparticles in the core are well isolated from each other allowing thermal treatment without disintegration of their structure. During annealing above the glass transition temperature of the PS block, the transition temperature is shifted gradually to higher temperatures from the as‐synthesized product (T_1/2↓=163 K and T_1/2↑=170 K) to the annealed product (T_1/2↓=203 K and T_1/2↑=217 K) along with an increase in hysteresis width from 6 K to 14 K. Thus, the spin‐crossover properties can be shifted towards the properties of the related bulk material. The stability of the nanocomposite allows further processing, such as electrospinning from solution.