The dual form of Beck type identities

The Ramanujan Journal - Inspired by Andrews and Merca’s recent work on the number of even parts over all partitions into distinct parts, we introduce a new kind of Beck type identities, which...     

An AIE-Active probe for detection and bioimaging of pH values based on lactone hydrolysis reaction

Cellular pH homeostasis is essential for many physiological and pathological processes. pH monitoring is helpful for the diagnosis, treatment and prevention of disorders and diseases. Herein, we developed a ratiometric fluorescent pH probe (TCC) based on a coumarin derivative containing a highly active lactone ring. TCC exhibited a typical AIE effect and emitted blue fluorescence under weak acidic condition. When under weak basic condition, the active lactone moiety underwent a hydrolysis reaction to afford a water-soluble product, which gave red-shifted emission. The emission color change from blue through cyan and then to yellow within pH 6.5–9.0 which is approximate to the biological pH range. And the fluorescence color change along with pH value is reversible. Furthermore, TCC was successfully utilized in the detection of the intracellular pH change of live HeLa cells, which indicated that TCC had practical potential in biomedical research.

     

A boundary expansion of solutions to nonlinear singular elliptic equations

In this paper we establish an asymptotic expansion near the boundary for solutions to the Dirichlet problem of elliptic equations with singularities near the boundary.This expansion formula shows the singularity profile of solutions at the boundary.We deal with both linear and nonlinear elliptic equations,including fully nonlinear elliptic equations and equations of Monge-Ampère type.     

Characterizations of $$\sigma$$ -Solvable Finite Groups

Mathematical Notes - All the groups considered in this paper are finite, and $$G$$ always denotes a finite group; $$\sigma$$ is a partition of the set $$\mathbb{P}$$ of all primes, i.e.,...     

Extension/Compression-Controlled Complete Band Gaps in 2D Chiral Square-Lattice-Like Structures

Achieving tunable band gaps in a structure by external stimuli is of great importance in acoustic applications. This paper aims to investigate the tunability of band gaps in square-lattice-like elastic periodic structures that are usually not featured with notable band gaps.Endowed with chirality, the periodic structures here are able to undergo imperfection-insensitive large deformation under extension or compression. The influences of geometric parameters on band gaps are discussed via the nonlinear finite element method. It is shown that the band gaps in such structures with curved beams can be very rich and, more importantly, can be efficiently and robustly tuned by applying appropriate mechanical loadings without inducing buckling. As expected, geometry plays a more significant role than material nonlinearity does in the evolution of band gaps. The dynamic tunability of band gaps through mechanical loading is further studied. Results show that closing, opening, and shifting of band gaps can be realized by exerting real-time global extension or compression on the structure. The proposed periodic structure with well-designed chiral symmetry can be useful in the design of particular acoustic devices.     

Multi-scale Fractured Coal Gas–Solid Coupling Model and Its Applications in Engineering Projects

With coal mining entering the geological environment of “high stress, rich gas, strong adsorption and low permeability,” the difficulty of joint coal and gas extraction clearly augments, the risk of solid–gas coupling dynamic disasters greatly increases, and the underlying mechanisms become more complex. In this paper, based on the characteristics of coal’s multi-scale structure and spatiotemporal variation, the multi-scale fractured coal gas–solid coupling model (MSFM) was built. In this model, the interaction between coal matrix and its fractures and the mechanical characteristics of gas-bearing coal were considered, as well as their coupling relationship. By MATLAB software, the stress–damage–seepage numerical computation programs were developed, which were applied into Comsol Multiphysics to simulate gas flow caused by coal mining. The simulation results showed the spatial variability of coal elastic modulus and cross-flow behaviors of coal seam gas, which were superior to the results of traditional gas–solid coupling model. And the numerical results obtained from MSFM were closer to the measured results in field, while the computation results of traditional model were slightly higher than the measured results. Furthermore, the MSFM in a large scale was verified by field engineering project.     

Complex Study of the Spearhead Superficial Crust from Burial Mound no. 1 near Novosvobodnaya Village

A complex study of a spearhead dated back to IV mill. BC from burial mound no. 1 near Novosvobodnaya village (collection of the State Historical Museum) and, in particular, the material of spearhead superficial crust has been performed. The elemental and phase composition of the metal of spearhead and the superficial crust on its surface have been determined by scanning electron microscopy, jointly with energydispersive X-ray microanalysis and X-ray phase analysis. A comparative analysis of the results of studying the spearhead superficial crust and similar crusts on other artifacts from the mounds near Novosvobodnaya village suggest natural origin of the crust on copper?arsenic artifacts.

     

硫化镉反蛋白石光子晶体制备及光解水制氢

对硫化镉反蛋白石结构光子晶体薄膜进行了可控合成,用巯基乙酸修饰的纳米晶和P(St-MMA-SPMAP)高分子小球共组装,成功地构筑了反蛋白石结构并用于可见光光解水产氢。结果表明,在可见光(λ≥420 nm)照射下,Cd S-310反蛋白石结构薄膜的光解水产氢性能比硫化镉纳米颗粒提高了一倍。这主要是因为等级孔结构反蛋白石光子晶体特性对催化剂的光催化性能的提升:首先,反蛋白石的周期性结构增加了光子在材料中的传播,提高了催化剂对太阳光的利用率;同时,大孔孔壁是由纳米颗粒堆积而成的,在反应中提供了更多的反应活性位点;此外,孔结构有利于物质的传输和分子的吸附。     

Nickel (II) tetrapyridyl complexes as electrocatalysts and precatalysts for water oxidation

Two nickel complexes, [Ni(tpen)](ClO₄)₂.0.5CH₃COCH₃ ( 1 ) and [Ni(tpbn)](ClO₄)₂ ( 2 ), of tetrapyridyl ligands N,N,N′,N′-tetrakis(2-pyridyl-methyl)-1,2-ethanediamine (tpen) and N,N,N′,N′-tetrakis(2-pyridyl-methyl)-1,4-butanediamine (tpbn) were prepared and their catalysis for water oxidation reaction (WOR) studied. In 0.1 M phosphate buffer solution (PBS) of pH 8.0, complex 1 is a homogeneous molecular catalyst with an overpotential of ~440 mV and a Faradaic efficiency of 89%. At pH ≥ 9.0, complex 1 degraded gradually during the catalytic process and formed NiO_x composite (nickel oxide with general formula Ni_xO_yH_z) active for WOR. In contrast, complex 2 deteriorated under measured conditions (pH 8.0–12.0) and formed NiO_x composite active for WOR. The NiO_x composite derived from 1 in 0.1 M PBS at pH 11.0 showed an activity with an overpotential of ~500 mV, a Tafel slope of ~90 mV/decade and a Faradaic efficiency of 97%. Mechanisms were proposed for water oxidation catalyzed by 1 and 2 . This work revealed that the catalytic activity of the nickel complexes was related to the flexibility of the tetrapyridyl ligands and the adaptability of the coordination sphere of the nickel(II) center.