Berberine isolated from Mahonia nepalensis as an eco-friendly and thermally stable corrosion inhibitor for mild steel in acid medium

BackgroundThe environmental and economic benefits have been the driving force in search of efficient corrosion inhibitors for iron/steel used in industrial acidic medium. This study reports on berberine isolated from methanol extract of high-altitude (1347 m) shrub Mahonia nepalensis as a highly efficient and thermally stable corrosion inhibitor for mild steel (MS) in 1.0 M H₂SO₄ simulating acid pickling condition.MethodsThe weight-loss and electrochemical methods revealed the fast adsorption of berberine.Significant Findings: It achieved above 91% inhibition efficiency (IE) in 0.25 h and reached 94% in 6 h for 1000 ppm berberine. The IE increased with concentration and temperature, giving an IE of 97.2% at 328 K, which makes it a promising candidate for industrial application. It behaved as a mixed type of inhibitor as revealed by open circuit potential and polarization curves. The results indicated suppression of the corrosion by effectively forming an adsorbed berberine layer on the MS surface. Adsorption of the berberine followed a Langmuir adsorption isotherm. The thermodynamic parameters such as activation energy (43.19 kJ/mol), free energy (−35.05 kJ/mol), enthalpy (40.55 kJ/mol), and entropy (−97.83 J/molK) of adsorption supported both physical and chemical interactions of berberine with MS surface. The obtained results also revealed that the adsorption process was endothermic and spontaneous in nature.     

Weighted Weierstrass' theorem with first derivatives

We characterize the set of functions which can be approximated by continuous functions with the norm ‖f_‖L^∞(w) for every weight w. This fact allows to determine the closure of the space of polynomials in L^∞(w) for every weight w with compact support. We characterize as well the set of functions which can be approximated by smooth functions with the norm

‖f_‖W1,∞(w₀,w₁):=‖f_‖L^∞(w₀)+‖f^′_‖L^∞(w₁),     

较为精密的Hardy-Hilbert等式的一个加强

本文证明了如下权系数的不等式：这里,（Ｃ为Ｅｕｌｅｒ常数）．从而建立了一个加强的Ｈａｒｄｙ－Ｈｉｌｂｅｒｔ不等式,并建立了一个新的Ｈａｒｄｙ－Ｈｉｌｂｅｒｔ类不等式及其加强式.     

扩充的Hermite-Fejér插值算子平均收敛性

讨论了以Ｊａｃｏｂｉ正交多项式零点为插值结点的扩充Ｈｅｒｍｉｔｅ－Ｆｅｊｅｒ插值算子在Ｌｐｕ空间的平均收敛性。首先给出了算子加权平均收敛的条件,进一步得到了收敛阶。     

等效均衡函数的性质及均衡函数的构造

从均衡函数的等效性出发研究均衡函数的性质,证明了等效的均衡函数之和、积以及数乘仍为均衡函数,并且得到的新均衡函数与原均衡函数等效,这些性质表明等效的均衡函数关于加法和乘法运算均具有半群的代数结构。另外,进一步讨论了构造均衡函数的方法,给出了两个构造均衡函数的定理,该方法具有一般性,现有文献中的均衡函数几乎都能由其构造得到。     

Organocatalyzed Photo-Controlled Synthesis of Ultrahigh-Molecular-Weight Fluorinated Alternating Copolymers

Ultrahigh-molecular-weight (UHMW) polymers with tailored structures are highly desirable for the outstanding properties. In this work, we developed a novel photoorganocatalyzed controlled radical alternating copolymerizations of fluoroalkyl maleimide and diverse vinyl comonomers, enabling efficient preparation of fluorinated copolymers of predetermined UHMWs and well-defined structures at high conversions. Versatility of this method was demonstrated by expanding to controlled terpolymerization, which allows facial access toward fluorinated terpolymers of UHMWs and functional pendants. The obtained copolymers exhibited attractive physical properties and furnished thermoplastic, anticorrosive and (super)hydrophobic attributes as coatings on different substrates. Molecular simulations provided insights into the coating morphology, which unveiled a fluorous protective layer on the top surface with polar groups attached to the bottom substrate, resulting in good adhesion and hydrophobicity, simultaneously. This synthetic method and customized copolymers shed light on the design of high-performance coatings by macromolecular engineering.     

Analysis of dynamic stress intensity factors of thick-walled cylinder under internal impulsive pressure

Dynamic stress intensity factors are evaluated for thick-walled cylinder with a radial edge crack under internal impulsive pressure. Firstly, the equation for stress intensity factors under static uniform pressure is used as the reference case, and then the weight function for a thick-walled cylinder containing a radial edge crack can be worked out. Secondly, the dynamic stresses in uncracked thick-walled cylinders are solved under internal impulsive pressure by using mode shape function method. The solution consists of a quasi-static solution satisfying inhomogeneous boundary conditions and a dynamic solution satisfying homogeneous boundary condi- tions, and the history and distribution of dynamic stresses in thick-walled cylinders are derived in terms of Fourier-Bessel series. Finally, the dynamic stress intensity factor equations for thick-walled cylinder containing a radial edge crack sub- jected to internal impulsive pressure are given by dynamic weight function method. The finite element method is utilized to verify the results of numerical examples, showing the validity and feasibility of the proposed method.     

Calderón-Zygmund-Type Operators on Weighted Weak Hardy Spaces over ℝn

We introduce certain Calderón-Zygmund-type operators and discuss their boundedness on spaces such as weighted Lebesgue spaces, weighted weak Lebesgue spaces, weighted Hardy spaces and weighted weak Hardy spaces. The sharpness of some results is also investigated. Received December 1, 1998, Revised May 2, 1999, Accepted May 19, 1999     

激光解吸/傅里叶变换质谱法研究聚醚的平均分子量和分布

激光解吸/傅里叶变换质谱(Laser Desorption/Fourier Transform MassSpectrometry,LD/FTMS)技术是测定高分子低聚物(MW=1000-10000)平均分子量和分布的一种新的有效方法。采用这项技术,本文研究了一系列的均聚醚和共聚醚,得到了占主导地位的含K~+的准分子离子分布图,用自编程序处理这些数据得到的数均分子量与VPO、GPC、NMR等方法的测定值相一致。还讨论了样品制备中的碱金属盐和实验参数对测定结果的影响等问题。