END样本最近邻密度估计的强相合速度

本文研究了扩展负相依(END)样本最近邻密度估计的强相合性问题.利用END序列的Bernstein型不等式和截尾的方法,获得了END样本最近邻密度估计的强相合速度,推广了NA样本和ND样本最近邻密度估计的相应结果.     

Extended X‐ray absorption fine structure and multiple‐scattering simulation of nickel dithiolene complexes Ni[S2C2(CF3)2]2n (n = −2, −1, 0) and an olefin adduct Ni[S2C2(CF3)2]2(1‐hexene)

A series of Ni dithiolene complexes Ni[S₂C₂(CF₃)]₂ⁿ (n = ?2, ?1, 0) ( 1 , 2 , 3 ) and a 1‐hexene adduct Ni[S₂C₂(CF₃)₂]₂(C₆H₁₂) ( 4 ) have been examined by Ni K‐edge X‐ray absorption near‐edge structure (XANES) and extended X‐ray absorption fine‐structure (EXAFS) spectroscopies. Ni XANES for 1 – 3 reveals clear pre‐edge features and approximately +0.7 eV shift in the Ni K‐edge position for `one‐electron' oxidation. EXAFS simulation shows that the Ni—S bond distances for 1 , 2 and 3 (2.11–2.16 Å) are within the typical values for square planar complexes and decrease by ～0.022 Å for each `one‐electron' oxidation. The changes in Ni K‐edge energy positions and Ni—S distances are consistent with the `non‐innocent' character of the dithiolene ligand. The Ni—C interactions at ～3.0 Å are analyzed and the multiple‐scattering parameters are also determined, leading to a better simulation for the overall EXAFS spectra. The 1‐hexene adduct 4 presents no pre‐edge feature, and its Ni K‐edge position shifts by ?0.8 eV in comparison with its starting dithiolene complex 3 . Consistently, EXAFS also showed that the Ni—S distances in 4 elongate by ～0.046 Å in comparison with 3 . The evidence confirms that the neutral complex is `reduced' upon addition of olefin, presumably by olefin donating the π‐electron density to the LUMO of 3 as suggested by UV/visible spectroscopy in the literature.     

Selective etching of ZnTe in HF:H2O2:H2O solution: Interpretation of extended defect‐related etch figures

HF:H₂O₂:H₂O solution (40%wt.HF: 30wt.%H₂O₂: H₂O, 3:2:1 by volume) was used to reveal extended defects (line, face and volume defects) in bulk ZnTe crystals grown from Te solution. The etch patterns were analyzed based on their size, shape and distribution. The etch figures, both in the shape of pits and hillocks with high resolution, show forms controlled by the symmetries of the respective faces were produced. Two different sizes of pits were observed, the larger‐size pits correspond to dislocations penetrating the surface, however, the smaller‐size texture pits are produced on the defect‐free region, which serve as standard pits on respect faces. The face defects, such as grain boundaries, sub‐grain boundaries, dislocation walls, twins and stacking faults, can be all displayed clearly. Another essential feature of the etchant is that, it can effectively dissolve Te‐rich phase (Te inclusion/precipitates), which makes it promising to reveal the shape of this volume defect.     

A mathematical discussion of Pons Viver's implementation of Löwdin's spin projection operator

Recently, the molecular electronic structure theories for efficiently treating static (or strong) correlation in a black-box manner have attracted much attention. In these theories, a spin projection operator is used to recover the spin symmetry of a broken-symmetry Slater determinant. Very recently, Pons Viver proposed the practical and exact implementation of Löwdin's spin projection operator (Int. J. Quantum Chem. 2019, 119, e25770). In the present study, we attempt to supply mathematical proofs to Pons Viver's proposals and show a condition for establishing Pons Viver's implementation. Moreover, we explicitly derive the (spin projected) extended Hartree-Fock (EHF) equations on the basis of the model of common orbitals (ie, closed-shell orbitals used in the restricted open-shell Hartree-Fock (ROHF) method), which was combined by Pons Viver with the EHF method.     

Predicting the Standard Enthalpy (ΔHo f) and Entropy (So) of Alkanes by Artificial Neural Networks

Abstract

Artificial Neural Networks (ANNs) with Extended Delta-Bar-Delta (EDBD) back propagation learning algorithm have been developed to predict the standard enthalpy and entropy of 87 acyclic alkanes. Molecular weight, boiling point and density of the compounds were used as input parameters. The network's architecture and parameters were optimized to give maximum performances. The best network was a 3-6-2 ANN, and the optimum learning epoch was about 1320. The results show that the maximum relative errors of enthalpy and entropy are less than 3%. They reveal that the performances of ANNs for predicting the enthalpy and entropy of alkanes are satisfying.     

Anion-controlled geometrically different Cu(II) ion-based coordination polymers and green synthetic route for copper nanoparticles: a combined experimental and computational insight

Abstract

The Cu(II) ion-based polymeric complexes [Cu(2,2′-bpy).(N₃)₂]_n (I), [Cu₂(2,2′-bpy)₂.(N₃)₄]_n (II), and monomeric complex [Cu(2,2′-bpy).(NO₃)₂].5H₂O (III) have been synthesized with rigid (–N₃) and aromatic (2,2′-bpy = 2,2′-bipyridyl) ligand. The rigid azide group is responsible for the formation of 1-D extended structures in complexes I and II where as in the case of complex III, a monomeric complex is formed due to lack of a bridging group like –N₃, resulting in limitation in dimensionality. The thermal stability of the 1-D complexes is comparatively higher than monomeric complex III. Hirshfeld surface analysis has also been applied to investigate other weak interactions and compared with the results from single-crystal X-ray data. Due to the presence of paramagnetic metal centers and long metal···metal distances in complexes I and II and presence of lattice water molecules in complex III, decrease in luminescence intensities have been observed. To attain further insights into the aforementioned interesting species, some chemical concepts such as highest occupied molecular orbital–lowest unoccupied molecular orbital gap, electronic chemical potential, chemical hardness, and electrophilicity index, identified as a derivative of electronic energy, have also been emphasized employing the quantum chemical calculations in the framework of the density functional theory method using the M06-2X/ 6-31G** level of study. Further, these complexes have been used to synthesize copper nanoparticles by applying a green synthetic route.     

Abundant Multisoliton Structure of (3+1)-Dimensional Breaking Soliton Equation

Using the extended homogeneous balance method, we obtained abundant exact solution structures of the (3 1 )-dimensional breaking soliton equation. By means of the leading order term analysis, the nonlinear transformations of the (3t1)-dimensional breaking soliton equation are given first, and then some special types of single solitary wave solutions and the multisoliton solutions are constructed.     

MSE's of prediction in growth curve model with covariance structures

We consider the growth curve model with covariance structures: positive-definite, uniform covariance structure and serial covariance structure. Two types of prediction problems are studied in this paper. One is called the conditional prediction problem and the other is called the extended prediction problem. For both types of prediction problems, the mean squared error for a serial covariance structure is obtained for the estimates based on the conditional expectation: the mean squared error for an unrestricted covariance structure is compared with the mean squared error for a uniform covariance structure or a serial covariance structure. These results are exemplified by two sets of real data.This research was supported in part by Grant-in-Aid for general Scientific Research, The Ministry of Education, Science and Culture under Contract Number 03640239.