Optimality of Balanced Proper Orthogonal Decomposition for Data Reconstruction

Proper orthogonal decomposition (POD) finds an orthonormal basis yielding an optimal reconstruction of a given dataset. We consider an optimal data reconstruction problem for two general datasets related to balanced POD, which is an algorithm for balanced truncation model reduction for linear systems. We consider balanced POD outside of the linear systems framework, and prove that it solves the optimal data reconstruction problem. The theoretical result is illustrated with an example.     

Normal Feedback Stabilization of Periodic Flows in a Three-Dimensional Channel

We present an extension from two dimensions to three dimensions of a boundary control law, which stabilizes the parabolic profile of an infinite channel flow. The controller acts on the normal component of the velocity only. The stability is achieved without any a priori condition on the viscosity coefficient, that is on Reynolds number.     

Train Algèbres Alternatives: Relation Entre Nilindice et Degré

We determine train polynomials for power associative algebras and for alternative train algebras. We show bonds between polynomials and nilindices of some factors of the Peirce decomposition.     

Complex-valued preplaces and the nonring cmc subsets of a ring

We show that the torsion free Krull-Schmidt-Azumaya Theorem holds for the integral group ring Z D ₈ Were D ₈ is the group of order 8, but torsion free cancellation (and hence also the torsion free Krull-Schmidt-Azumaya theorem) fails for the integral group ring Z D ₃₂ We summarize the cases for which the integral group ring Z G is known to satisfy the torsion free Krull-Schmidt-Azumaya Theorem, Z D ₁₆ being the only open case.     

Localized orbitals for optimal decomposition of molecular properties

We present the procedure for transforming delocalized molecular orbitals into the localized property-optimized orbitals (LPOs) designed for building the most accurate, in the Frobenius norm sense, approximation to the first-order reduced density matrix in form of the sum of localized monoatomic and diatomic terms. In this way, a decomposition of molecular properties into contributions associated with individual atoms and the pairs of atoms is obtained with the a priori known upper bound for the decomposition accuracy. Additional algorithm is proposed for obtaining the set of “the Chemist's LPOs” (CLPOs) containing a single localized orbital, with nearly double occupancy, per a pair of electrons. CLPOs form an idealized Lewis structure optimized for the closest possible reproduction of one-electron properties derived from the original many-electron wavefunction. The computational algorithms for constructing LPOs and CLPOs from a general wavefunction are presented and their implementation within the open-source freeware program JANPA ( http://janpa.sourceforge.net /) is discussed. The performance of the proposed procedures is assessed using the test set of density matrices of 33 432 small molecules obtained at both Hartree-Fock and second-order Moller-Plesset theory levels and excellent agreement with the chemist's Lewis-structure picture is found.     

Rhodium catalyzed hydroformylation of olefins

DFT and CCSD(T) methods were used to examine 61 different rhodium catalysts for the hydroformylation of ethylene. The carbon monoxide (CO) stretching frequency was a key electronic parameter to understand the π-accepting nature of the ligand. Normally, π-accepting ligands lead to increased CO stretching frequencies and a reduction in CO dissociation energy. There was no relationship between CO dissociation energy and CO stretching frequency. However, a clear relationship exists between the ethylene insertion barrier (from the rhodium dicarbonyl hydride resting state) and the CO stretching frequency as stronger π-accepting ligands systematically led to a reduction in the barrier. Due to the multistep nature of the rate-limiting step, the overall barrier can be divided into the CO/ethylene equilibrium and an intrinsic ethylene insertion barrier and both are systematically reduced as the π-accepting nature of the ligand is increased. A comparison of the carbonylation transition state (TS) to the ethylene insertion TS allowed us to understand reversibility of olefin insertion. While the ethylene insertion TS systematically decreases with increasing CO stretching frequency, the carbonylation TS is relatively flat. The lines cross at 2156 cm⁻¹ implying a change in the rate-limiting step in this region given a standard set of process conditions. © 2018 Wiley Periodicals, Inc.     

Quantitative Analysis of Main Components of Natural Gas Based on Raman Spectroscopy

Natural gas is composed of methane, ethane, propane, carbon dioxide, nitrogen, hydrogen, carbon monoxide and unknown alkane components of C4 or more (denoted as C4⁺) after desulfurization and dehydration treatment. The concentrations of the first seven components account for more than 90% of natural gas. When analyzing the natural gas composition using Raman spectral analysis methods, a small amount of unknown alkane components C4⁺ will have a negative impact on the analytical precision. In this work, a novel method that consists of an automatic decomposition algorithm of Raman spectra and a model for quantitative analysis was developed for the analysis of components of natural gas. The Raman spectrum of a natural gas sample could be decomposed into the sum of the Raman spectra of pure constituents and several Lorentz peaks by a nonlinear least-square optimization algorithm based on a linear additivity of Raman spectra. The concentration of the unknown alkane component C4⁺ was determined according to the area of the C-H deformation vibration peak which was common for most alkane molecules. Some training samples were used to establish the model between Raman characteristic peak areas and corresponding concentrations for each component. Compared with the existing Raman analysis methods, the new method solved the problem of analyzing natural gas containing unknown alkane components with good stability and accuracy. The experiments showed that the maximum absolute errors of this algorithm for methane, ethane, propane, carbon dioxide, nitrogen, hydrogen, and carbon monoxide respectively reached 0.57%, 0.37%, 0.21%, 0.07%, 0.18%, 0.04%, 0.13%, and the correlation coefficient to gas chromatographic results also reached 0.997, 0.986, 0.991, 0.998, 0.993, 1.000, 0.995, 0.982, respectively.     

Analysis of the Dynamic Decomposition of Unsaturated Fatty Acids and Tocopherols in Commercial Oils During Deep Frying

The decomposition of unsaturated fatty acids and tocopherols in 10 commercial edible oils during deep frying was investigated. The dominant tocopherol in oils rich in polyunsaturated fatty acids (PUFAs) was γ-tocopherol, except for natural perilla oil (δ-tocopherol dominant), and the main tocopherol in oleic acid-rich oils was α-tocopherol. The PUFA-rich oils had higher tocopherol contents than the oleic acid-rich oils. Both the reduction rate of total unsaturated fatty acid (TUFA) and total tocopherol (TToc) were linear with frying time (t). The decomposition rate of TToc is faster than that of TUFA since the slope values obtained from fitting equations (Y?=?k t) k_TToc (1.520–14.483) were obviously larger than for k_TUFA (0.155–0.270). By establishing a dynamic decomposition index, unsaturated fatty acids and tocopherol in oils showed dynamic decomposition over multiple frying cycles. The obtained results showed that decomposition characteristics of oils are related to their fatty acid compositions.     

NPK 2.0: Introducing tensor decompositions to the kinetic analysis of gas–solid reactions

A method for deriving kinetic models of gas–solid reactions for reactor and process design is presented. It is based on the nonparametric kinetics (NPK) method and resolves many of its shortcomings by applying tensor rank-1 approximation methods. With this method, it is possible to derive kinetic models based on the general kinetic equation from any combination of experiments without additional a priori assumptions. The most notable improvements over the original method are that it is computationally much simpler and that it is not limited to two variables. Two algorithms for computing the rank-1 approximation as well as a tailored initialization method are presented, and their performance is assessed. Formulae for the variance estimation of the solution values are derived to improve the accuracy of the model identification and to provide a tool for diagnosing the quality of the kinetic model. The methods effectiveness and performance are assessed by applying it to a simulated data set. A Matlab implementation is available as Supporting Information.     

对三氧化二铁催化性能的思考

用Fe2O3作催化剂分解过氧化氢制氧气的实验中发现其催化效果微弱,与文献比较严重不符。据此,阐述了Fe2O3在化工生产中的催化性能及其催化作用机理,指出不同晶型Fe2O3的催化剂性能差异较大,并分析了其催化过氧化氢分解时会产生不同效果的原因。研究发现,在实验室条件下,γ-Fe2O3晶型具有较强的催化活性,而长期保存的Fe2O3粉末经灼烧30 min后有助于提高其催化活性。