Is Aerogen–π Interaction Capable of Initiating the Noncovalent Chemistry of Group 18?

The interactions between atoms of noble gases and π systems are generally considered as van der Waals interaction, which have not attracted attention yet. Herein, we present high‐level ab initio calculations to show the unexpected noncovalent interaction between a covalently bonded noble gas atom and a delocalized aromatic π electron using XeO₃?benzene as the prototype. The CCSD(T)/CBS reference data show its strength amounting to ?10.2 kcal mol^?1, comparable to a typical H‐bond or an anion–π interaction. The energy decomposition analysis reveals that the aerogen–π interaction is favored by the electrostatic interaction (27.7 %), the induction (13.4 %), and the dispersion (21.6 %). This interaction may prompt us to consider the noncovalent chemistry of aerogen derivatives in the near future.     

A two‐dimensional layered CdII coordination polymer with a three‐dimensional supramolecular architecture incorporating mixed multidentate N‐ and O‐donor ligands

The combination of N‐heterocyclic and multicarboxylate ligands is a good choice for the construction of metal–organic frameworks. In the title coordination polymer, poly[bis{μ₂‐1‐[(1H‐benzimidazol‐2‐yl)methyl]‐1H‐tetrazole‐κ²N³:N⁴}(μ₄‐butanedioato‐κ⁴O¹:O^1′:O⁴:O^4′)(μ₂‐butanedioato‐κ²O¹:O⁴)dicadmium], [Cd(C₄H₄O₄)(C₉H₈N₆)]_n, each Cd^II ion exhibits an irregular octahedral CdO₄N₂ coordination geometry and is coordinated by four O atoms from three carboxylate groups of three succinate (butanedioate) ligands and two N atoms from two 1‐[(1H‐benzimidazol‐2‐yl)methyl]‐1H‐tetrazole (bimt) ligands. Cd^II ions are connected by two kinds of crystallographically independent succinate ligands to generate a two‐dimensional layered structure with bimt ligands located on each side of the layer. Adjacent layers are further connected by hydrogen bonding, leading to a three‐dimensional supramolecular architecture in the solid state. Thermogravimetric analysis of the title polymer shows that it is stable up to 529 K and then loses weight from 529 to 918 K, corresponding to the decomposition of the bimt ligands and succinate groups. The polymer exhibits a strong fluorescence emission in the solid state at room temperature.     

DMA-80测汞仪直接测定固体样品中的汞

利用DMA-80测汞仪直接测定固体样品中的汞,采用升温加热直接进行热分解、金汞齐反应,采用长、短双检测池,可直接测定固体、液体样品,汞含量在0.n~600.0ng/g范围内的样品都能准确地测定,每个样品测定时间约为5min。测定结果证明方法具有可靠性。     

On Lorentzian Ricci solitons on nilpotent Lie groups

The aim of this article is to exhibit the variety of different Ricci soliton structures that a nilpotent Lie group can support when one allows for the metric tensor to be Lorentzian. In stark contrast to the Riemannian case, we show that a nilpotent Lie group can support a number of non‐isometric Lorentzian Ricci soliton structures with decidedly different qualitative behaviors and that Lorentzian Ricci solitons need not be algebraic Ricci solitons. The analysis is carried out by classifying all left invariant Lorentzian metrics on the connected, simply‐connected five‐dimensional Lie group having a Lie algebra with basis vectors and and non‐trivial bracket relations and , investigating the various curvature properties of the resulting families of metrics, and classifying all Lorentzian Ricci soliton structures.     

Unit-linked life insurance policies: Optimal hedging in partially observable market models

In this paper we investigate the hedging problem of a unit-linked life insurance contract via the local risk-minimization approach, when the insurer has a restricted information on the market. In particular, we consider an endowment insurance contract, that is a combination of a term insurance policy and a pure endowment, whose final value depends on the trend of a stock market where the premia the policyholder pays are invested. To allow for mutual dependence between the financial and the insurance markets, we use the progressive enlargement of filtration approach. We assume that the stock price process dynamics depends on an exogenous unobservable stochastic factor that also influences the mortality rate of the policyholder. We characterize the optimal hedging strategy in terms of the integrand in the Galtchouk–Kunita–Watanabe decomposition of the insurance claim with respect to the minimal martingale measure and the available information flow. We provide an explicit formula by means of predictable projection of the corresponding hedging strategy under full information with respect to the natural filtration of the risky asset price and the minimal martingale measure. Finally, we discuss applications in a Markovian setting via filtering.     

A Note on normalizations of orbit closures

We give a negative answer to a question by J. M. Landsberg on the nature of normalizations of orbit closures. A counterexample originates from the study of complex, ternary, cubic forms.     

Adaptive Fourier decomposition‐based Dirac type time‐frequency distribution

The Dirac‐type time‐frequency distribution (TFD), regarded as ideal TFD, has long been desired. It, until the present time, cannot be implemented, due to the fact that there has been no appropriate representation of signals leading to such TFD. Instead, people have been developing other types of TFD, including the Wigner and the windowed Fourier transform types. This paper promotes a practical passage leading to a Dirac‐type TFD. Based on the proposed function decomposition method, viz., adaptive Fourier decomposition, we establish a rigorous and practical Dirac‐type TFD theory. We do follow the route of analytic signal representation of signals founded and developed by Garbo, Ville, Cohen, Boashash, Picinbono, and others. The difference, however, is that our treatment is theoretically throughout and rigorous. To well illustrate the new theory and the related TFD, we include several examples and experiments of which some are in comparison with the most commonly used TFDs. Copyright © 2016 John Wiley & Sons, Ltd.     

Composite generalized Laguerre spectral method for nonlinear Fokker–Planck equations on the whole line

In this paper, we propose a composite Laguerre spectral method for the nonlinear Fokker–Planck equations modelling the relaxation of fermion and boson gases. A composite Laguerre spectral scheme is constructed. Its convergence is proved. Numerical results show the efficiency of this approach and coincide well with theoretical analysis. Some results on the Laguerre approximation and techniques used in this paper are also applicable to other nonlinear problems on the whole line. Copyright © 2016 John Wiley & Sons, Ltd.     

Error estimates for space–time discontinuous Galerkin formulation based on proper orthogonal decomposition

In this study, proper orthogonal decomposition (POD) method is applied to diffusion–convection–reaction equation, which is discretized using space–time discontinuous Galerkin (dG) method. We provide estimates for POD truncation error in dG-energy norm, dG-elliptic projection, and space–time projection. Using these new estimates, we analyze the error between the dG and the POD solution, and the error between the exact and the POD solution. Numerical results, which are consistent with theoretical convergence rates, are presented.     

Direct analysis of free amino acids by mixed‐mode chromatography with tandem mass spectrometry

We developed a straightforward, robust, and relatively fast method for the analysis of amino acids by mixed‐mode high‐performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry. The method does not involve derivatization and allows the detection of 21 amino acids, representing a wide range of isoelectric points, in less than 40 min. Chromatographic separation was governed by a silica‐based mixed‐mode column providing simultaneous hydrophobic and ion exchange separation mechanisms. The use of tandem mass spectrometry increased selectivity, reducing potential problems associated with poor selectivity in the chromatographic system. For an injection volume of 1 μL, we obtained detection limits <3 μM for the majority of analytes. For all analytes, a linearity of r > 0.99 was obtained, recovery in matrix was >86%, and the retention times were highly reproducible. The method was successfully applied to soil solution and fungal culture samples, demonstrating the advantages in successfully avoiding issues associated with high amounts of substances that may interfere with derivatization‐based methods. This method represents an alternative to derivatization‐based methods and can be applied in areas where sample matrices are highly complex.