On the computation of all extensions of a -adic field of a given degree

Let be a -adic field. It is well-known that has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions of a given degree and discriminant.

     

Evolution of magnetic order in mechanically alloyed Al–1 at%Fe

The evolution of ferromagnetic order in high-energy ball-milled Al–1 at% Fe before the onset of a considerable Fe–Al solid solution phase has been investigated using ⁵⁷Fe Mössbauer and bulk magnetization studies. The unmilled sample does not exhibit bulk magnetic properties and an onset of bulk magnetization is observed only after 30 min of milling, when the grain size becomes comparable to the ferromagnetic exchange length. The Curie temperatures of all the samples are less than that of pure iron. The reduction in grain size is accompanied by an increase in coercivity and reduced remanence and a decrease in T_C. The effective magnetic moment per iron atom decreases with the development of a non-magnetic, Al-rich Fe–Al solution on longer milling. The clustering of Fe at grain boundaries is responsible for the observed bulk magnetic ordering. The systematic variation of the magnetic properties has been qualitatively correlated with the evolution of microstructure, reduction in grain size and enhanced inter-granular exchange coupling.     

Tunable microlens arrays using polymer network liquid crystal

A tunable-focus microlens array based on polymer network liquid crystal (PNLC) is demonstrated. The PNLC was prepared using an ultraviolet (UV) light exposure through a patterned photomask. The photocurable monomer in each of the UV exposed spot forms an inhomogeneous centro-symmetrical polymer network which acts as a lens when a homogeneous electric field is applied to the cell. The focal length of the microlens arrays is tunable with the applied voltage.     

Sufficient Conditions for Maximally Edge-connected and Super-edge-connected Digraphs Depending on the Size

Let D be a finite and simple digraph with vertex set V (D). The minimum degree δ of a digraph D is defined as the minimum value of its out-degrees and its in-degrees. If D is a digraph with minimum degree δ and edge-connectivity λ, then λ ≤ δ. A digraph is maximally edge-connected if λ=δ. A digraph is called super-edge-connected if every minimum edge-cut consists of edges incident to or from a vertex of minimum degree. In this note we show that a digraph is maximally edge-connected or super-edge-connected if the number of arcs is large enough.     

Molecular Photochemistry: Recent Developments in Theory

Photochemistry is a fascinating branch of chemistry that is concerned with molecules and light. However, the importance of simulating light‐induced processes is reflected also in fields as diverse as biology, material science, and medicine. This Minireview highlights recent progress achieved in theoretical chemistry to calculate electronically excited states of molecules and simulate their photoinduced dynamics, with the aim of reaching experimental accuracy. We focus on emergent methods and give selected examples that illustrate the progress in recent years towards predicting complex electronic structures with strong correlation, calculations on large molecules, describing multichromophoric systems, and simulating non‐adiabatic molecular dynamics over long time scales, for molecules in the gas phase or in complex biological environments.     

Thermally Activated Delayed Fluorescence in a Y3N@C80 Endohedral Fullerene: Time‐Resolved Luminescence and EPR Studies

The endohedral fullerene Y₃N@C₈₀ exhibits luminescence with reasonable quantum yield and extraordinary long lifetime. By variable‐temperature steady‐state and time‐resolved luminescence spectroscopy, it is demonstrated that above 60 K the Y₃N@C₈₀ exhibits thermally activated delayed fluorescence with maximum emission at 120 K and a negligible prompt fluorescence. Below 60 K, a phosphorescence with a lifetime of 192±1 ms is observed. Spin distribution and dynamics in the triplet excited state is investigated with X‐ and W‐band EPR and ENDOR spectroscopies and DFT computations. Finally, electroluminescence of the Y₃N@C₈₀/PFO film is demonstrated opening the possibility for red‐emitting fullerene‐based organic light‐emitting diodes (OLEDs).     

Pt@MOF-177: synthesis, room-temperature hydrogen storage and oxidation catalysis

The gas-phase loading of [Zn(4)O(btb)(2)](8) (MOF-177; H(3)btb=1,3,5-benzenetribenzoic acid) with the volatile platinum precursor [Me(3)PtCp'] (Cp'=methylcyclopentadienyl) was confirmed by solid state (13)C magic angle spinning (MAS)-NMR spectroscopy. Subsequent reduction of the inclusion compound [Me(3)PtCp'](4)@MOF-177 by hydrogen at 100 bar and 100 degrees C for 24 h was carried out and gave rise to the formation of platinum nanoparticles in a size regime of 2-5 nm embedded in the unchanged MOF-177 host lattice as confirmed by transmission electron microscopy (TEM) micrographs and powder X-ray diffraction (PXRD). The room-temperature hydrogen adsorption of Pt@MOF-177 has been followed in a gravimetric fashion (magnetic suspension balance) and shows almost 2.5 wt % in the first cycle, but is decreased down to 0.5 wt % in consecutive cycles. The catalytic activity of Pt@MOF-177 towards the solvent- and base-free room temperature oxidation of alcohols in air has been tested and shows Pt@MOF-177 to be an efficient catalyst in the oxidation of alcohols.     

Self-similar asymptotic behavior for the solutions of a linear coagulation equation

In this paper we consider the long-time asymptotics of a linear version of the Smoluchowski equation which describes the evolution of a tagged particle moving in a random distribution of fixed particles. The volumes v of these particles are independently distributed according to a probability distribution which decays asymptotically as a power law $v^{?\sigma }$. The validity of the equation has been rigorously proved in [22] taking as a starting point a particle model and for values of the exponent $\sigma >3$, but the model can be expected to be valid, on heuristic grounds, for $\sigma >\frac{5}{3}$. The resulting equation is a non-local linear degenerate parabolic equation. The solutions of this equation display a rich structure of different asymptotic behaviors according to the different values of the exponent σ. Here we show that for $\frac{5}{3}<\sigma <2$ the linear Smoluchowski equation is well-posed and that there exists a unique self-similar profile which is asymptotically stable.     

Selective C(sp3)−H Aerobic Oxidation Enabled by Decatungstate Photocatalysis in Flow

A mild and selective C(sp³)?H aerobic oxidation enabled by decatungstate photocatalysis has been developed. The reaction can be significantly improved in a microflow reactor enabling the safe use of oxygen and enhanced irradiation of the reaction mixture. Our method allows for the oxidation of both activated and unactivated C?H bonds (30 examples). The ability to selectively oxidize natural scaffolds, such as (?)‐ambroxide, pregnenolone acetate, (+)‐sclareolide, and artemisinin, exemplifies the utility of this new method.