Karhunen–Loeve representations of turbulent channel flows using the method of snapshots

For three‐dimensional flows with one inhomogeneous spatial coordinate and two periodic directions, the Karhunen–Loeve procedure is typically formulated as a spatial eigenvalue problem. This is normally referred to as the direct method (DM). Here we derive an equivalent formulation in which the eigenvalue problem is formulated in the temporal coordinate. It is shown that this so‐called method of snapshots (MOS) has some numerical advantages when compared to the DM. In particular, the MOS can be formulated purely as a matrix composed of scalars, thus avoiding the need to construct a matrix of matrices as in the DM. In addition, the MOS avoids the need for so‐called weight functions, which emerge in the DM as a result of the non‐uniform grid typically employed in the inhomogeneous direction. The avoidance of such weight functions, which may exhibit singular behaviour, guarantees satisfaction of the boundary conditions. The MOS is applied to data sets recently obtained from the direct simulation of turbulence in a channel in which viscoelasticity is imparted to the fluid using a Giesekus model. The analysis reveals a steep drop in the dimensionality of the turbulence as viscoelasticity is increased. This is consistent with the results that have been obtained with other viscoelastic models, thus revealing an essential generic feature of polymer‐induced drag reduced turbulent flows. Published in 2006 by John Wiley & Sons, Ltd.     

镍-酸性铬兰K络合物吸附波

用微分脉冲溶出伏安法研究了镍(11)与酸性铬兰K(ACBK)所生成的络合物在悬汞电极上的电化学特性及电化学反应机理，发现电极反应为镍与酸性铬兰K所生成的络合物吸附在电极表面后发生的不可逆还原。在HCl-硼砂介质中(pH8．67)，络合物在-316mV处有一吸附还原峰，其峰电流与镍浓度在0．001～0．010μ/mL范围内呈现良好的线性关系，其最低检出浓度为0．0005μg／mL。     

Oxidation and Reduction Processes During NO x Removal with Corona-Induced Nonthermal Plasma

In this paper, the NO-to-NO ₂ conversion in various gaseous mixtures is experimentally investigated. Streamer coronas are produced with a dc-superimposed high-frequency ac power supply (10–60 kHz). According to NO _x removal experiments in N ₂ +NO _x and N ₂ +O ₂ +NO _x gaseous mixtures, it is supposed that the reverse reaction NO ₂ +ONO+O ₂ may not only limit NO ₂ production in N ₂ +NO _x mixtures, but also increase the energy cost for NO removal. Oxygen could significantly suppress reduction reactions and enhance oxidation processes. The reduction reactions, such as N+NON ₂ +O, induce negligible NO removal provided the O ₂ concentration is larger than 3.6%. With adding H ₂ O into the reactor, the produced NO ₂ per unit removed NO can be significantly reduced due to NO ₂ oxidation. NH ₃ injection could also significantly decrease the produced NO ₂ via NH and NH ₂ - related reduction reactions. Almost 100% of NO ₂ can be removed in gaseous mixtures of N ₂ +O ₂ +H ₂ O+NO ₂ with negligible NO production.     

The influence of the mercury and thallium atoms in organomercury and organothallium nitroxyl radicals on their reactivity

An increase is found in the reactivity of organomercury and organothallium nitroxyl mono- and biradicals of the imidazoline type in comparison with the analogous compounds without organometallic fragments. This is explained by the formation of coordination bonds NHg, NTl, and NOHg.Translated fromIzvestiya Akademii Nauk, Seriya Khimicheskaya, No. 1, pp. 224–226, January, 1993.     

Minimum energy configurations on a toric lattice as a quadratic assignment problem

We consider three known bounds for the quadratic assignment problem (QAP): an eigenvalue, a convex quadratic programming (CQP), and a semidefinite programming (SDP) bound. Since the last two bounds were not compared directly before, we prove that the SDP bound is stronger than the CQP bound. We then apply these to improve known bounds on a discrete energy minimization problem, reformulated as a QAP, which aims to minimize the potential energy between repulsive particles on a toric grid. Thus we are able to prove optimality for several configurations of particles and grid sizes, complementing earlier results by Bouman et al. (2013). The semidefinite programs in question are too large to solve without pre-processing, and we use a symmetry reduction method by Permenter and Parrilo (2020) to make computation of the SDP bounds possible.     

Synthesis of new functional derivatives of pyrazolidine from 1-acetyl-3-methyl-5-nitromethyl-2-phenylpyrazolidine

3-Nitromethylpyrazolidine reacts with derivatives of unsaturated acids and reducing agents with the formation of polyfunctional compounds of the pyrazolidine nucleus. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 9, pp. 1365–1369, September, 2006.     

Notiz zur Darstellung von 4-Hydroxy-6-methyl-5,6-dihydro-2H-pyran-2-on

Meldrum's acid (2) is acylated by diketen affording the acylMeldrum's acid3. In aqueous bicarbonate its 3-oxogroup is selectively reduced by sodium tetrahydroborate giving the alcohol4, which readily undergoes cyclization in refluxing dioxane leading to the title pyrone7. Under identical conditions3 produces the pyrone6 with the pyrone carboxylic acid5 as intermediate.

     

Direct Electrochemistry of Multi‐Copper Oxidases at Carbon Nanotubes Noncovalently Functionalized with Cellulose Derivatives

This study describes the direct electron transfer of multi‐copper oxidases, i.e., laccase (from Trametes versicolor) and bilirubin oxidase (BOD, from Myrothecium verrucaria) at multiwalled carbon nanotubes (MWNTs) noncovalently functionalized with biopolymers of cellulose derivatives, i.e., hydroxyethyl cellulose (HEC), methyl cellulose (MC), and carboxymethyl cellulose (CMC). The functionalization of the MWNTs with the cellulose derivatives is found to substantially solubilize the MWNTs into aqueous media and to avoid their aggregation on electrode surface. Under anaerobic conditions, the redox properties of laccase and BOD are difficult to be defined with cyclic voltammetry at either laccase/MWNT‐modified or BOD/MWNT‐modified electrodes. The direct electron transfer properties of laccase and BOD are thus studied in terms of the bioelectrocatalytic activities of the laccase/MWNT‐modified and BOD/MWNT‐modified electrodes toward the reduction of oxygen and found to be facilitated at the functionalized MWNTs. The possible application of the laccase‐catalyzed O₂ reduction at the laccase/MWNT‐modified electrode is illustrated by constructing a CNT‐based ascorbate/O₂ biofuel cell with the MWNT‐modified electrode as the anode for the oxidation of ascorbate biofuel.     

Effect of conformational control of chiral oxazaborolidine by π-π stacking interaction of a pentafluorophenyl group toward asymmetric borane reduction

A pentafluorophenyl group can act as a stereo-controlling group in oxazaborolidine-catalyzed asymmetric borane reduction through intramolecular π-π stacking interaction with a phenyl group. The intramolecular π-π interaction in oxazaborolidine bearing pentafluorophenyl group is confirmed by calculations and ¹H NMR study. The interaction affects the enantioselectivity of the asymmetric reduction of acetophenone while the extent is small.     

The Mitsunobu Reaction: Origin,Mechanism, Improvements,and Applications

The Mitsunobu reaction is a widely used and versatile method for the dehydrative oxidation–reduction condensation of an acid/pronucleophile usually with a primary or secondary alcohol that requires the combination of a reducing phosphine reagent together with an oxidizing azo reagent. The utility of this reaction stems from the fact that it is generally highly stereoselective and occurs with inversion of the stereochemical configuration of the alcohol starting material. Furthermore, as carboxylic acids, phenols, imides, sulfonamides, and other compounds can be used as the acid/pronucleophile, this reaction is useful for the preparation of a wide variety of functional groups. This Focus Review of the Mitsunobu reaction summarizes its origins, the current understanding of its mechanism, and recent improvements and applications.