A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

Adaptive finite-time prescribed performance control for stochastic nonlinear systems with unknown virtual control coefficients

Nonlinear Dynamics - This paper is devoted to the adaptive finite-time prescribed performance control (FTPPC) for stochastic nonlinear systems with unknown virtual control coefficients (UVCCs),...     

Quantum dots modified with the Al(III)-pefloxacin complex as a novel bioprobe for the sensitive turn-on and dual-fluorescence detection of dsDNA

Microchimica Acta - We describe a novel fluorescent bioprobe for the sensitive and selective detection of double-stranded DNA (dsDNA). It consists of quantum dots (Q-dots) whose fluorescence is...     

Polarization in D-shaped fiber modulated by magneto-optical dichroism of magnetic fluid

The polarization of a D-shaped fiber is modulated after immersing it in magnetic fluid(MF)and applying a magnetic field.Theoretical analysis predicts that magneto-optical dichroism of MF plays a key role in light polarization modulation.During light polarization modulation,the evanescent wave polarized parallel to the magnetic field has greater loss than its orthogonal component.Light polarization of a D-shaped fiber with a wide polished surface can be modulated easily.High concentration MF and a large magnetic field all have great ability to modulate light polarization.     

Copper-Catalyzed ortho-Functionalization of Quinoline N-Oxides with Vinyl Arenes

An efficient copper-catalyzed regioselective C−H alkenylation and borylative alkylation of quinoline N-oxides with vinyl arenes in the presence of pinacol diborane has been developed. The reaction proceeds through the borylcupration of the vinyl arenes followed by nucleophilic attack of the resulting alkyl copper species to the quinoline N-oxides. Benzoquinone and KO^tBu were identified as the necessary additives at the second step of the reaction that are crucial for the success of the reaction. A wide range of C2-functionalizaed quinolines were obtained with good functional group tolerance, which may find utilities in pharmaceuticals and synthetic chemistry.     

Polyhydrido Copper Nanoclusters with a Hollow Icosahedral Core: [Cu30H18{E2P(OR)2}12] (E=S or Se; R=nPr,iPr or iBu)

Although atomically precise polyhydrido copper nanoclusters are of prime interest for a variety of applications, they have so far remained scarce. Herein, this work describes the synthesis of a dithiophosphate-protected copper(I) hydride-rich nanocluster (NC), [Cu₃₀H₁₈{S₂P(OnPr)₂}₁₂] ( 1_H ), fully characterized by various spectroscopic methods and single-crystal X-ray diffraction. The X-ray structure of 1_H reveals an unprecedented central Cu₁₂ hollow icosahedron. Six faces of this icosahedron are capped by Cu₃ triangles, the whole Cu₃₀ core being wrapped by twelve dithiophosphate ligands and the whole cluster has ideal S₆ symmetry. The locations of the 18 hydrides in 1_H were ascertained by a single-crystal neutron diffraction study. They are composed of three types: capping μ₃-H, interstitial μ₄-H (seesaw) and μ₅-H ligands (square pyramidal), in good agreement with the DFT simulations. The numbers of hydrides and ligand resonances in the ¹H NMR spectrum of 1_H are in line with their coordination environment in the solid state, retaining the S₆ symmetry in solution. Furthermore, two new Se-protected polyhydrido copper nanoclusters, [Cu₃₀H₁₈{Se₂P(OR)₂}₁₂] ( 2_H : R=iPr 3_H : R=iBu) were synthesized from their sulfur relative 1_H via ligand displacement reaction and their X-ray structures feature the exceptional case where both the NC shape and size are fully conserved during the course of ligand exchange. DFT and TD-DFT calculations allow understanding the bonding and optical properties of clusters 1_H – 3_H . In addition, the reaction of 1_H with [Pd(PPh₃)₂Cl₂] in the presence of terminal alkynes led to the formation of new bimetallic Cu−Pd alloy clusters [PdCu₁₄H₂{S₂P(OnPr)₂}₆(C≡CR)₆] ( 4 : R=Ph; 5 : R = C₆H₄F).     

[Cu32(H)20{S2P(OiPr)2}12]: The Largest Number of Hydrides Recorded in a Molecular Nanocluster by Neutron Diffraction

An air‐ and moisture‐stable nanoscale polyhydrido copper cluster [Cu₃₂(H)₂₀{S₂P(OiPr)₂}₁₂] ( 1_H ) was synthesized and structurally characterized. The molecular structure of 1_H exhibits a hexacapped pseudo‐rhombohedral core of 14 Cu atoms sandwiched between two nestlike triangular cupola fragments of (2×9) Cu atoms in an elongated triangular gyrobicupola polyhedron. The discrete Cu₃₂ cluster is stabilized by 12 dithiophosphate ligands and a record number of 20 hydride ligands, which were found by high‐resolution neutron diffraction to exhibit tri‐, tetra‐, and pentacoordinated hydrides in capping and interstitial modes. This result was further supported by a density functional theory investigation on the simplified model [Cu₃₂(H)₂₀(S₂PH₂)₁₂].