A New Variational Formulation for a Kind of Reaction-diffusion Problem in Broken Sob olev Space

In this paper, a new variational formulation for a reaction-diffusion problem in broken Sobolev space is proposed. And the new formulation in the broken Sobolev space will be proved that it is well-posed and equivalent to the standard Galerkin variational formulation. The method will be helpful to easily solve the original partial differential equation numerically. And the method is novel and interesting, which can be used to deal with some complicated problem, such as the low regularity problem, the differential-integral problem and so on.     

Metal(II) Ion Complexes with 5‐(Pyrazin‐2‐yl)‐2,4‐dihydro‐3H‐1,2,4‐triazole‐3‐thione; Synthesis,Structural Characterization,Acid‐base,and Complexing Properties in Solution

The study reports the synthesis of complexes Co(HL)Cl₂ ( 1 ), Ni(HL)Cl₂ ( 2 ), Cu(HL)Cl₂ ( 3 ), and Zn(HL)₃Cl₂ ( 4 ) with the title ligand, 5‐(pyrazin‐2‐yl)‐1,2,4‐triazole‐5‐thione (HL), and their characterization by elemental analyses, ESI‐MS (m/z), FT‐IR and UV/Vis spectroscopy, as well as EPR in the case of the Cu^II complex. The comparative analysis of IR spectra of the metal ion complexes with HL and HL alone indicated that the metal ions in 1 , 2 , and 3 are chelated by two nitrogen atoms, N(4) of pyrazine and N(5) of triazole in the thiol tautomeric form, whereas the Zn^II ion in 4 is coordinated by the non‐protonated N(2) nitrogen atom of triazole in the thione form. pH potentiometry and UV/Vis spectroscopy were used to examine Co^II, Ni^II, and Zn^II complexes in 10/90 (v/v) DMSO/water solution, whereas the Cu^II complex was examined in 40/60 (v/v) DMSO/water solution. Monodeprotonation of the thione triazole in solution enables the formation of the L:M = 1:1 species with Co^II, Ni^II and Zn^II, the 2:1 species with Co^II and Zn^II, and the 3:1 species with Zn^II. A distorted tetrahedral arrangement of the Cu^II complex was suggested on the basis of EPR and Vis/NIR spectra.     

Equilibrium phase behavior of aqueous two-phase systems containing 17R4/L64 and citrates

The cloud points (CPs) of the copolymers 17R4 and L64 were first measured, and then the effects of salts ((NH₄)₃C₆H₅O₇, K₃C₆H₅O₇) on 17R4 and L64 were researched. After finishing the work described above, the temperature (278.15, 283.15, and 288.15) K of aqueous two-phase systems was determined, which consist of 17R4-(NH₄)₃C₆H₅O₇, 17R4-K₃C₆H₅O₇, L64-(NH₄)₃C₆H₅O₇, and L64-K₃C₆H₅O₇. Finally, the liquid–liquid equilibrium (LLE) data of binodal curve and the tie line for 17R4-(NH₄)₃C₆H₅O₇ aqueous two- phase systems (ATPSs) 17R4-K₃C₆H₅O₇ ATPSs, L64-(NH₄)₃C₆H₅O₇ ATPSs, and L64-K₃C₆H₅O₇ ATPSs were obtained. Nonlinear fitting of the empirical equation was used for making the diagram. The results showed that the change in the size of the two-phase areas increases with the increase of temperature. The capacity of the salts to induce phase segregation follows the Hofmeister series, that is, K₃C₆H₅O₇?>?(NH₄)₃C₆H₅O₇. In addition, the findings also showed that the phase separation ability of 17R4 is better than that of L64.     

局部上循环的3-Hom李双代数和3-李经典Hom-杨巴克斯方程

本文介绍了局部上循环的3-Hom李双代数,它的乘法和余乘两种运算的相容条件由局部上循环条件给出.作者研究了扭的3元版本的杨巴克斯方程,称为3-李Hom-杨巴克斯方程,它是文献[1]中3- 李杨巴克斯方程的一种广义化.文章证明由3-李Hom-杨巴克斯方程的解所诱导的双代数,可得到上边缘的局部上循环的3-Hom 李双代数.     

Aqueous microwave-assisted DMAP catalyzed synthesis of β-phosphonomalonates and 2-amino-4H-chromen-4-ylphosphonates via a domino Knoevenagel-phospha-Michael reaction

An aqueous microwave (mw)-assisted DMAP catalyzed one-pot highly efficient route to synthesize β-phosphonomalonates and 2-amino-4H-chromen-4-yl phosphonates has been demonstrated via the domino Knoevenagel-phospha-Michael reaction of aryl aldehyde/salicylaldehyde, malononitrile/ethyl cyanoacetate and alkyl phosphite ester. Optimization of reaction conditions were performed by using conventional and microwave synthetic approaches. This conversion proceeded smoothly to deliver the desired product in good to excellent yields (75–95%) in a short reaction time (10–12 min). The present methodology is very simple, environmentally benign, high yielding and has very well demonstrated the synergistic effect of water and microwaves.     

Stochastic partial functional differential equations with locally monotone coefficients,locally Lipschitz non-linearity and delay

In this paper, we study the existence and uniqueness of strong solutions for stochastic partial functional differential equations with locally monotone coefficients, locally Lipschitz non-linearity, and time delay. Our results extend previous results obtained by Liu–Röckner, Caraballo et al. and Taniguchi et al. Examples are given to illustrate the wide applicability of our results.     

电感耦合等离子体质谱(ICP-MS)法测定地质样品中的金

建立了王水溶解-聚氨酯泡沫塑料吸附-电感耦合等离子体质谱(ICP-MS)法测定地质样品中的金。探讨了振荡时间对回收率的影响,最终确定振荡时间为1h。在优化条件下,方法的相对标准偏差(RSD,n=12)在4.2%~9.0%,加标回收率在92.00%~114.6%,方法检出限为0.11ng/g。方法操作简单,测定精密度高,检出限低,满足大批量地质样品的分析需要。     

An eco‐epidemiological predator–prey model where predators distinguish between susceptible and infected prey

A predator–prey model with disease amongst the prey and ratio‐dependent functional response for both infected and susceptible prey is proposed and its features analysed. This work is based on previous mathematical models to analyse the important ecosystem of the Salton Sea in Southern California and New Mexico where birds (particularly pelicans) prey on fish (particularly tilapia). The dynamics of the system around each of the ecologically meaningful equilibria are presented. Natural disease control is considered before studying the impact of the disease in the absence of predators and the interaction of predators and healthy prey and the disease effects on predators in the absence of healthy prey. Our theoretical results are confirmed by numerical simulation. Copyright © 2016 John Wiley & Sons, Ltd.