Electron distribution in 1-organo-1H-tetrazole-5-thiols. Crystal and molecular structure of 1-methyl-1H-tetrazole-5-thiol and its potassium (18-crown-6) salt

The crystal and molecular structures of both neutral and anionic 1-methyl-1H-tetrazole-5-thiol, as its potassium(18-crown-6) salt, are reported. In the solid state, the molecular thiotetrazole adopts a planar, dimeric arrangement, in which two neighboring molecules are hydrogen bridged. Each monomeric unit exhibits considerable π electron delocalization over the CN₂S fragment. The anionic form displays extensive, but not uniform, π electron delocalization within the ring, which also extends to the exocyclic carbon–sulfur bond, the structure being best described as a hybrid. The potassium cation is coordinated to the macrocyclic 18-crown-6 ether as expected, but it also interacts with the NCS fragment of the tetrazolethiolate ring.     

Phenyllead(IV) diorganophosphinodithioates,PhnPb(S2PR2)4−n. Synthesis,spectroscopic characterization,and NMR study of the redistribution/decomposition of diphenyllead(IV) derivatives

Tri- and diphenyllead(IV) diorganophosphinodithioates, Ph_nPb(S₂PR₂)_4−n (n = 2 and 3; R = Me, Et, Ph) were prepared by reacting the corresponding organolead(IV) chloride with the sodium or ammonium salt of the phosphinodithioic acid. The title compounds were investigated by infrared, ¹H and ³¹P NMR, and mass spectroscopy, and possible structures were proposed. The diphenyllead(IV) phosphinodithioates, Ph₂Pb(S₂PR₂)₂, undergo decomposition on standing or on moderate heating, the least stable being the ethyl derivative. The process was monitored by using ¹H and ³¹P NMR spectroscopy, and a reaction pathway leading to Ph₃PbS₂PR₂, Pb(S₂PR₂)₂, and R₂P(S)SPh was established.     

Information Geometry in Roegenian Economics

We characterise the geometry of the statistical Roegenian manifold that arises from the equilibrium distribution of an income of noninteracting identical economic actors. The main results for ideal income are included in three subsections: partition function in distribution, scalar curvature, and geodesics. Although this system displays no phase transition, its analysis provides an enlightening contrast with the results of Van der Waals Income in Roegenian Economics, where we shall examine the geometry of the economic Van der Waals income, which does exhibit a “monetary policy as liquidity—income” transition. Here we focus on three subsections: canonical partition function, economic limit, and information geometry of the economic Van der Waals manifold.     

Bismuth(III) dimethyldithioarsinate,Bi(S2AsMe2)3: A new dimer formed through Bi … S secondary bonding

The crystal and molecular structures of bismuth(III) dimethyldithioarsinate, Bi(S₂AsMe₂)₂, were investigated by X-ray diffraction. The compound is a centrosymmetric dimer in which pentagonal-bipyramidal monomeric units are associated through secondary Bi–S interactions. The structure is compared with that of the analogous dithiophosphinate, Bi(S₂PMe₂)₂. © 1997 John Wiley & Sons, Inc.     

Hardy–Littlewood–Polya’s Inequality and a New Concept of Weak Majorization

In this paper, we study some weak majorization properties with applications for the trees. A strongly notion of majorization is introduced and Hardy–Littlewood–Polya’s inequality is generalized.     

An efficient goal‐based reduced order model approach for targeted adaptive observations

An efficient adjoint sensitivity technique for optimally collecting targeted observations is presented. The targeting technique incorporates dynamical information from the numerical model predictions to identify when, where and what types of observations would provide the greatest improvement to specific model forecasts at a future time. A functional (goal) is defined to measure what is considered important in modelling problems. The adjoint sensitivity technique is used to identify the impact of observations on the predictive accuracy of the functional, then placing the sensors at the locations with high impacts. The adaptive (goal) observation technique developed here has the following features: (i) over existing targeted observation techniques, its novelty lies in that the interpolation error of numerical results is introduced to the functional (goal), which ensures the measurements are a distance apart; (ii) the use of proper orthogonal decomposition (POD) and reduced order modelling for both the forward and backward simulations, thus reducing the computational cost; and (iii) the use of unstructured meshes. The targeted adaptive observation technique is developed here within an unstructured mesh finite element model (Fluidity). In this work, a POD reduced order modelling is used to form the reduced order forward model by projecting the original complex model from a high dimensional space onto a reduced order space. The reduced order adjoint model is then constructed directly from the reduced order forward model. This efficient adaptive observation technique has been validated with two test cases: a model of an ocean gyre and a model of 2D urban street canyon flows. Copyright © 2016 John Wiley & Sons, Ltd.     

An indirect shooting method based on the POD/DEIM technique for distributed optimal control of the wave equation

This paper presents a fast numerical method, based on the indirect shooting method and Proper Orthogonal Decomposition (POD) technique, for solving distributed optimal control of the wave equation. To solve this problem, we consider the first‐order optimality conditions and then by using finite element spatial discretization and shooting strategy, the solution of the optimality conditions is reduced to the solution of a series of initial value problems (IVPs). Generally, these IVPs are high‐order and thus their solution is time‐consuming. To overcome this drawback, we present a POD indirect shooting method, which uses the POD technique to approximate IVPs with smaller ones and faster run times. Moreover, in the presence of the nonlinear term, to reduce the order of the nonlinear calculations, a discrete empirical interpolation method (DEIM) is applied and a POD/DEIM indirect shooting method is developed. We investigate the performance and accuracy of the proposed methods by means of 4 numerical experiments. We show that the presented POD and POD/DEIM indirect shooting methods dramatically reduce the CPU time compared to the full indirect shooting method, whereas there is no significant difference between the accuracy of the reduced and full indirect shooting methods.     

A spirobicyclic complex of Schmidpeter's ligand,bis(tetraphenylimidodiphosphinato)beryllium,Be(OPh2PNPPh2O)2, an inorganic analog of beryllium bis(β‐diketonates)

The crystal structure of bis(tetra‐phenylimidodiphosphinato)beryllium (as a benzene solvate), Be(OPh₂PNPPh₂O)₂. C₆H₆, was determined by X‐ray diffraction and compared with that of beryllium acetylacetonate, Be(OCMeCHCMeO)₂. The imidodiphosphinate is an inorganic spirobicyclic system, Be(OPNPO)₂, with tetrahedrally coordinated beryllium. Unlike the planar BeO₂C₃ rings in the acetylacetonate, the two six‐membered BeO₂P₂N inorganic rings are nonplanar and display a skew boat conformation. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:244–248, 2000     

The method of dynamic mode decomposition in shallow water and a swirling flow problem

In this paper, a new vector‐filtering criterion for dynamic modes selection is proposed that is able to extract dynamically relevant flow features from dynamic mode decomposition of time‐resolved experimental or numerical data. We employ a novel modes selection criterion in parallel with the classic selection based on modes amplitudes, in order to analyze which of these procedures better highlight the coherent structures of the flow dynamics. Numerical tests are performed on two distinct problems. The efficiency of the proposed criterion is proved in retaining the most influential modes and reducing the size of the dynamic mode decomposition model. By applying the proposed filtering mode technique, the flow reconstruction error is shown to be significantly reduced. Copyright © 2016 John Wiley & Sons, Ltd.     

Sampling and resolution characteristics in reduced order models of shallow water equations: Intrusive vs nonintrusive

We investigate the sensitivity of reduced order models (ROMs) to training data spatial resolution as well as sampling rate. In particular, we consider proper orthogonal decomposition (POD), coupled with Galerkin projection (POD-GP), as an intrusive ROM technique. For nonintrusive ROMs, we consider two frameworks. The first is using dynamic mode decomposition (DMD), and the second is based on artificial neural networks (ANNs). For ANN, we utilized a residual deep neural network, and for DMD we have studied two versions of DMD approaches; one with hard thresholding and the other with sorted bases selection. Also, we highlight the differences between mean subtracting the data (centering) and using the data without mean subtraction. We tested these ROMs using a system of 2D shallow water equations for four different numerical experiments, adopting combinations of sampling rates and spatial resolutions. For these cases, we found that the DMD basis obtained with hard thresholding is sensitive to sampling rate. The sorted DMD algorithm helps to mitigate this problem and yields more stabilized and converging solution. Furthermore, we demonstrate that both DMD approaches without mean subtraction provide significantly more accurate results than DMD with mean subtracting the data. On the other hand, POD is relatively insensitive to sampling rate and yields better representation of the flow field. Meanwhile, spatial resolution has little effect on both POD and DMD performances. Numerical results reveal that an ANN on POD subspace (POD-ANN) performs remarkably better than POD-GP and DMD in capturing system dynamics, even with a small number of modes.