Composite generalized Laguerre spectral method for nonlinear Fokker–Planck equations on the whole line

In this paper, we propose a composite Laguerre spectral method for the nonlinear Fokker–Planck equations modelling the relaxation of fermion and boson gases. A composite Laguerre spectral scheme is constructed. Its convergence is proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. Some results on the Laguerre approximation and techniques used in this paper are also applicable to other nonlinear problems on the whole line. Copyright © 2016 John Wiley & Sons, Ltd.     

Non‐Doped Sky‐Blue OLEDs Based on Simple Structured AIE Emitters with High Efficiencies at Low Driven Voltages

Blue organic light‐emitting diodes (OLEDs) are necessary for flat‐panel display technologies and lighting applications. To make more energy‐saving, low‐cost and long‐lasting OLEDs, efficient materials as well as simple structured devices are in high demand. However, a very limited number of blue OLEDs achieving high stability and color purity have been reported. Herein, three new sky‐blue emitters, 1,4,5‐triphenyl‐2‐(4‐(1,2,2‐triphenylvinyl)phenyl)‐1H‐imidazole (TPEI), 1‐(4‐methoxyphenyl)‐4,5‐diphenyl‐2‐(4‐(1,2,2‐triphenylvinyl)phenyl)‐1H‐imidazole (TPEMeOPhI) and 1‐phenyl‐2,4,5‐tris(4‐(1,2,2‐triphenylvinyl)phenyl)‐1H‐imidazole (3TPEI), with a combination of imidazole and tetraphenylethene groups, have been developed. High photoluminescence quantum yields are obtained for these materials. All derivatives have demonstrated aggregation‐induced emission (AIE) behavior, excellent thermal stability with high decomposition and glass transition temperatures. Non‐doped sky‐blue OLEDs with simple structure have been fabricated employing these materials as emitters and realized high efficiencies of 2.41 % (4.92 cd A⁻¹, 2.70 lm W⁻¹), 2.16 (4.33 cd A⁻¹, 2.59 lm W⁻¹) and 3.13 % (6.97 cd A⁻¹, 4.74 lm W⁻¹) for TPEI, TPEMeOPhI and 3TPEI, with small efficiency roll‐off. These are among excellent results for molecules constructed from the combination of imidazole and TPE reported so far. The high performance of a 3TPEI‐based device shows the promising potential of the combination of imidazole and AIEgen for synthesizing efficient electroluminescent materials for OLED devices.     

Trichalcogenasumanene ortho‐Quinones: Synthesis,Properties, and Transformation into Various Heteropolycycles

The regioselective transformation of heterobuckybowl trichalcogenasumanenes 1 a , b at peripheral butoxy groups afforded trichalcogenasumanene ortho ‐quinones 2 a , b . Compounds 2 a , b are distinct from 1 a , b in terms of their molecular geometry and electronic state; that is, they have a shallower bowl depth and show absorbance in the NIR region. The reaction of 2 a , b with diamines resulted in a variety of heteropolycycles, including molecular spoon 3 a – 6 a , planar π‐systems 3 b – 6 b , and highly twisted [7‐6‐6]‐fused systems 7 a , b . These new heteropolycycles had different optical/electrical properties: 4 a,b showed hole mobility of approximately 0.002 cm² V⁻¹ s⁻¹, 6 a displayed red emission in both solution and the solid state, and 7 a , b formed tight stacks of the curved π‐surface.     

Combining Charge‐Transfer Pathways to Achieve Unique Thermally Activated Delayed Fluorescence Emitters for High‐Performance Solution‐Processed,Non‐doped Blue OLEDs

Two efficient blue thermally activated delayed fluorescence compounds, B‐oCz and B‐oTC , composed of ortho‐donor (D)–acceptor (A) arrangement were designed and synthesized. The significant intramolecular D–A interactions induce a combined charge transfer pathway and thus achieve small ΔE _ST and high efficiencies. The concentration quenching can be effectively inhibited in films of these compounds. The blue non‐doped organic light emitting diodes (OLEDs) based on B‐oTC prepared from solution processes shows record‐high external quantum efficiency (EQE) of 19.1 %.     

A Unified Continuous Flow Assembly-Line Synthesis of Highly Substituted Pyrazoles and Pyrazolines

A rapid and modular continuous flow synthesis of highly functionalized fluorinated pyrazoles and pyrazolines has been developed. Flowing fluorinated amines through sequential reactor coils mediates diazoalkane formation and [3+2] cycloaddition to generate more than 30 azoles in a telescoped fashion. Pyrazole cores are then sequentially modified through additional reactor modules performing N-alkylation and arylation, deprotection, and amidation to install broad molecular diversity in short order. Continuous flow synthesis enables the safe handling of diazoalkanes at elevated temperatures, and the use of aryl alkyne dipolarphiles under catalyst-free conditions. This assembly-line synthesis provides a flexible approach for the synthesis of agrochemicals and pharmaceuticals, as demonstrated by a four-step, telescoped synthesis of measles therapeutic, AS-136A, in a total residence time of 31.7 min (1.76 g h⁻¹).     

3D Laser Micro‐ and Nanoprinting: Challenges for Chemistry

3D printing is a powerful emerging technology for the tailored fabrication of advanced functional materials. This Review summarizes the state‐of‐the art with regard to 3D laser micro‐ and nanoprinting and explores the chemical challenges limiting its full exploitation: from the development of advanced functional materials for applications in cell biology and electronics to the chemical barriers that need to be overcome to enable fast writing velocities with resolution below the diffraction limit. We further explore chemical means to enable direct laser writing of multiple materials in one resist by highly wavelength selective (λ‐orthogonal) photochemical processes. Finally, chemical processes to construct adaptive 3D written structures that are able to respond to external stimuli, such as light, heat, pH value, or specific molecules, are highlighted, and advanced concepts for degradable scaffolds are explored.     

Expression for the Number of Spanning Trees of Line Graphs of Arbitrary Connected Graphs

For any graph G, let be the number of spanning trees of G, be the line graph of G, and for any nonnegative integer r, be the graph obtained from G by replacing each edge e by a path of length connecting the two ends of e. In this article, we obtain an expression for in terms of spanning trees of G by a combinatorial approach. This result generalizes some known results on the relation between and and gives an explicit expression if G is of order and size in which s vertices are of degree 1 and the others are of degree k. Thus we prove a conjecture on for such a graph G.     

An adaptive nonmonotone global Barzilai–Borwein gradient method for unconstrained optimization

The Barzilai–Borwein (BB) gradient method has received many studies due to its simplicity and numerical efficiency. By incorporating a nonmonotone line search, Raydan (SIAM J Optim. 1997;7:26–33) has successfully extended the BB gradient method for solving general unconstrained optimization problems so that it is competitive with conjugate gradient methods. However, the numerical results reported by Raydan are poor for very ill-conditioned problems because the effect of the degree of nonmonotonicity may be noticeable. In this paper, we focus more on the nonmonotone line search technique used in the global Barzilai–Borwein (GBB) gradient method. We improve the performance of the GBB gradient method by proposing an adaptive nonmonotone line search based on the morphology of the objective function. We also prove the global convergence and the R-linear convergence rate of the proposed method under reasonable assumptions. Finally, we give some numerical experiments made on a set of unconstrained optimization test problems of the CUTEr collection. The results show the efficiency of the proposed method in the sense of the performance profile introduced (Math Program. 2002;91:201–213) by Dolan and Moré.     

SL(n+1,R)/S(GL(1,R)×GL(n,R))上线丛的一个超几何方程

本文研究了伪黎曼对称空间SL（n+1,R）/S（GL（1,R）×GL（n,R））线丛上的微分方程.利用李代数方法,即Casimir算子得到这个微分算子.这个微分算子是一个超几何方程,这个结论推广了文献[1,3,5]中的微分方程.     

Aggregation-induced Emission Materials for High-efficiency Perovskite Solar Cells

The perovskite solar cells (PSCs) with high efficiency and stability are in great demand for commercial applications. Although the remarkable photovoltaic feature of perovskite layer plays a great role in improving the PCE of PSCs, the inevitable defects and poor stability of perovskite, etc. are the bottleneck and restrict the commercialization of PSCs. Herein, a review provides a strategy of applying aggregation-induced emission (AIE) molecules, containing passivation functional groups and distinct AIE character, which serves as the alternative materials for fabricating high-efficiency and high-stability PSCs. The methods of introducing AIE molecules to PSCs are also summarized, including additive engineering, interfacial engineering, hole transport materials and so on. In addition, the functions of AIE molecule are discussed, such as defects passivation, morphology modulation, well-matched energy level, enhanced stability, hole transport ability, carrier recombination suppression. Finally, the detailed functions of AIE molecules are offered and further research trend for high performance PSCs based on AIE materials is proposed.