Two questions on semi-clean group rings

It was proved in [4] that every group ring of a torsion abelian group over a commutative local ring is a semi-clean ring. It was asked in [4] whether every group ring of a torsion abelian group over a commutative clean ring is a semi-clean ring and whether every group ring of a torsion abelian group over a commutative semi-clean ring is a semi-clean ring. In this paper, we give a positive answer to question 1 and a negative answer to question 2.     

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.     

Local well-posedness for quasi-linear NLS with large Cauchy data on the circle

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrödinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions.     

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.     

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.     

Oscillation theorems for symplectic difference systems

We consider symplectic difference systems involving a spectral parameter, together with the Dirichlet boundary conditions. The main result of the paper is a discrete version of the so-called oscillation theorem which relates the number of finite eigenvalues less than a given number to the number of focal points of the principal solution of the symplectic system. In two recent papers the same problem was treated and an essential ingredient was to establish the concept of the multiplicity of a focal point. But there was still a rather restrictive condition needed, which is eliminated here by using the concept of finite eigenvalues (or zeros) from the theory of matrix pencils.     

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.