Structural versatility and electrochemical properties of four copper(II) complexes based on 1<Emphasis Type="Italic">H</Emphasis>-indazole-3-carboxylic acid

Copper (Cu)(II) complexes were synthesized by Ind-3-COOH combined with N-containing auxiliary ligands via a combinatorial strategy involving hydrothermal and solvent-evaporation method. The synthesized complexes had the following formulas: [Cu(Ind-3-COO)₂] (1), [Cu(PHEN)(Ind-3-COO)]₂·2H₂O (2), [Cu₂(DPP)(Ind-3-COO)₂(H₂O)]·H₂O, (3) and [Cu(BPY)(Ind-3-COO)₂]·4H₂O (4). Meanwhile, the symbol abbreviations were listed as follows: Ind-3-COOH = 1H-indazole-3-carboxylic acid, 1,3-bis(4-pyridyl)propane (DPP), 1,10-phenanthroline (PHEN) and 4,4′-bipyridine (BPY). The crystalline structure and spectroscopy of each complex were characterized by single-crystal X-ray diffraction, elemental analysis, Fourier transform infrared spectroscopy and powder X-ray diffraction. The redox reactions in the complexes were then investigated by performing cyclic voltammetry under nitrogen conditions at room temperature. Two pairs of distinctive irreversible reduction potentials were identified, which could be attributed to the processes of Cu(II)–Cu(I) and Cu(I)–Cu(0).     

Phenolic constituents from <Emphasis Type="Italic">Alisma plantago</Emphasis>-<Emphasis Type="Italic">aquatica</Emphasis> Linnaeus and their anti-chronic prostatitis activity

Background

The plant Alisma plantago-aquatica Linnaeus, which is widely distributed in southwest of China, is the main material of traditional Chinese medicine “Zexie”. It was used as folk medicine for immune-modulation, anti-tumor, anti-inflammatory and antibacterial. Previous chemical studies on A. plantago-aquatica reported the identification of triterpenes, diterpenes, sesquiterpenes, steroids, alkaloids and phenolic acid. Terpenes and phenolic acid were regard as major secondary metabolites from this medicine plant.

Results

A new phenolic acid, plantain A (1), along with four known compounds (2–5) were isolated and identified from A. plantago-aquatica by extensive chromatographic and spectrometric methods. In the present study, the levels of TNF-α, IL-1β, COX-2, PEG2 and TGF-β1 were increased in model group rats, whereas on treatment with the isolated compound (1 and 4) at 50 mg/kg, there was a significant decrease in the cytokine levels. Therefore, the anti-CNP effect of 1 and 4 may be related to their anti-inflammatory properties.

Conclusions

A new phenolic acid and four known phenolic compounds were isolated from A. plantago-aquatica. Moreover, compounds 1 and 4 shows significant anti-chronic prostatitis activity in rats.

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Exact separation theorem for closed sets in Asplund spaces

In this paper, in terms of the Fréchet normal cone, we establish exact separation results for finitely many disjoint closed sets in an Asplund space, which supplement the extremal principle and some fuzzy separation theorems. As an application, we provide a new optimality condition for a constraint optimization problem in terms of Fréchet subdifferential and Fréchet normal cone.     

Asymptotic behavior of solutions to the compressible nematic liquid crystal system in ℝ3

In this paper, we study a nematic liquid crystals system in three-dimensional whole space ?³ and obtain the time decay rates of the higher-order spatial derivatives of the solution by the method of spectral analysis and energy estimates if the initial data belongs to L¹?³ additionally.     

Certain properties related to well posedness of switching diffusions

This work is devoted to switching diffusions that have two components (a continuous component and a discrete component). Different from the so-called Markovian switching diffusions, in the setup, the discrete component (the switching) depends on the continuous component (the diffusion process). The objective of this paper is to provide a number of properties related to the well posedness. First, the differentiability with respect to initial data of the continuous component is established. Then, further properties including uniform continuity with respect to initial data, and smoothness of certain functionals are obtained. Moreover, Feller property is obtained under only local Lipschitz continuity. Finally, an example of Lotka–Volterra model under regime switching is provided as an illustration.     

Infinite Horizon Controlled Diffusions with Randomly Varying and State-Dependent Discount Cost Rates

This work focuses on optimal controls of diffusions in an infinite horizon. It has several distinct features in contrast to the existing literature. The discount factor is allowed to be randomly varying and state dependent. The existence and uniqueness of the viscosity solution to the associated Hamilton–Jacobi–Bellman equation are established. The verification theorem is also obtained. Because closed-form solutions are virtually impossible to obtain in most cases, we develop numerical methods. Using the Markov chain approximation methods, numerical schemes are constructed; viscosity solution methods are used to prove the convergence of the algorithm. In addition, examples are given for demonstration purpose.     

An alternating direction and projection algorithm for structure-enforced matrix factorization

Structure-enforced matrix factorization (SeMF) represents a large class of mathematical models appearing in various forms of principal component analysis, sparse coding, dictionary learning and other machine learning techniques useful in many applications including neuroscience and signal processing. In this paper, we present a unified algorithm framework, based on the classic alternating direction method of multipliers (ADMM), for solving a wide range of SeMF problems whose constraint sets permit low-complexity projections. We propose a strategy to adaptively adjust the penalty parameters which is the key to achieving good performance for ADMM. We conduct extensive numerical experiments to compare the proposed algorithm with a number of state-of-the-art special-purpose algorithms on test problems including dictionary learning for sparse representation and sparse nonnegative matrix factorization. Results show that our unified SeMF algorithm can solve different types of factorization problems as reliably and as efficiently as special-purpose algorithms. In particular, our SeMF algorithm provides the ability to explicitly enforce various combinatorial sparsity patterns that, to our knowledge, has not been considered in existing approaches.     

采用二次等参体元时的接触判据

当二次等参体元用于分析接触问题时,接触面上节点集中接触力不同号给建立接触判据造成困难。本文建立了由节点集中接触力计算接触面上分布接触力节点值的方法,从而可顺利建立接触判据。此方法已成功应用于工程中的弹性固体接触问题分析,文末给出了一个计算实例。     

各向异性晶体滑移有限元程序及其应用

本文全面介绍了各向异性晶体滑移结构强度和蠕变分析有限元程序的原理、功能特点及其在镍基单晶涡轮叶片中的应用实例。