Product structure of heat phase space and branching Brownian motion

A generical formalism for the discussion of Brownian processes with non-constant particle number is developed, based on the observation that the phase space of heat possesses a product structure that can be encoded in a commutative unit ring. A single Brownian particle is discussed in a Hilbert module theory, with the underlying ring structure seen to be intimately linked to the non-differentiability of Brownian paths. Multi-particle systems with interactions are explicitly constructed using a Fock space approach. The resulting ring-valued quantum field theory is applied to binary branching Brownian motion, whose Dyson-Schwinger equations can be exactly solved. The presented formalism permits the application of the full machinery of quantum field theory to Brownian processes.     

CO Hydrogenation on Cobalt‐Based Catalysts: Tin Poisoning Unravels CO in Hollow Sites as a Main Surface Intermediate

Site poisoning is a powerful method to unravel the nature of active sites or reaction intermediates. The nature of the intermediates involved in the hydrogenation of CO was unraveled by poisoning alumina‐supported cobalt catalysts with various concentrations of tin. The rate of formation of the main reaction products (methane and propylene) was found to be proportional to the concentration of multi‐bonded CO, likely located in hollow sites. The specific rate of decomposition of these species was sufficient to account for the formation of the main products. These hollow‐CO are proposed to be main reaction intermediates in the hydrogenation of CO under the reaction conditions used here, while linear CO are mostly spectators.     

A Facile Molecular Precursor‐based Synthesis of Ag2Se Nanoparticles and Its Composites with TiO2 for Enhanced Photocatalytic Activity

The reactions of different silver(I) reagents AgX (X^?=iodide, trifluoroacetate, triflate) with selenoethers R₂Se (R=Me, tBu) in a variety of solvents were investigated in relation with their use as precursors for Ag₂Se nanomaterials. Different reaction conditions led to different reactivities and afforded either molecular complexes or metal selenide nanoparticles. The reactions leading to in situ formation of the metal selenide nanoparticles were then extended in the presence of commercial TiO₂ (P25) to prepare silver selenide–titania nanocomposites with different Ag/Ti ratios. These nanocomposites, well characterized by elemental analysis (Ag, Se), PXRD, TEM, BET, XPS and UV/Vis studies, were investigated as photocatalysts for the degradation of formic acid (FA) solution. The xAg₂Se‐TiO₂ nanocomposites (x=0.01, 0.13 and 0.25 mol %) exhibited a much higher catalytic activity as compared to P25, which is an established benchmark for the photocatalysis under UV light, and retained a good photocatalytic stability after recycling for several times.     

Lanthanum nitride endohedral fullerenes La3N@C2n (43 <or= n <or= 55): preferential formation of La3N@C96

While the trimetallic nitrides of Sc, Y and the lanthanides between Gd and Lu preferentially template C(80) cages, M(3)N@C(80), and while those of Ce, Pr and Nd preferentially template the C(88) cage, M(3)N@C(88), we show herein that the largest metallic nitride cluster, La(3)N, preferentially leads to the formation of La(3)N@C(96) and to a lesser extent the La(3)N@C(88). This is the first time that La(3)N is successfully encapsulated inside fullerene cages. La(3)N@C(2n) metallofullerenes were synthesized by arcing packed graphite rods in a modified Kr?tschmer-Huffman arc reactor, extracted from the collected soot and identified by mass spectroscopy. They were isolated and purified by high performance liquid chromatography (HPLC). Different arcing conditions were studied to maximize fullerene production, and results showed that yields have a high La(2)O(3)/C dependence. Relatively high yields were obtained when a 1:5 ratio was used. Three main fractions, La(3)N@C(88), La(3)N@C(92), and La(3)N@C(96), were characterized by UV/Vis-NIR and cyclic voltammetry. Unlike other trimetallic nitride metallofullerenes of the same carbon cage size, La(3)N@C(88) exhibits a higher HOMO-LUMO gap and irreversible reduction and oxidation steps.     

Dynamique sur le rayon modulaire et fractions continues en caracteristique p

Let be the field of formal Laurentseries in X^–1 over the finite field k, and let A be thering of polynomials in X over k. One of the main results ofthe paper is to give a natural coding of the (discrete) geodesicflow on the quotient of the Bruhat–Tits tree of PGL₂() by PGL₂(A), using the continued fractionexpansion of the endpoints of the geodesic lines in (the spaceof ends of identifies with ₁().In particular, the invariance of the Haar measure by the Artintransformation can be deduced from the invariance of the Bowen–Margulismeasure by the geodesic flow.     

Stability and Computation of Topological Invariants of Solids in ${\Bbb R}^n$

In this work one proves that under quite general assumptions one can deduce the topology of a bounded open set in from an approximation of it. For this, one introduces the weak feature size (wfs) that extends for nonsmooth objects the notion of local feature size. Our results apply to open sets with positive wfs. This class includes subanalytic open sets which cover many cases encountered in practical applications. The proofs are based upon the study of distance functions to closed sets and their critical points. The notion of critical point is the same as the one used in riemannian geometry [22], [9], [20] and nonsmooth analysis [10]. As an application, one gives a way to compute the homology groups of open sets from noisy samples of points on their boundary.     

Validation of RAPID E. coli 2 for enumeration and differentiation of Escherichia coli and other coliform bacteria in selected foods--Performance-Tested Method 050601

RAPID'E. coli 2 agar (Bio-Rad Laboratories, Hercules, CA) is a chromogenic medium for differentiation and enumeration of E. coli and non-E. coli coliform bacteria in food. The principle of RAPID'E. coli 2 medium relies on simultaneous detection of 2 enzymatic activities, P-D-glucuronidase (GLUC) and beta-D-galactosidase (GAL). Coliforms, other than E. coli (GAL+/GLUC-), form blue to green colonies, whereas, specifically, E. coli (GAL+/GLUC+) form violet colonies. Eleven foods (raw ground beef, raw boneless pork, fermented sausage, processed ham, processed turkey, frozen turkey breast, raw ground chicken, cottage cheese, ricotta cheese, raw milk, and dry infant formula) were validated, comparing the performance of RAPID'E. coli 2 agar to the reference method AOAC 966.24. Two sample incubation temperatures were evaluated, 37 and 44 degrees C, testing a mixture of naturally and artificially contaminated foods. If naturally contaminated food was not available, the matrix was artificially inoculated with one E. coli strain and one non-E. coli coliform strain. Method comparison studies demonstrated some statistical differences between the 2 methods, which are expected when a plating method is compared to a most probable number method. Inclusivity and exclusivity rates of the medium were 99 and 94%, respectively. The RAPID'E. coli 2 method was shown to be stable when minor variations were introduced.     

Investigations of acidity and nucleophilicity of diphenyldithiophosphinate ligands using theory and gas-phase dissociation reactions

Diphenyldithiophosphinate (DTP) ligands modified with electron-withdrawing trifluoromethyl (TFM) substitutents are of high interest because they have demonstrated potential for exceptional separation of Am (3+) from lanthanide (3+) cations. Specifically, the bis( ortho-TFM) (L 1 (-)) and ( ortho-TFM)( meta-TFM) (L 2 (-)) derivatives have shown excellent separation selectivity, while the bis( meta-TFM) (L 3 (-)) and unmodified DTP (L u (-)) did not. Factors responsible for selective coordination have been investigated using density functional theory (DFT) calculations in concert with competitive dissociation reactions in the gas phase. To evaluate the role of (DTP + H) acidity, density functional calculations were used to predict p K a values of the free acids (HL n ), which followed the trend of HL 3 < HL 2 < HL 1 < HL u. The order of p K a for the TFM-modified (DTP+H) acids was opposite of what would be expected based on the e (-)-withdrawing effects of the TFM group, suggesting that secondary factors influence the p K a and nucleophilicity. The relative nucleophilicities of the DTP anions were evaluated by forming metal-mixed ligand complexes in a trapped ion mass spectrometer and then fragmenting them using competitive collision induced dissociation. On the basis of these experiments, the unmodified L u (-) anion was the strongest nucleophile. Comparing the TFM derivatives, the bis( ortho-TFM) derivative L 1 (-) was found to be the strongest nucleophile, while the bis( meta-TFM) L 3 (-) was the weakest, a trend consistent with the p K a calculations. DFT modeling of the Na (+) complexes suggested that the elevated cation affinity of the L 1 (-) and L 2 (-) anions was due to donation of electron density from fluorine atoms to the metal center, which was occurring in rotational conformers where the TFM moiety was proximate to the Na (+)-dithiophosphinate group. Competitive dissociation experiments were performed with the dithiophosphinate anions complexed with europium nitrate species; ionic dissociation of these complexes always generated the TFM-modified dithiophosphinate anions as the product ion, showing again that the unmodified L u (-) was the strongest nucleophile. The Eu(III) nitrate complexes also underwent redox elimination of radical ligands; the tendency of the ligands to undergo oxidation and be eliminated as neutral radicals followed the same trend as the nucleophilicities for Na (+), viz. L 3 (-) < L 2 (-) < L 1 (-) < L u (-).     

Detailed characterisation of the flow resistance of commercial sub-2 micrometer reversed-phase columns

The pressure-drop characteristics of six sub-2 microm columns of three different manufacturers but with the same surface chemistry (C(18)) have been studied using the recently introduced total pore blocking method for the determination of the external porosity and by using scanning electron microscopy pictures to measure the actual size of the particles. Having used the Sauter-mean particle size to correctly account for the particle size spread, and having corrected for the influence of the intra-particle porosity, it was found that all columns yielded Kozeny-Carman constant (f(KC)) values close to 180, in agreement with the theory. This agreement could subsequently be used to quantify how the different system parameters such as mean particle size, packing density and intra-particle porosity (all tending to vary significantly from manufacturer to manufacturer) each contributes to the observed total bed permeability. Small (upward) deviations from the f(KC)=180-value could be correlated to a larger width of the particle size distribution, and more notably to the existence of a high size ratio of the largest to the smallest particles present in the particle batches.