Construction of Spatiotemporal-Coupling Optimal Low-Dimensional Dynamical Systems for Compressible Navier-Stokes Equations; [可压缩 Navier-Stokes 方程的时空耦合优化低维动力系统建模方法]北大核心CSCD

For the low-dimensional dynamical system model to study dynamics properties of Navier-Stokes equations, it is very important that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. However, to date, there is no universal approach to ensure this purpose for general problems. Herein, it is found that any low-dimensional model based on spatial bases, such as proper orthogonal decomposition bases, optimal spatial bases, and other classical spatial bases, is not predictable, i.e., the error increases with the time evolution of the flow field. With the theoretical framework for building optimal dynamical systems and the new concept of spatiotemporal-coupling spectrum expansion, the low-dimensional model for compressible Navier-Stokes equations was constructed to approximate the numerical solution to large-eddy simulation equations, and the numerical results and novel time evolution of spatiotemporal-coupling bases were given. The entire field error is typically below 10−2%, and the average error at each grid point is below 10−8%. The spatiotemporal-coupling optimal low-dimensional dynamical systems can ensure that the attraction domain of the low-dimensional model is the same as that of Navier-Stokes equations. Therefore, characteristic dynamics properties of spatiotemporal-coupling optimal low-dimensional dynamical systems are the same as those of real flow. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Electric field effects on roto-vibrational transitions of13CD3OH1

We used a Stark-Optoacoustic cell and hybrid waveguide resonators to perform an Infrared and Far Infrared Stark Spectroscopy study on some transitions of¹³CD₃OH. Different behaviours of the transitions in the presence of a d.c. electric field were observed. The Stark splittings of six FIR laser lines ranging from 34 to 136 MHz/kVcm^–1 were determined. The analysis of the behaviour of the IR and FIR transitions in the presence of the external electric fields gives important and exclusive information on the levels involved in the transitions.Work Supported by FAPESP, CNPq, FAEP - Brazil, and CNR - Italy.     

The Boolean Prime Ideal Theorem Plus Countable Choice Do Not Imply Dependent Choice

Two Fraenkel-Mostowski models are constructed in which the Boolean Prime Ideal Theorem is true. In both models, AC for countable sets is true, but AC for sets of cardinality 2 and the 2m = m principle are both false. The Principle of Dependent Choices is true in the first model, but false in the second. Mathematics Subject Classification: 03E25, 03E35, 04A25.     

Solvent effects on 17O nuclear magnetic shielding: N-methylformamide in polar and apolar solutions

The solvent effect on ¹⁷O isotropic shielding was computed by different methods: the polarizable continuum model and a mixed approach, including a few real solvent molecules treated as the solute. The experimental data show that the behavior of protic and aprotic solvents is markedly different: we found that the continuum approach describes well the observed shielding at various dielectric constants for aprotic solvents, while the mixed procedure is needed when hydrogen bonds to the magnetic centre are present.Contribution to the Jacopo Tomasi Honorary Issue     

Quantitative weight of evidence method for combining predictions of quantitative structure-activity relationship models

ABSTRACT

A method for combining statistical-based QSAR predictions of two or more binary classification models is presented. It was assumed that all models were independent. This facilitated the combination of positive and negative predictions using a quantitative weight of evidence (qWoE) procedure based on Bayesian statistics and the additivity of the logarithms of the likelihood ratios. Previous studies combined more than one prediction but used arbitrary strengths for positive and negative predictions. In our approach, the combined models were validated by determining the sensitivity and specificity values, which are performance metrics that are a point of departure for obtaining values that measure the weight of evidence of positive and negative predictions. The developed method was experimentally applied in the prediction of Ames mutagenicity. The method achieved a similar accuracy to that of the experimental Ames test for this endpoint when the overall prediction was determined using a combination of the individual predictions of more than one model. Calculating the qWoE value would reduce the requirement for expert knowledge and decrease the subjectivity of the prediction. This method could be applied to other endpoints such as developmental toxicity and skin sensitisation with binary classification models.     

On hydrogen-bonded complexes: the case of (HF)2

The hydrogen fluoride dimer (HF)₂ is the most completely characterized hydrogen bonded species incorporating a donor molecule and an acceptor molecule. We provide a summary of experimental and theoretical information pertinent to the fundamental and harmonic vibrational frequencies, equilibrium geometry and dissociation energiesD _e andD ₀ as well as a brief critical discussion including some new results on the potential function and current best estimates of experimental quantities.     

Zur Chemie der Pyrrolpigmente, 56. Mitt.

From an investigation of the ICD of bilatrienes-abc and 2,3-dihydrobilatrienes-abc induced by mixtures of CCl₄ with (+)-cis-Pinane, (–)-lactic and (+)-tartaric acid esters it is concluded that specific interactions between chromophore and the chiral reagents afford a partial resolution of the labile racemate of helices. Attaching chiral residues covalently to the chromophore induces very low resolution of the same kind in case of apolar ligands like a cholesteryl-residue. However, with polar ligands as in the case ofBoc-lysyl derivatives enantiomeric excesses up to 90% are achieved depending on the solvent used.

Herrn Prof. Dr.Karl Schlögl zu seinem 60. Geburtstag gewidmet.     

Chemical species produced in the reaction between ethanedial (glyoxal) and 5-amino-1,10-phenanthroline and their iron(II) complexes: preparation and some spectrometric studies

Chemical species obtained by reaction of 5-amino-1, 10-phenanthroline with ethanedial (glyoxal) are reported with regard to their preparation, chemical composition and spectrometric characterization (UV-visible, infrared and liquid secondary ion mass spectrometry). Products of the reaction are postulated to be a mixture of species with molecular weights of 339, 371,480 and 524 u. Chemical reactions leading to these products and possible structural formulas for each of these species are presented. The iron complexes of these ligands, because of their extremely low solubility in most solvents, find application as redox mediators when incorporated in carbon paste electrodes, particularly for sensing in continuous-flow systems.     

Comparison of quantitative methods for analysis of polyphasic pharmaceuticals

Adequate very sensitive quantification methods are needed for the development and are also now required for the monitoring of undesirable solid form(s) as routine tests. The pre-requisite for quantitation are selectivity, sensitivity and most important the purity of standards and their proper storage, what is a challenge for metastable forms. Several analytical techniques are available such as X-ray diffraction, spectroscopy, thermal analysis and microcalorimetry. The different steps of the validation of the analytical methods and problems to be solved are discussed. Examples illustrate the different techniques and compare their possible advantages and limits. The relative standard deviation of measurements should allow for checking the homogenization procedure of mixtures for calibration. The validation should be carried out following ICH guidelines for validation of analytical methods. Comparison of different techniques in adequate concentration range add confidence in the analytical results.     

Comparison of micro- and mesoporous inorganic materials in the uptake and release of the drug model fluorescein and its analogues

The uptake of the three species of the drug model fluorescein (fluorescein sodium salt (FNa), fluorescein free acid (F), and fluorescein diacetate (FDA)) by zeolite NaX and the mesoporous zeotype MCM-41 was investigated as well as their release rates into solutions at pH 7 and pH 4.5. UV/Vis analysis was carried out at a wavelength of 490 nm. Uptakes of the sodium salt of 9 % for zeolite X and 14 % for MCM suggest little penetration of the pores. The use of ethanol as the loading solvent for F resulted in little uptake for both zeolitic materials due to the successful competition of the ethanol for binding sites. Use of acetone (weaker proton acceptor) as loading solvent significantly improved the uptake of F to 17 % and 12 % for zeolite X and MCM, respectively, whilst the uptake of FDA in acetone increased still further to 22 % and 17 % for zeolite X and MCM, respectively. Generally there was a large initial release of the fluorescein analogues from the surface of the zeolites with very little further increase over time. The prescence of an esterase enzyme in the release medium of FDA tripled the release from MCM to 15 % but left the release from zeolite X unaffected at 6 %. The results obtained show that uptake of fluorescein and its analogues is dependent on the loading solvent used, the amount released is influenced by not only the solvent but the pH and the presence of enzymes in the release medium.