Transformations and Tautomeric Equilibrium among Different Intermediates in Proline-Catalyzed Reactions of Aldehydes or Ketones

The enamines, iminium ions, and oxazolidinones are thought to be the key intermediates in the proline-catalyzed reactions of aldehydes or ketones, but there is an extensive contro-versy about their roles. Here, the corresponding transition states connecting any two of the three kinds of species are located at the ωB97XD/6-311++G** level of theory. The calcula-tions demonstrate that the oxazolidinones are the predominant species in both the gas phase and solvents; there exists tautomeric equilibrium among these species and the equilibriums are controlled by the employed solvents and temperature in the reaction. These results demonstrate that the concentration and role of the mentioned species are controlled by the employed solvent and temperature. A new reaction pathway is presented herein for the trans-formation between iminium ions and oxazolidinones through iminium ion-water complex and oxazolidinone-water complex. The calculations demonstrate that the rate-limiting step in proline-catalyzed Mannich reaction between acetaldehyde/keteones and N-Boc imines is the formation of the C-C bond rather than the intermediates tautomerization. These calcula-tions rationalize the available experimental observations and can be valuable in optimizing the experimental conditions of asymmetric organic-catalyzed reactions of aldehydes or ke-tones.     

A kind of noise-induced transition to noisy chaos in stochastically perturbed dynamical system

We investigate a kind of noise-induced transition to noisy chaos in dynamical systems. Due to similar phenomenological structures of stable hyperbolic attractors excited by various physical realizations from a given stationary random process, a specific Poincar map is established for stochastically perturbed quasi-Hamiltonian system. Based on this kind of map, various point sets in the Poincar's cross-section and dynamical transitions can be analyzed. Results from the customary Duffing oscillator show that, the point sets in the Poincar's global cross-section will be highly compressed in one direction, and extend slowly along the deterministic period-doubling bifurcation trail in another direction when the strength of the harmonic excitation is fixed while the strength of the stochastic excitation is slowly increased. This kind of transition is called the noise-induced point-overspreading route to noisy chaos.     

Optimal system,group invariant solutions and conservation laws of the CGKP equation

In this paper, the (2 + 1)-dimensional cubic generalized Kadomtsev–Petviashvili (CGKP) equation that is derived from the Maxwell–Bloch equations is investigated. By means of Lie symmetry analysis method, we obtain the Lie point symmetries for the equation and the optimal system of the symmetry algebra. Based on the optimal system, a lot of group invariant solutions are obtained. In addition, explicit conservation laws of the equation are studied.     

Crystal structures of four inclusion compounds of 2,2′-dithiosalicylic acid and tetraalkylammonium

Herein four inclusion compounds of 2,2′-dithiosalicylic acid and tetraalkylammonium, 2(CH₃)₄N⁺·C₁₄H₈O₄S₂^2?·H₂O (1), (C₂H₅)₄N⁺·C₁₄H₉O₄S₂^?·0.25H₂O(2), (n-C₃H₇)₄N⁺·C₁₄H₉O₄S₂^? (3) and (n-C₄H₉)₄N⁺·C₁₄H₉O₄S₂^?(4) are prepared and characterized by X-ray single crystal diffraction. As shown in the results, compounds 1 and 3 belong to orthorhombic crystal system with different space groups of P2₁2₁2₁ and Pca2₁, and 2 and 4 are monoclinic system with similar groups of P2₁/n and P2₁/c. The crystallography data are displayed below: 1: a = 10.5903(7) Å, b = 10.6651(7) Å, c = 21.9476(13) Å, V = 2478.9(3) ų, Z = 4, R₁ = 0.0359; 2: a = 8.13340(1) Å, b = 22.0741(3)Å, c = 13.2143(2)Å, β = 101.6360(1) °, V = 2323.70(6) ų, Z = 1, R₁ = 0.0385; 3: a = 15.7857(2) Å, b = 8.24830(1) Å, c = 20.2599(2) Å, V = 2637.94(5) ų, Z = 4, R₁ = 0.0308_degree4: a = 11.7476(2) Å, b = 17.1346(1) Å, c = 16.3583(3)Å, β = 109.4560(1) °, V = 3104.74(9)ų, Z = 4, R₁ = 0.0562. Interestingly, although the carbon chains of the guest templates vary from methyl group to butyl group, the host molecules of 2,2′-dithiosalicylic acid all construct the similar 2D hydrogen-bonded host layers with or without the existence of water molecules to contain the guest templates to yield analogous sandwich-like inclusion compounds. Obviously, although the guest templates will have certain effects on the ultimate formation of these crystal structures, the host molecule of 2,2′-dithiosalicylic acid is a controlling factor to form these four inclusion compounds.     

Combine Harvester Bearing Fault-Diagnosis Method Based on SDAE-RCmvMSE

In the fault monitoring of rolling bearings, there is always loud noise, leading to poor signal stationariness. How to accurately and efficiently identify the fault type of rolling bearings is a challenge. Based on multivariate multiscale sample entropy (mvMSE), this paper introduces the refined composite mvMSE (RCmvMSE) into the fault extraction of the rolling bearing. A rolling bearing fault-diagnosis method based on stacked auto encoder and RCmvMSE (SDAE-RCmvMSE) is proposed. In the actual environment, the fault-diagnosis method use the multichannel vibration signals of the bearing as the input of stacked denoising autoencoders (SDAEs) to filter the noise of the vibration signals. The features of denoise signals are extracted by RCmvMSE and the rolling bearing operation-state diagnosis is completed with a support-vector machine (SVM) model. The results show that in the original test data, the accuracy rates of SDAE-RCmvMSE, RCmvMSE, and commonplace features of vibration signals combined with SVM (CFVS-SVM) methods are 99.5%, 100%, and 96% respectively. In the data with noise, the accuracy rates of RCmvMSE and CFVS-SVM are 97.75% and 93.08%, respectively, but the accuracy of SDAE-RCmvMSE is still 100%.     

On-column liquid–liquid–liquid microextraction coupled with base stacking as a dual preconcentration method for capillary zone electrophoresis

A simple and efficient dual preconcentration method of on-column liquid–liquid–liquid microextraction (LLLME) coupled with base stacking was developed for capillary zone electrophoresis (CZE) in this paper. Four N-methyl carbamates were used as target compounds to evaluate the enrichment means. The carbamates in sample solutions (donor phase) were extracted into a dodecanol phase immobilized on a porous hollow fiber, hydrolyzed and back extracted into 0.20 μL running buffer (acceptor phase) of 30 mmol/L methylamine hydrochloride (pH 11.6) containing 0.5 mmol/L tetradecyltrimethylammonium bromide inside the hollow fiber, stacked further with 0.5 mol/L NaOH injected at −10 kV for 60 s, and separated by CZE. Analytical parameters affecting the LLLME, base stacking and CZE were investigated, including sample solution volume, pH and temperature, extraction time, stirring rate, buffer component, buffer pH, NaOH concentration, stacking time, etc. The enrichment factors of the carbamates were higher than 1100. The relative standard deviation (RSD) of peak height and limits of detection (LODs) were 4.5–5.5% (n = 6) and 2–4 ng/mL (S/N = 3) for standard solutions, respectively. The proposed method was applied to the analysis of vegetable and fruit samples with the RSD less than 6.0% (n = 3) and LODs of 6–10 ng/g (S/N = 3). The calibration solutions were prepared by diluting the stock solutions with blank sample solutions, and the calibration concentrations ranged from 0.012 to 1.0 μg/mL (r > 0.9951). The analytical results demonstrated that the LLLME coupled with base stacking was a simple, convenient and reliable on-column sample pretreatment method for the analysis of anionic analytes in CZE.     

Synthesis and Structural Characterization of two Novel Copper(I) Complexes with Oxygen Donor

Two novel copper(I) complexes with Cu‐O bonds, [Cu₂L₂(PPh₃)₂](BF₄)₂ ( 1 ) and [Cu(L)(dppeo)](BF₄) ( 2 ) ( L = 6‐(4‐diethylmethylphosphonatephenyl)‐2,2′‐bipyridine, dppeo = bis(diphenylphosphino)ethane monoxide), have been prepared and their structures characterized. In the binuclear complex 1 , the ligand L serves as tridentate donor with the N, N′ and O as coordination atoms, and the two Cu^I atoms are bridged through both P = O donor atoms in different ligand L with a triphenylphosphine molecule as auxiliary ligand. While in mononuclear complex 2 , both ligands L and dppeo behave as bidentate with N^∧N from L and P^∧O from dppeo chelating to Cu^I atom.     

Limit-periodic Schrödinger operators with uniformly localized eigenfunctions

We exhibit limit-periodic Schrödinger operators that are uniformly localized in the strongest sense possible. That is, for these operators there are uniform exponential decay rates such that every element of the hull has a complete set of eigenvectors that decay exponentially off their centers of localization at least as fast as prescribed by the uniform decay rate. Consequently, these operators exhibit uniform dynamical localization.