Empirical Likelihood Estimation for the Two-Sample Mean under Density Ratio Models Using Auxiliary Information

Auxiliary population information is often available in finite population inference problems, and the empirical likelihood (EL) approach has been demonstrated to be flexible and useful for such problems. The present paper concerns EL when interest centers on inference for the mean of the baseline distribution under two-sample density ratio models. Although dual EL is a convenient technical tool since it has the same maximum point and maximum likelihood as DRM-based EL, it can not combine such auxiliary information into the likelihood conveniently and may have loss of efficiency. By contrast, the classical EL approach of Qin and Lawless\ucite{21} does not have this problem and incorporate seamlessly auxiliary information. Based on the EL using auxiliary information and the dual EL methods, we construct both point and interval estimations and make a careful comparison. Though the point estimation efficiency gain obtained by the former is not noticeable, we find that they may have different performances in interval estimation. In terms of coverage accuracy, the two intervals are comparable for not or moderate skewed populations, and the EL interval using auxiliary information can be much superior for severely skewed populations.     

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for .     

Photoredox/Cobalt Dual-Catalyzed Decarboxylative Elimination of Carboxylic Acids: Development and Mechanistic Insight

Recently, dual-catalytic strategies towards the decarboxylative elimination of carboxylic acids have gained attention. Our lab previously reported a photoredox/cobaloxime dual catalytic method that allows the synthesis of enamides and enecarbamates directly from N-acyl amino acids and avoids the use of any stoichiometric reagents. Further development, detailed herein, has improved upon this transformation's utility and further experimentation has provided new insights into the reaction mechanism. These new developments and insights are anticipated to aid in the expansion of photoredox/cobalt dual-catalytic systems.     

Simultaneous separation and determination of seven isoflavones in Radix Puerariae by capillary electrophoresis with a dual cyclodextrin system

A simple, comprehensive and efficient capillary electrophoresis method using a dual cyclodextrin system was developed for the simultaneous determination of seven isoflavones (3′‐methoxypuerarin, puerarin, 3′‐hydroxypuerarin, ononin, daidzin, daidzein and genistin). Baseline separations of the seven isoflavones were achieved within 11 min with the running buffer consisting of 35 mm sodium tetraborate, 9.0 mm sulfobutylether‐β‐cyclodextrin and 30 mm α‐cyclodextrin at pH 9.34, and peaks were detected at 254 nm. Other separation parameters included the separation voltage for 15 kV and the working temperature for 25°C. Under the optimum conditions, good linearities were obtained with linear correlation coefficients of seven isoflavones of 0.9978–0.9992. The limits of detection and the limits of quantification were 0.7–2.9 and 2.5–9.5 μg/mL, respectively. Excellent precision and accuracy were obtained. The intraday and interday precision ranged from 0.7 to 2.0% and from 0.8 to 1.9%, respectively. The recoveries of seven analytes were from 97.7 to 103.1%. This method was successfully applied to determine the seven analytes in Radix Puerariae and its preparations.     

Necessary and Sufficient Conditions for Qualitative Properties of Infinite Dimensional Linear Programming Problems

Necessary and sufficient conditions for qualitative properties of infinite dimensional linear programing problems such as solvability, duality, and complementary slackness conditions are studied in this article. As illustrations for the results, we investigate the parametric version of Gale’s example.     

非交换加权Lorentz空间的对偶空间

设μ是一个半有限von Neumann代数.对于0P∞,0q≤∞,定义了非交换加权Lorentz空间Λ_ω~(p,q)(μ)及其associate空间Λ_ω~(p,q)(μ)',给出了空间Λ_ω~(p,q)(μ)'和Λ_ω~(p,q)(μ)'的一些基本性质.应用这些性质,还给出了非交换加权Lorentz空间Λ_ω~p(μ),0P∞的对偶空间.     

OBSERVATIONS ON INFEASIBILITY DETECTORS FOR CLASSIFYING CONIC CONVEX PROGRAMS

Abstract

New insights are presented from a convex duality classification theory of over 25 years ago for recent computational complexity results developed for recognizing some of the asymptotic duality states that prevail for an arbitrary convex programming pair.     

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.     

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.