A benchmark solution for 2D Stokes flow over cavity

Two-dimensional Stokes flow in a half plane with coupled cavity having the form of semi-ellipse is considered. The exact solution for the boundary problem is obtained. The solution can be a benchmark for numerical approaches. An example of the benchmarking is given.     

On pseudorandom numbers from multivariate polynomial systems

We bound exponential sums along the orbits of essentially arbitrary multivariate polynomial dynamical systems, provided that the orbits are long enough. We use these bounds to derive nontrivial estimates on the discrepancy of pseudorandom vectors generated by such polynomial systems. We generalize several previous results and in particular suggest a new approach that eliminates the need to control the degree growth of the iterations of these polynomial systems, which has been an obstacle in all previous approaches.     

Existence and uniqueness of solutions for the hydrostatic Euler equations on a bounded domain with analytic data

We address the question of well-posedness in spaces of analytic functions for the hydrostatic incompressible Euler equations (inviscid primitive equations) on domains with boundary, with a novel side-boundary condition.     

On the distribution of solutions to polynomial congruences

We use a result of é. Fouvry about the distribution of solutions to systems of congruences with multivariate polynomials in small cubic boxes and some ideas of W. Schmidt to derive an asymptotic formula for the number of such solutions in very general domains.     

Nitrogen/sulphur dual-doped hierarchical carbonaceous fibers boosting potassium-ion storage

The carbon materials as anode electrodes have been widely studied for potassium ion batteries(PIBs).However,the large size of potassium ions prevents their intercalation/deintercalation,resulting in poor storage behaviors.Herein,a novel design of N/S codoped hierarchical carbonaceous fibers(NSHCF)formed from nanosheets self-assembled by catalyzing Aspergillus niger with Sn is reported.The asprepared NSHCF at 600℃(NSHCF-600)exhibits a high reversible capacity of 345.4 m Ah g^-1 at 0.1 A g^-1 after 100 cycles and an excellent rate performance of 124.5 m Ah g^-1 at 2 A g^-1.The excellent potassium storage performance can be ascribed to the N/S dual-doping,which enlarges interlayer spacing(0.404 nm)and introduces more defects.The larger interlayer spacing and higher pyridinic N active sites can promote K ions diffusion and storage.In addition,the ex situ transmission electron microscopy reveals the high reversibility of potassiation/depotassiation process and structural stability.     

Synthesis of sulfolanopyranochromenones by the reaction of 2-benzylidene-3-methyl-4-nitro-2,5-dihydrothiophene 1,1-dioxides with 4-hydroxycoumarin

Chemistry of Heterocyclic Compounds - A number of tetracyclic compounds with annulated nitrosulfolane and pyranochromenone rings were synthesized by reacting...     

Non-emissive RuII Polypyridyl Complexes as Efficient and Selective Photosensitizers for the Photooxidation of Benzylamines

Five new Ru^II polypyridyl complexes bearing N-(arylsulfonyl)-8-amidoquinolate ligands and three of their biscyclometalated Ir^III congeners have been prepared and employed as photocatalysts ( PC s) in the photooxidation of benzylamines with O₂. In particular, the new Ru^II complexes do not exhibit photoluminescence, rather they harvest visible light efficiently and are very stable in solution under irradiation with blue light. Their non-emissive behavior has been related to the low electrochemical energy gaps and rationalized on the basis of theoretical calculations (DFT analysis) that predict low S₀←T₁ energy values. Moreover, the Ru^II complexes, despite being non-emissive, display excellent activities in the selective photocatalytic transformation of benzylamines into the corresponding imines. The presence of an electron-withdrawing group (-CF3) on the arene ring of the N-(arylsulfonyl)-8-amidoquinolate ligand improves the photocatalytic activity of the corresponding photocatalyst. Furthermore, all the experimental evidence, including transient absorption spectroscopy measurements suggest that singlet oxygen is the actual oxidant. The Ir^III analogues are considerably more photosensitive and consequently less efficient photosensitizers ( PS s).     

Integrability,existence of global solutions,and wave breaking criteria for a generalization of the Camassa–Holm equation

Recent generalizations of the Camassa–Holm equation are studied from the point of view of existence of global solutions, criteria for wave breaking phenomena and integrability. We provide conditions, based on lower bounds for the first spatial derivative of local solutions, for global well-posedness in Sobolev spaces for the family under consideration. Moreover, we prove that wave breaking phenomena occurs under certain mild hypothesis. Based on the machinery developed by Dubrovin [Commun. Math. Phys. 267, 117–139 (2006)] regarding bi-Hamiltonian deformations, we introduce the notion of quasi-integrability and prove that there exists a unique bi-Hamiltonian structure for the equation only when it is reduced to the Dullin–Gotwald–Holm equation. Our results suggest that a recent shallow water model incorporating Coriollis effects is integrable only in specific situations. Finally, to finish the scheme of geometric integrability of the family of equations initiated in a previous work, we prove that the Dullin–Gotwald–Holm equation describes pseudo-spherical surfaces.     

Ternary MIn2S4 (M = Mn,Fe, Co,Ni) Thiospinels – Crystal Structure and Thermoelectric Properties

A combined structural, magnetic and thermoelectric study of polycrystalline ternary MIn₂S₄ (M = Mn, Fe, Co, Ni) thiospinels is presented. All compounds crystallize with MgAl₂O₄-type structure. Rietveld refinement analysis confirmed that the preferred crystallographic position of transition metal element changes from mainly tetrahedral 8a for Mn to exclusively octahedral 16d for Ni (i.e. increase of the inversion parameter). Magnetic susceptibility measurements revealed M-elements to possess 2+ oxidation state in MIn₂S₄. All these compounds order antiferromagnetically with Néel temperatures T_N ranging from 5–13 K. The studied thiospinels are n-type semiconductors with large values of electrical resistivity ρ > 0.6 Ω · m at room temperature. An increase of the inversion parameter leads to a reduction of the determined activation energies, as well as to a more disorder-like behavior of thermal conductivity. The highest thermoelectric Figure of merit ZT was observed for MIn₂S₄ with M = Fe, Ni, which adopt inverse spinel structure.