Markov processes conditioned on their location at large exponential times

Suppose that ${\left(X_t\right)}_{t\ge 0}$ is a one-dimensional Brownian motion with negative drift $?\mu$. It is possible to make sense of conditioning this process to be in the state 0 at an independent exponential random time and if we kill the conditioned process at the exponential time the resulting process is Markov. If we let the rate parameter of the random time go to 0, then the limit of the killed Markov process evolves like $X$ conditioned to hit 0, after which time it behaves as $X$ killed at the last time $X$ visits 0. Equivalently, the limit process has the dynamics of the killed “bang–bang” Brownian motion that evolves like Brownian motion with positive drift $+\mu$ when it is negative, like Brownian motion with negative drift $?\mu$ when it is positive, and is killed according to the local time spent at 0.An extension of this result holds in great generality for a Borel right process conditioned to be in some state $a$ at an exponential random time, at which time it is killed. Our proofs involve understanding the Campbell measures associated with local times, the use of excursion theory, and the development of a suitable analogue of the “bang–bang” construction for a general Markov process.As examples, we consider the special case when the transient Borel right process is a one-dimensional diffusion. Characterizing the limiting conditioned and killed process via its infinitesimal generator leads to an investigation of the $h$-transforms of transient one-dimensional diffusion processes that goes beyond what is known and is of independent interest.     

Local boundedness of weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

In this paper we prove that weak solutions to the Diffusive Wave Approximation of the Shallow Water equations

${?}_{t}u?\mathrm{?}?({(u?z)}^{\alpha }|\mathrm{?}u{|}^{\gamma ?1}\mathrm{?}u)=f$

are locally bounded. Here, u describes the height of the water, z is a given function that represents the land elevation and f is a source term accounting for evaporation, infiltration or rainfall.     

Classical Backfitting for Smooth-Backfitting Additive Models

Smooth backfitting has been shown to have better theoretical properties than classical backfitting for fitting additive models based on local linear regression. In this article, we show that the smooth backfitting procedure in the local linear case can be alternatively performed as a classical backfitting procedure with a different type of smoother matrices. These smoother matrices are symmetric and shrinking and some established results in the literature are readily applicable. The connections allow the smooth backfitting algorithm to be implemented in a much simplified way, give new insights on the differences between the two approaches in the literature, and provide an extension to local polynomial regression. The connections also give rise to a new estimator at data points. Asymptotic properties of general local polynomial smooth backfitting estimates are investigated, allowing for different orders of local polynomials and different bandwidths. Cases of oracle efficiency are discussed. Computer-generated simulations are conducted to demonstrate finite sample behaviors of the methodology and a real data example is given for illustration. Supplementary materials for this article are available online.     

Development of a syn‐Selective Mannich Reaction of Aldehydes with Propargylic Imines by Dual Catalysis: Asymmetric Synthesis of Functionalized Propargylic Amines

Direct coupling of enolizable aldehydes with C‐alkynyl imines is realized affording the corresponding propargylic Mannich adducts of syn configuration, thus complementing previous methods that gave access to the anti‐isomers. The combination of proline and a urea Brønsted base cocatalyst is key for the reactions to proceed under very mild conditions (3–10 mol % catalyst loading, dichloromethane as solvent, ?20 °C, 1.2 molar equivalents of aldehyde) and with virtually total stereocontrol (syn/anti ratio up to 99:1; ee up to 99 %). Some possibilities of further chemical elaboration of adducts are also briefly illustrated.     

An Atomically Precise Au10Ag2 Nanocluster with Red–Near‐IR Dual Emission

A red–near‐IR dual‐emissive nanocluster with the composition [Au₁₀Ag₂(2‐py?C≡C)₃(dppy)₆](BF₄)₅ ( 1 ; 2‐py?C≡C is 2‐pyridylethynyl, dppy=2‐pyridyldiphenylphosphine) has been synthesized. Single‐crystal X‐ray structural analysis reveals that 1 has a trigonal bipyramidal Au₁₀Ag₂ core that contains a planar Au₄(2‐py?C≡C)₃ unit sandwiched by two Au₃Ag(dppy)₃ motifs. Cluster 1 shows intense red–NIR dual emission in solution. The visible emission originates from metal‐to‐ligand charge transfer (MLCT) from silver atoms to phosphine ligands in the Au₃Ag(dppy)₃ motifs, and the intense NIR emission is associated with the participation of 2‐pyridylethynyl in the frontier orbitals of the cluster, which is confirmed by a time‐dependent density functional theory (TD‐DFT) calculation.     

Plasmonic nanostructures for local field enhancement in the UV region

In this work we describe an ultraviolet subwavelength focusing in plasmonic nanostructures. A system which provides a 20–25 times local field enhancement at a wavelength of 350 nm is proposed. This system represents a metalized V-shaped groove in a surface of a dielectric medium. Subwavelength focusing is achieved by a plasmon wave propagation along the surface of metal film and by the transfer of electromagnetic field through the dielectric medium. The influence of system parameters on a local field enhancement is investigated. A simplified model that allows for determining the geometric parameters of an optimized resonator is proposed.     

The band gap and transmission characteristics investigation of local resonant quaternary phononic crystals with periodic coating

In this article, the investigation of the Lamb wave propagation in two-dimensional phononic crystals (PCs) composed of an array of periodic coating on a thin plate is presented. Compared with the traditional PCs usually consist of cylindrical scatters with uniform coatings in their exterior structure, the newly exterior coating structures with periodic alternant arrangement of two different materials are proposed. The band structures are calculated using finite element method. We discover that a complete band gap can be exhibited at low frequency. Furthermore, for a finite PCs plate, the computed transmission and resonance spectra shown an evident resonance nature which can be directly related to formation of the low-frequency gaps. The effects of different material parameters and arrangement mode of coating on the acoustic energy transmission and attenuation are also studied. Finally, the experimental transmission spectrum of the periodic coating PCs are also presented and compared with the numerical results. This study will provide useful support to the design of tuning band gaps and isolators in the low-frequency range.     

Bivalent Organophosphorus Compounds—Synthesis and Acetylcholinesterase Inhibitory Activity

Abstract

A series of novel symmetric S,S′-2,2′-(ethane-1,2-diylbis(azanediyl)) bis(2-oxoethane-2,1-diyl) O,O,O′,O′-tetraethyl diphosphorodithioate derivatives (12) was designed and synthesized based on the cluster effect and the multiple binding sites of acetylcholinesterase (AChE). The structures of all the newly synthesized title compounds were characterized by ¹ Choi, S. K. Synthetic Multivalent Molecules: Concepts and Biomedical Application, 20–21. New Jersey: John Wiley & Sons, Inc. 2004, chapter 1 [Google Scholar]H and ¹³ Tang, H., Zhao, L. Z., Zhao, H. T., Huang, S. L., Zhong, S. M., Qin, J. K., Chen, Z. F., Huang, Z. S. and Liang, H. 2011. Euro. J. Med. Chem., 46: 4970–4979. [Crossref], [PubMed], [Web of Science ®] , [Google Scholar]C NMR as well as elemental analyses. Their inhibitory activities against AChE were tested, and compound 12b exhibited the best activity (6.60-fold higher than ethion). The results suggested that the compound would bind to the catalytic center and the narrow gorge of the AChE simultaneously.

Supplementary materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfer, and Silicon and the Related Elements for the following free supplemental files: Additional table.     

Novel matrix invariants for characterization of changes of proteomics maps

Previous studies on mathematical characterization of proteomics maps by sets of map invariants were based on the construction of a set of distance-related matrices obtained by matrix multiplication of a single matrix by itself. Here we consider an alternative characterization of proteomics maps based on a set of matrices characterizing local features of an embedded zigzag curve over the map. It is shown that novel invariants can well characterize proteomics maps. Advantages of the novel approach are discussed.     

Enantioseparation of chiral aromatic acids by multiple dual mode counter‐current chromatography using hydroxypropyl‐β‐cyclodextrin as chiral selector

This work concentrates on extending the utilization of multiple dual mode (MDM) counter‐current chromatography in chiral separations. Two aromatic acids, 2‐(6‐methoxy‐2‐naphthyl)propionic acid (NAP) and 2‐phenylpropionic acid (2‐PPA), were enantioseparated by MDM counter‐current chromatography using hydroxypropyl‐β‐cyclodextrin (HP‐β‐CD) as chiral selector. The two‐phase solvent systems consisting of n‐hexane/ethyl acetate 0.1 mol/L phosphate buffer pH 2.67 containing 0.1 mol/L HP‐β‐CD (7.5:2.5:10 for NAP and 7:3:10 for 2‐PPA, v/v/v) were used. Conventional MDM and modified MDM were compared according to peak resolution under current separation mechanism. The influence of elution time after the first‐phase inversion and number of cycles for MDM were investigated. Peak resolution of NAP and 2‐PPA increased from 0.62 to 1.05 and 0.72 to 0.84, respectively, using optimized MDM conditions. Being an alternative elution method for counter‐current chromatography, MDM elution greatly improved peak resolution in chiral separations.