Electrophotocatalytic Undirected C−H Trifluoromethylations of (Het)Arenes

Electrophotochemistry has enabled arene C−H trifluoromethylation with the Langlois reagent CF₃SO₂Na under mild reaction conditions. The merger of electrosynthesis and photoredox catalysis provided a chemical oxidant-free approach for the generation of the CF₃ radical. The electrophotochemistry was carried out in an operationally simple manner, setting the stage for challenging C−H trifluoromethylations of unactivated arenes and heteroarenes. The robust nature of the electrophotochemical manifold was reflected by a wide scope, including electron-rich and electron-deficient benzenes, as well as naturally occurring heteroarenes. Electrophotochemical C−H trifluoromethylation was further achieved in flow with a modular electro-flow-cell equipped with an in-operando monitoring unit for on-line flow-NMR spectroscopy, providing support for the single electron transfer processes.     

Solution-Based,Anion-Doping of Li4Ti5O12 Nanoflowers for Lithium-Ion Battery Applications

Solution-based, anionic doping represents a convenient strategy with which to improve upon the conductivity of candidate anode materials such as Li₄Ti₅O₁₂ (LTO). As such, novel synthetic hydrothermally-inspired protocols have primarily been devised herein, aimed at the large-scale production of unique halogen-doped, micron-scale, three-dimensional, hierarchical LTO flower-like motifs. Although fluorine (F) doping has been explored, the use of chlorine (Cl) dopants is the primary focus here. Several experimental variables, such as dopant amount, lithium hydroxide concentration, and titanium butoxide purity, were probed and perfected. Furthermore, the Cl doping process did not damage the intrinsic LTO morphology. The analysis, based on interpreting a compilation of SEM, XRD, XPS, and TEM-EDS results, was used to determine an optimized dopant concentration of Cl. Electrochemical tests demonstrated an increased capacity via cycling of 12 % for a Cl-doped sample as compared with pristine LTO. Moreover, the Cl-doped LTO sample described in this study exhibited the highest discharge capacity yet reported at an observed rate of 2C for this material at 143mAh g⁻¹. Overall, these data suggest that the Cl dopant likely enhances not only the ion transport capabilities, but also the overall electrical conductivity of our as-prepared structures. To help explain these favorable findings, theoretical DFT calculations were used to postulate that the electronic conductivity and Li diffusion were likely improved by the presence of increased Ti³⁺ ion concentration coupled with widening of the Li migration channel.     

Baer cotorsion Pairs

LetR be a unital associative ring and two classes of leftR-modules. In [St3] the notion of a ( ) pair was introduced. In analogy to classical cotorsion pairs, a pair (V,W) of subclasses is called a ( ) pair if it is maximal with respect to the classes and the condition Ext _R ¹ (V, W)=0 for all . In this paper we study pairs whereR = ℤ and is the class of all torsion-free abelian groups andT is the class of all torsion abelian groups. A complete characterization is obtained assumingV=L. For example, it is shown that every pair is singly cognerated underV=L. The author was supported by a DFG grant.     

Fully transitive -groups with finite first Ulm subgroup

An abelian -group is called (fully) transitive if for all with ( ) there exists an automorphism (endomorphism) of which maps onto . It is a long-standing problem of A. L. S. Corner whether there exist non-transitive but fully transitive -groups with finite first Ulm subgroup. In this paper we restrict ourselves to -groups of type , this is to say -groups satisfying . We show that the answer to Corner's question is no if is finite and is of type .

     

Operator–valued Fourier multiplier theorems on Besov spaces

We investigate analytical properties of a measure geometric Laplacian which is given as the second derivative w.r.t. two atomless finite Borel measures μ and ν with compact supports supp μ ? supp ν on the real line. This class of operators includes a generalization of the well‐known Sturm‐Liouville operator as well as of the measure geometric Laplacian given by . We obtain for this differential operator under both Dirichlet and Neumann boundary conditions similar properties as known in the classical Lebesgue case for the euclidean Laplacian like Gauß‐Green‐formula, inversion formula, compactness of the resolvent and its kernel representation w.r.t. the corresponding Green function. Finally we prove nuclearity of the resolvent and give two representations of its trace.     

A finite element method for the numerical solution of convection-dominated anisotropic diffusion equations

Summary. The proposed method is based on an additive decomposition of the differential operator and the subsequent fitted discretization of the resulting components. For standard situations, the derived stability and error estimates in the energy norm qualitatively coincide with well-known estimates. In the case of small diffusion, a uniform error estimate with reduced order is obtained. Received August 7, 1997 / Revised version received July 15, 1998 / Published online December 6, 1999     

Change of evaporation rate of single monocomponent droplet with temperature using time-resolved phase rainbow refractometry

Droplet evaporation characterization, although of great significance, is still challenging. The recently developed phase rainbow refractometry (PRR) is proposed as an approach to measuring the droplet temperature, size as well as evaporation rate simultaneously, and is applied to a single flowing n-heptane droplet produced by a droplet-on-demand generator. The changes of droplet temperature and evaporation rate after a transient spark heating are reflected in the time-resolved PRR image. Results show that droplet evaporation rate increases with temperature, from ?1.28$\times {10}^{?8}$ m²/s at atmospheric 293 K to a range of (?1.5, ?8)$\times {10}^{?8}$ m²/s when heated to (294, 315) K, agreeing well with the Maxwell and Stefan–Fuchs model predictions. Uncertainty analysis suggests that the main source is the indeterminate gradient inside droplet, resulting in an underestimation of droplet temperature and evaporation rate. With the demonstration on simultaneous measurements of droplet refractive index as well as droplet transient and local evaporation rate in this work, PRR is a promising tool to investigate single droplet evaporation in real engine conditions.     

The <Emphasis Type="Italic">k</Emphasis>-domatic number of a graph

Let k be a positive integer, and let G be a simple graph with vertex set V (G). A k-dominating set of the graph G is a subset D of V (G) such that every vertex of V (G)-D is adjacent to at least k vertices in D. A k-domatic partition of G is a partition of V (G) into k-dominating sets. The maximum number of dominating sets in a k-domatic partition of G is called the k-domatic number d _k (G). In this paper, we present upper and lower bounds for the k-domatic number, and we establish Nordhaus-Gaddum-type results. Some of our results extend those for the classical domatic number d(G) = d ₁(G).      

The π N → e +e−N reaction close to the vector-meson production threshold

The π^? p→e ⁺ e ^? n and π⁺ n→e ⁺ e ^? p reaction cross sections are calculated below and in the vicinity of the vector-meson (?⁰,ω) production threshold. These processes are largely responsible for the emission of e ⁺e^? pairs in pion-nucleus reactions and contribute to the dilepton spectra observed in relativistic heavy ion collisions. They are dominated by the decay of low-lying baryon resonances into vector-meson-nucleon channels. The vector mesons materialize subsequently into e ⁺ e^? pairs. Using πN→?⁰ N and πN→ωN, amplitudes calculated in the center of mass energy interval 1.4 < √s<1.8 GeV, we compute the π^? p→e ⁺ e ^? n and π⁺ n→e ⁺ e ^? p reaction cross sections in these kinematics. Below the vector-meson production threshold, the π⁰?ω interference in the e ⁺ e^? channel appears largely destructive for the π^? p→e ⁺ e ^? n cross section and constructive for the π⁺ n→e ⁺ e ^? p cross section. The pion beam and the HADES detector at GSI offer a unique possibility to measure these effects. Such data would provide strong constraints on the coupling of vector-meson-nucleon channels to low-lying baryon resonances.