New higher-order compact finite difference schemes for 1D heat conduction equations

In this paper, we present two higher-order compact finite difference schemes for solving one-dimensional (1D) heat conduction equations with Dirichlet and Neumann boundary conditions, respectively. In particular, we delicately adjust the location of the interior grid point that is next to the boundary so that the Dirichlet or Neumann boundary condition can be applied directly without discretization, and at the same time, the fifth or sixth-order compact finite difference approximations at the grid point can be obtained. On the other hand, an eighth-order compact finite difference approximation is employed for the spatial derivative at other interior grid points. Combined with the Crank–Nicholson finite difference method and Richardson extrapolation, the overall scheme can be unconditionally stable and provides much more accurate numerical solutions. Numerical errors and convergence rates of these two schemes are tested by two examples.     

Hölder continuity of the solutions for a class of nonlinear SPDE’s arising from one dimensional superprocesses

The Hölder continuity of the solution X _t (x) to a nonlinear stochastic partial differential equation (see (1.2) below) arising from one dimensional superprocesses is obtained. It is proved that the Hölder exponent in time variable is arbitrarily close to 1/4, improving the result of 1/10 in Li et al. (to appear on Probab. Theory Relat. Fields.). The method is to use the Malliavin calculus. The Hölder continuity in spatial variable x of exponent 1/2 is also obtained by using this new approach. This Hölder continuity result is sharp since the corresponding linear heat equation has the same Hölder continuity.     

An Infeasible Mizuno–Todd–Ye Type Algorithm for Convex Quadratic Programming with Polynomial Complexity

Infeasible interior point methods have been very popular and effective. In this paper, we propose a predictor–corrector infeasible interior point algorithm for convex quadratic programming, and we prove its convergence and analyze its complexity. The algorithm has the polynomial numerical complexity with O(nL)-iteration.     

Effect of surface tension‐driven flow on BaB2O4 crystal growth from high temperature melt‐solution

The surface tension driven‐flow in BaB₂O₄ (BBO) melt‐solution is visualized by differential interference microscope coupled with Schlieren technique, and the streamline of the steady thermocapillary convection is found to be in form of an axially symmetric pattern. Based on the observation of BBO crystal rotation caused by the convective vortex, the widths of interfacial concentration, heat and momentum boundary layer are calculated. The effect of thermocapillary convection on boundary layer thickness is also investigated. Results show that the width of boundary layer decreases linearly with the increasing of dimensionless Marangoni number. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Development of [3]ferrocenophane-derived N/B frustrated Lewis pairs for the metal-free catalytic hydrogenation of imines

A series of novel [3]ferrocenophane-derived N/B frustrated Lewis pairs (FLPs) were synthesized and successfully applied to the catalytic hydrogenation of imines in 71–93% yields. This approach could be easily conducted on gram scale and provided versatile synthetic route for the key intermediate of sertraline hydrochloride without heavy metal residues.     

Facile synthesis of 1-(arylimino)naphthalen-2(1H)-ones from anilines and 2-naphthols promoted by NaBr/K2S2O8/CAN

An efficient method has been developed for the synthesis of 1-(arylimino)naphthalen-2(1H)-ones through the cascade reaction of anilines and 2-naphthols promoted by NaBr/K₂S₂O₈/Ce(NH₄)₂(NO₃)₆. Using this protocol, a series of 1-(arylimino)naphthalen-2(1H)-ones was obtained in good to excellent yields (17 examples, 70–92% yields). The reactions may proceed through the following steps: bromination of 2-naphthols by in-situ-generated bromine from NaBr and K₂S₂O₈ to afford 1-bromonaphthalen-2-ols, coupling of 1-bromonaphthalen-2-ols with anilines to afford the corresponding amines, and subsequent oxidation of the amines into the products by Ce(NH₄)₂(NO₃)_6. These newly obtained α-imine ketones have great potentials for synthesis of special optical materials bearing naphthalene moiety.     

A series of fluorenone-carbazole based regioisomers as bipolar host materials for efficient organic light emitting diodes

A series of fluorenone-carbazole based regioisomers (1–4) have been synthesized and applied as host materials for red OLEDs to investigate the effect of different connection configuration on the optoelectronic properties, charge transport capability and device performance. The optoelectronic properties, thermal stability, redox behaviors and charge transport characteristics of these four compounds were fully characterized. These four hosts demonstrated high thermal stability, bipolar charge transport properties and good EL performance. Although these four compounds demonstrated similar HOMO and LUMO energy levels, the twisted structure of 1 led to the smallest singlet-triplet energy gap, which could account in part for the observation of its better EL performance.     

Organic base-promoted efficient dehydrogenative/decarboxylative aromatization of tetrahydro-β-carbolines into β-carbolines under air

Organic base DBN has been identified as an efficient reagent for promoting the dehydrogenative/decarboxylative aromatization of tetrahydro-β-carbolines under air atmosphere, to access the corresponding β-carbolines in moderate to good yields. The utility of this protocol for the gram-scale synthesis of β-carboline alkaloids eudistomin U (7) and harmane (10) has also been demonstrated.     

Synthesis,Crystal Structures,and Anti‐cervical Cancer Activity Evaluation of Three Trinuclear Transition Metal(II) Complexes with N,O‐Donor Schiff Base Ligand

A new bi‐nucleating Schiff base ligand, 2‐(((3‐(dimethylamino)propyl)imino)methyl)‐6‐methoxyphenol (HL₁) was prepared by a one‐pot condensation reaction, which was further used in the construction of three trinuclear Schiff base transition metal(II) complexes [Cu₃(L1)₂(OH)₂(H₂O)₂](NO₃)₂ ( 1 ), [Co₃(L1)₂(OH)₂(H₂O)₂](NO₃)₂ ( 2 ), and [Cu₃(L1)₂(N₃)₄] ( 3 ). Furthermore, a green hand grinding technique was implemented to reduce the particle size of the coordination complexes to generate the nanoscale compounds. The SEM studies reveal the formation of square and spherical particles for nano 1 and 2 , and nanorod for nano 3 . In addition, the anti‐proliferation activity of nano 1 – 3 was detected on the human cervical cancer Hela cells with CCK‐8 assay. The cell viability curves and IC₅₀ values indicated that only nano 1 has anti‐proliferation activity on Hela cells. To further investigate the mechanism of nano 1 induced Hela cell death, the Annexin V‐FITC/PI double staining assay, western blot assay, and ROS level detection was conducted.     

Syntheses,Structures, and Magnetic Properties of Two DMTCNQ and DETCNQ Gadolinium Complexes

Two DMTCNQ (DMTCNQ = 2,5‐dimethyl‐7,7,8,8‐tetracyano‐p‐quinodimethane) and DETCNQ (DETCNQ = 2,5‐diethyl‐7,7,8,8‐tetracyano‐p‐quinodimethane) gadolinium complexes [Gd(DMTCNQ)₂(CH₃OH)(H₂O)₆][DMTCNQ] · 4H₂O ( 1 ) and [Gd(DETCNQ)(H₂O)₇][2DETCNQ] ( 2 ) were synthesized by reactions of GdCl₃ · 6H₂O with Li(DMTCNQ) or Li(DETCNQ). X‐ray diffraction analysis reveals that complexes 1 and 2 are discrete complexes. The central metal atom in 1 is coordinated by two DMTCNQ ligand radicals whereas that in 2 is coordinated by just one DETCNQ ligand radical. The adjacent molecules are connected by the intermolecular hydrogen bonds to form the two‐dimensional (2D) supramolecular layer structures, which are further packed into a three‐dimensional (3D) supramolecular architecture through the π–π interactions between ligand radicals in 1 and 2 . Magnetic investigation indicates that the antiferromagnetic interactions between spin carriers exists in 1 and 2 .