An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

正following Cayley-Hamilton theorem:(1)where I1, I2, and I3denote the first, second, and third principal invariants of and N-dimensional space,(2)     

Delannoy数与Schröder数的一些和式公式

研究了Delannoy数与Schr?der数.利用分析方法和组合技巧,建立了任意多个Delannoy数乘积的一些和式公式,并对Schroder数的和式公式进行了类似的研究.     

Alkaline oxygen evolution: exploring synergy between fcc and hcp cobalt nanoparticles entrapped in N-doped graphene

Herein, we report a Mott-Schottky catalyst by entrapping cobalt nanoparticles inside the N-doped graphene shell (Co@NC). The Co@NC delivered excellent oxygen evolution activity with an overpotential of merely 248 mV at a current density of 10 mA cm^–2 with promising long-term stability. The importance of Co encapsulated in NC has further been demonstrated by synthesizing Co nanoparticles without NC shell. The synergy between the hexagonal close-packed (hcp) and face-centered cubic (fcc) Co plays a major role to improve the OER activity, whereas the NC shell optimizes the electronic structure, improves the electron conductivity, and offers a large number of active sites in Co@NC. The density functional theory calculations have revealed that the hcp Co has a dominant role in the surface reaction of electrocatalytic oxygen evolution, whereas the fcc phase induces the built-in electric field at the interfaces with N-doped graphene to accelerate the H⁺ ion transport.     

Synthesis and Structural Characterization of a Di-nuclear Uranyl Complex with Quinoline-6-carboxylate

Crystallography Reports - A di-nuclear uranyl complex with the formula of [(UO2)2(L)4(H2O)2]?4H2O (1) (HL = quinoline-6-carboxylic acid) was synthesized hydrothermally and characterized by...     

Special John-Nirenberg-Campanato spaces via congruent cubes

Let p ∈ [1, ∞), q ∈ [1, ∞), α∈ R, and s be a non-negative integer. Inspired by the space JNp introduced by John and Nirenberg(1961) and the space B introduced by Bourgain et al.(2015), we introduce a special John-Nirenberg-Campanato space JN^con_(p,q,s) over Rⁿ or a given cube of R;with finite side length via congruent subcubes, which are of some amalgam features. The limit space of such spaces as p →∞ is just the Campanato space which coincides with the space BMO(the space of functions with bounded mean oscillations)when α = 0. Moreover, a vanishing subspace of this new space is introduced, and its equivalent characterization is established as well, which is a counterpart of the known characterization for the classical space VMO(the space of functions with vanishing mean oscillations) over Rⁿ or a given cube of Rⁿ with finite side length.Furthermore, some VMO-H¹-BMO-type results for this new space are also obtained, which are based on the aforementioned vanishing subspaces and the Hardy-type space defined via congruent cubes in this article. The geometrical properties of both the Euclidean space via its dyadic system and congruent cubes play a key role in the proofs of all these results.     

Flower-like titanium dioxide as novel co-reaction accelerator for ultrasensitive “off–on” electrochemiluminescence aptasensor construction based on 2D g-C3N4 layer for thrombin detection

Journal of Solid State Electrochemistry - An ultrasensitive “signal-off–on” electrochemiluminescence (ECL) biosensor is constructed based on f1-TiO2/g-C3N4/PDA for thrombin...     

Enhanced thermal conductivity and mechanical properties of polymeric composites through formation of covalent bonds between boron nitride and rubber chains

Hexagonal boron nitride (BN) platelets, also known as white graphite, are often used to improve the thermal conductivities of polymeric matrices. Due to the poor interfacial compatibility between BN platelets and polymeric matrices, in this study, polyrhodanine (PRd) was used to modify BN platelets and prepared functionalized BN-PRd platelets, thereby enhancing the interfacial interaction between the thermal conductive filler and polymeric matrix. Then, BN-PRd platelets were dispersed into the nitrile butadiene rubber (NBR) matrix to yield high thermally conductive composites. The presence of N? C═S groups in PRd allowed the combination of PRd and NBR chains containing stable covalent bonds via vulcanization reaction. The thermal conductivity of the as-prepared 30 vol% BN-PRd/NBR composite reached 0.40 W/mK, representing an increment of 135% over pure NBR (0.17 W/mK). In addition, the largest tensile strength of NBR composite containing 30 vol% BN-PRd platelets was 880% times of pure NBR. The 30 vol% BN-PRd/NBR composite also displayed a relatively high dielectric constant (9.35 at 100 Hz) and a low dielectric loss tangent value (0.07 at 100 Hz), indicating their usefulness as dielectric flexible materials of microelectronics. In sum, the simplicity and good efficiency of formation of covalent bonds between boron nitride and rubber chains look very promising for large-scale industrial production of high thermally conductive composites.     

Facile fabrication of oxygen-doped carbon nitride with enhanced visible-light photocatalytic degradation of methyl mercaptan

Research on Chemical Intermediates - Element doping has demonstrated an effective strategy for enhancing photocatalytic performance of carbon nitride (CN). Herein, we reported that oxygen-doped CN...     

Direct Synthesis of Adipic Esters and Adiponitrile via Photoassisted Cobalt-Catalyzed Alkene Hydrodimerization

The direct hydrodimerization of acrylates and acrylonitrile offers a general streamlined access to industrially important intermediates to nylon 6,6. However, a practical catalytic method for this process has thus far underdeveloped owing to the challenges in regioselectivity and environmental compatibility of applied reagents. Here, we report a cobalt-catalyzed tail-to-tail hydrodimerization of activated alkenes driven by a visible-light photoredox catalysis at ambient temperature, which is applicable to both adipates and adiponitrile synthesis from potentially renewable feedstocks. This protocol utilizes half equivalent of hantzsch ester as a recyclable two-electron and two-proton donor with the assistance of catalytic amount of base as a proton shuttle, and has been shown to be highly regioselective and efficient for hydrodimerizing various activated alkenes to 1,4-difunctionalized butane derivatives.