Weak edge-degree domination in hypergraphs

In this paper we extend the notion of weak degree domination in graphs to hypergraphs and find relationships among the domination number, the weak edge-degree domination number, the independent domination number and the independence number of a given hypergraph.     

ChemInform Abstract: Study of Phase Transformation in BaTe2O6 by in situ High‐Pressure X‐Ray Diffraction,Raman Spectroscopy,and First‐Principles Calculations.

The title compound is synthesized by solid state reaction of a stoichiometric mixture of BaCO₃ and TeO₂ (air, 550 °C for 6 h, and 650 °C for 12 h).     

Speeding up Exponentiation using an Untrusted Computational Resource

We present protocols for speeding up fixed-base variable-exponent exponentiation and variable-base fixed-exponent exponentiation using an untrusted computational resource. In the fixed-base protocols, the exponent may be blinded. In the variable-base protocols, the base may be blinded. The protocols are described for exponentiation in a cyclic group. We describe how to extend them to exponentiation modulo an integer where the modulus is the product of primes with single multiplicity. The protocols provide a speedup of over the square-and-multiply algorithm, where k is the bitlength of the exponent. One application of the protocols is to speed up exponentiation-based verification in discrete log-based signature and credential schemes. The protocols also allow signature verifiers to dynamically choose, for each message, the amount of work it would like to perform to verify the signature. This results in a work-security tradeoff. We introduce a fifth protocol to perform variable-base variable- exponent exponentiation, which also has this feature. Our model allows the trusted resource to perform computations in its idle time. The protocols facilitate the offloading of work to the offline stage, such that the work the trusted resource performs when it has to do an exponentiation is smaller. Our protocols are unconditionally secure.     

Electronic structure and structural stability of LaAl2 and LaAl3—A comparative study

The large structural stability regime of LaAl₂ and LaAl₃ as a function of pressure is investigated by the band structure calculations using the FP-LAPW method. An earlier experimental study has revealed that there is no structural phase transition at ∼35 and ∼30 GPa for LaAl₂ and LaAl₃, respectively. Our calculations indicate that in the density of states curve of LaAl₂, the Fermi level (E_F) lies in a slope between bonding maxima and antibonding minima. At high pressures the E_F moves slightly towards the valley, but this shifting does not affect its structural stability. In LaAl₃, the E_F falls in a flat region in the density of states and does not move even up to 33 GPa. The band dispersion curves for both the compounds show movement of bands under the influence of pressure. Some of them cross the Fermi level leading to so called Lifshitz transitions. However, it is seen that these electronic changes do not manifest into any volume anomaly in LaAl₃ under pressure. Our study clearly shows that the density of states behavior for LaAl₂ and LaAl₃ satisfies the Yamashita-Asano criterion for structural stability. The theoretical equations of state, bulk modulus and its pressure derivative values are compared with the experimental values.     

Synthesis of pyridazinones via molecular-iodine-mediated cleavage of 4-bromomethylcoumarin precursors

A facile and an efficient protocol for the synthesis of pyridazinones via molecular-iodine-mediated cleavage of 4-bromomethylcoumarin precursors in the presence of I₂ in ethanol at 70?°C is reported. The present approach replaced the basic condition (K₂CO₃) with Lewis acidic condition.     

Synthesis of 4-phenyloxazinones via DBU-catalyzed cleavage of 4-bromomethylcoumarins

A new route for ring transformation has been discovered during the reaction of 4-bromomethylcoumarins with hydroxyl amine in the presence of 1,8-diazabicyclo[5.4.0]undec-7-ene (DBU), leading to the formation of pharmacologically important 1,2-oxazinones in a single step with very high yields.     

The polynomial representation of the type An−1 rational Cherednik algebra in characteristic p | n

We study the polynomial representation of the rational Cherednik algebra of type A_n?1 with generic parameter in characteristic p for p | n. We give explicit formulas for generators for the maximal proper graded submodule, show that they cut out a complete intersection, and thus compute the Hilbert series of the irreducible quotient. Our methods are motivated by taking characteristic p analogues of existing characteristic 0 results.     

Sodalite‐type Cu‐based Three‐dimensional Metal–Organic Framework for Efficient Oxygen Reduction Reaction

Inspired by copper‐based oxygen reduction biocatalysts, we have studied the electrocatalytic behavior of a Cu‐based MOF (Cu‐BTT) for oxygen reduction reaction (ORR) in alkaline medium. This catalyst reduces the oxygen at the onset (E_onset) and half‐wave potential (E^1/2) of 0. 940 V and 0.778 V, respectively. The high halfway potential supports the good activity of Cu‐BTT MOF. The high ORR catalytic activity can be interpreted by the presence of nitrogen‐rich ligand (tetrazole) and the generation of nascent copper(I) during the reaction. In addition to the excellent activity, Cu‐BTT MOF showed exceptional stability too, which was confirmed through chronoamperometry study, where current was unchanged up to 12 h. Further, the 4‐electrons transfer of ORR kinetics was confirmed by hydrodynamic voltammetry. The oxygen active center namely copper(I) generation during ORR has been understood by the reduction peak in cyclic voltammetry as well in the XPS analysis.     

Blue luminescence of Au nanoclusters embedded in silica matrix

Photoluminescence study using the 325 nm He-Cd excitation is reported for the Au nanoclusters embedded in SiO(2) matrix. Au clusters are grown by ion beam mixing with 100 KeV Ar(+) irradiation on Au [40 nm]/SiO(2) at various fluences and subsequent annealing at high temperature. The blue bands above approximately 3 eV match closely with reported values for colloidal Au nanoclusters and supported Au nanoislands. Radiative recombination of sp electrons above Fermi level to occupied d-band holes are assigned for observed luminescence peaks. Peaks at 3.1 and 3.4 eV are correlated to energy gaps at the X- and L-symmetry points, respectively, with possible involvement of relaxation mechanism. The blueshift of peak positions at 3.4 eV with decreasing cluster size is reported to be due to the compressive strain in small clusters. A first principle calculation based on density functional theory using the full potential linear augmented plane wave plus local orbitals formalism with generalized gradient approximation for the exchange correlation energy is used to estimate the band gaps at the X- and L-symmetry points by calculating the band structures and joint density of states for different strain values in order to explain the blueshift of approximately 0.1 eV with decreasing cluster size around L-symmetry point.     

A note on the flow induced by a constantly accelerating plate in an Oldroyd-B fluid

The velocity field and the adequate tangential stress that is induced by the flow due to a constantly accelerating plate in an Oldroyd-B fluid, are determined by means of Fourier sine transforms. The solutions corresponding to a Maxwell, Second grade and Navier–Stokes fluid appear as limiting cases of the solutions obtained here. However, in marked contrast to the solution for a Navier–Stokes fluid, in the case of an Oldroyd-B fluid oscillations are set up which decay exponentially with time.