Uniform partition extensions,a generating functions perspective

In this paper, a bivariate generating function CF(x, y) =f(x)-yf(xy)1-yis investigated, where f(x)= n 0fnxnis a generating function satisfying the functional equation f(x) = 1 + r j=1 m i=j-1aij xif(x)j.In particular, we study lattice paths in which their end points are on the line y = 1. Rooted lattice paths are defined. It is proved that the function CF(x, y) is a generating function defined on some rooted lattice paths with end point on y = 1. So, by a simple and unified method, from the view of lattice paths, we obtain two combinatorial interpretations of this bivariate function and derive two uniform partitions on these rooted lattice paths.     

Twice Q-polynomial distance-regular graphs of diameter 4

It is known that a distance-regular graph with valency k at least three admits at most two Qpolynomial structures. We show that all distance-regular graphs with diameter four and valency at least three admitting two Q-polynomial structures are either dual bipartite or almost dual bipartite. By the work of Dickie(1995) this implies that any distance-regular graph with diameter d at least four and valency at least three admitting two Q-polynomial structures is, provided it is not a Hadamard graph, either the cube H(d, 2)with d even, the half cube 1/2H(2d + 1, 2), the folded cube?H(2d + 1, 2), or the dual polar graph on [2A2d-1(q)]with q 2 a prime power.     

Three-dimensional supramolecular crystalline materials based on Keggin-based polyoxometalates and 1,2-Bis (4-pyridyl) ethylene for supercapacitor electrodes

Transition Metal Chemistry - To research the application of polyoxometalates (POMs)-based supramolecular crystalline materials in supercapacitors, two new compounds,...     

Organic Proton‐Buffer Electrode to Separate Hydrogen and Oxygen Evolution in Acid Water Electrolysis

Hydrogen production from water via electrolysis in acid is attracting extensive attention as an attractive alternative approach to replacing fossil fuels. However, the simultaneous evolution of H₂ and O₂ requires a fluorine‐containing proton exchange membrane to prevent the gases from mixing while using the same space to concentrate the gases, which significantly increases the cost and reduces the flexibility of this approach. Here, a battery electrode based on the highly reversible enolization reaction of pyrene‐4,5,9,10‐tetraone is first introduced as a solid‐state proton buffer to separate the O₂ and H₂ evolution of acidic water electrolysis in space and time, through which the gas mixing issue can be avoided without using any membrane. This process allows us to separately consider H₂ and O₂ production according to the variation in input power (e.g., the renewable energy) and/or the location for H₂ concentration, thus showing high flexibility for H₂ production.     

Unusual Hypochlorous Acid (HClO) Recognition Mechanism Based on Chlorine–Oxygen Bond (Cl−O) Formation

One of the most important endogenous reactive oxygen species, hypochlorous acid (HClO), is involved in numerous pathological and physiological processes. Herein, a near-infrared fluorescence probe (CyHR) was designed and synthesized for ultrafast (within 0.2 s), sensitive (limit of detection=39.44 nm ), and selective response to HClO. The reaction mechanism was systematically analyzed by MS, ¹H NMR spectroscopy, HPLC-MS techniques, and theoretical calculations. The results indicated that HClO can be recognized by CyHR, which is based on chlorine–oxygen (Cl−O) bond formation. To the best of our knowledge, this study is the first to find Cl−O bonds among organic aromatic compounds, given that Cl−O bonds are common among inorganics. Through biological experiments, CyHR was successfully applied to image exogenous and endogenous HClO in macrophage cells (RAW 264.7). Thus, CyHR is a promising tool for HClO-related physiological and pathological studies and may provide a means for designing HClO-specific fluorescence probes.     

NO分子宏观气体热力学性质的理论研究

采用量子统计系综理论,研究了基态NO分子宏观气体摩尔熵、摩尔内能、摩尔热容等热力学性质.首先应用课题组前期建立的变分代数法(variational algebraic method, VAM)计算获得了基态NO分子的完全振动能级,得到的VAM振动能级作为振动部分,结合欧拉-麦克劳林渐进展开公式的转动贡献,应用于经典的热力学与统计物理公式中,从而计算得到了1000-5000 K温度范围内NO宏观气体的摩尔内能、摩尔熵和摩尔热容.将不同方法计算得到的摩尔热容结果分别与实验值进行比较,结果表明基于VAM完全振动能级获得的结果优于其他方法获得的理论结果.振动部分采用谐振子模型对无限能级求和计算热力学性质的方法有一定的局限性,应当使用有限的完全振动能级进行统计求和.     

Generation of 131 fs mode-locked pulses from 2.8μm Er:ZBLAN fiber laser

We demonstrated a femtosecond mode-locked Er:Zr F4-Ba F2-La F3-Al F3-Na F(Er:ZBLAN)fiber laser at 2.8μm based on the nonlinear polarization rotation technique.The laser generated an average output power of 317 m W with a repetition rate of 107 MHz and pulse duration as short as 131 fs.To the best of our knowledge,this is the shortest pulse generated directly from a mid-infrared mode-locked Er:ZBLAN fiber laser to date.Numerical simulation and experimental results confirm that reducing the gain fiber length is an effective way to shorten the mode-locked pulse duration in the Er:ZBLAN fiber laser.The work takes an important step towards sub-100-fs mid-infrared pulse generation from mode-locked Er:ZBLAN fiber lasers.