Ion Association in Lanthanide Chloride Solutions

A better understanding of the solution chemistry of the lanthanide (Ln) salts in water would have wide ranging implications in materials processing, waste management, element tracing, medicine and many more fields. This is particularly true for minerals processing, given governmental concerns about lanthanide security of supply and the drive to identify environmentally sustainable processing routes. Despite much effort, even in simple systems, the mechanisms and thermodynamics of Ln^III association with small anions remain unclear. In the present study, molecular dynamics (MD), using a newly developed force field, provide new insights into LnCl₃(aq) solutions. The force field accurately reproduces the structure and dynamics of Nd³⁺, Gd³⁺ and Er³⁺ in water when compared to calculations using density functional theory (DFT). Adaptive-bias MD simulations show that the mechanisms for ion pairing change from dissociative to associative exchange depending upon cation size. Thermodynamics of association reveal that whereas ion pairing is favourable, the equilibrium distribution of species at low concentration is dominated by weakly bound solvent-shared and solvent-separated ion pairs, rather than contact ion pairs, reconciling a number of contrasting observations of Ln^III–Cl association in the literature. In addition, we show that the thermodynamic stabilities of a range of inner sphere and outer sphere coordination complexes are comparable and that the kinetics of anion binding to cations may control solution speciation distributions beyond ion pairs. The techniques adopted in this work provide a framework with which to investigate more complex solution chemistries of cations in water.     

通过脱碳控制全球平均温度

Establishing a reliable method to predict the global mean temperature (T_e) is of great importance because CO₂ reduction activities require political and global cooperation and significant financial resources. The current climate models all seem to predict that the earth's temperature will continue to increase, mainly based on the assumption that CO₂ emissions cannot be lowered significantly in the foreseeable future. Given the earth's multifactor climate system, attributing atmospheric CO₂ as the only cause for the observed temperature anomaly is most likely an oversimplification; the presence of water (H₂O) in the atmosphere should at least be considered. As such, T_e is determined by atmospheric water content controlled by solar activity, along with anthropogenic CO₂ activities. It is possible that the anthropogenic CO₂ activities can be reduced in the future. Based on temperature measurements and thermodynamic data, a new model for predicting T_e has been developed. Using this model, past, current, and future CO₂ and H₂O data can be analyzed and the associated T_e calculated. This new, esoteric approach is more accurate than various other models, but has not been reported in the open literature. According to this model, by 2050, T_e may increase to 15.5 ℃ under "business-as-usual" emissions. By applying a reasonable green technology activity scenario, T_e may be reduced to approximately 14.2 ℃. To achieve CO₂ reductions, the scenario described herein predicts a CO₂ reduction potential of 513 gigatons in 30 years. This proposed scenario includes various CO₂ reduction activities, carbon capturing technology, mineralization, and bio-char production; the most important CO₂ reductions by 2050 are expected to be achieved mainly in the electricity, agriculture, and transportation sectors. Other more aggressive and plausible drawdown scenarios have been analyzed as well, yielding CO₂ reduction potentials of 1051 and 1747 gigatons, respectively, in 30 years, but they may reduce global food production. It is emphasized that the causes and predictions of the global warming trend should be regarded as open scientific questions because several details concerning the physical processes associated with global warming remain uncertain. For example, the role of solar activities coupled with Milankovitch cycles are not yet fully understood. In addition, other factors, such as ocean CO₂ uptake and volcanic activity, may not be negligible.     

Hypersurfaces of prescribed mean curvature enclosing a given body

Given a smooth domain Ω in ℝ ^m+1 with compact closure and a smooth integrable functionh: ℝ ^m+1→ℝ satisfyingh(x)≥H _∂Ω (x) on ∂Ω whereH _∂ω denotes the mean curvature of ∂Ω calculated w.r.t. the interior unit normal we show that there is a setA⊂ℝ ^m+1 with the properties andH _∂A=h on ∂A.     

Optimal convergence properties of kernel density estimators without differentiability conditions

Let X ₁, X ₂, ..., X _n be independent observations from an (unknown) absolutely continuous univariate distribution with density f and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiiYdd9qrFfea0dXdf9vqai-hEir8Ve% ea0de9qq-hbrpepeea0db9q8as0-LqLs-Jirpepeea0-as0Fb9pgea% 0lrP0xe9Fve9Fve9qapdbaqaaeGacaGaaiaabeqaamaabaabcaGcba% GabmOzayaajaGaaiikaiaadIhacaGGPaGaeyypa0Jaaiikaiaad6ga% caWGObGaaiykamaaCaaaleqabaGaeyOeI0IaaGymaaaakmaaqadaba% Gaam4saiaacUfadaWcgaqaaiaacIcacaWG4bGaeyOeI0Iaamiwamaa% BaaaleaacaWGPbaabeaakiaacMcaaeaacaWGObGaaiyxaaaaaSqaai% aadMgacqGH9aqpcaaIXaaabaGaamOBaaqdcqGHris5aaaa!5356!\[\hat f(x) = (nh)^{ - 1} \sum\nolimits_{i = 1}^n {K[{{(x - X_i )} \mathord{\left/ {\vphantom {{(x - X_i )} {h]}}} \right. \kern-\nulldelimiterspace} {h]}}} \] be a kernel estimator of f(x) at the point x, \s-<x<, with h=h _n (h _n O and nh _n , as n) the bandwidth and K a kernel function of order r. Optimal rates of convergence to zero for the bias and mean square error of such estimators have been studied and established by several authors under varying conditions on K and f. These conditions, however, have invariably included the assumption of existence of the r-th order derivative for f at the point x. It is shown in this paper that these rates of convergence remain valid without any differentiability assumptions on f at x. Instead some simple regularity conditions are imposed on the density f at the point of interest. Our methods are based on certain results in the theory of semi-groups of linear operators and the notions and relations of calculus of finite differences.This research was supported in part by grants from the Natural Sciences and Engineering Research Council of Canada and the University of Alberta Central Research Fund.     

Proof of some conjectures on the mean-value of Titchmarsh series — III

With some applications in view, the following problem is solved in some special case which is not too special. LetF(s) =Σ _n ^∞ =1a_n λ _n ^−s be a generalized Dirichlet series with 1 =λ ₁ <λ ₂ < …,λ _n≤Dn, andλ _n+1 -λ _n ≥D ^{− 1} λ _n+1 ^{− a} where α>0 andD(≥ 1) are constants. Then subject to analytic continuation and some growth conditions, a lower bound is obtained for . These results will be applied in other papers to appear later.     

Partition function zeros for the one-dimensional ordered plasma in Dirichlet boundary conditions

We consider the grand canonical partition function for the ordered one-dimensional, two-component plasma at fugacity in an applied electric fieldE with Dirichlet boundary conditions. The system has a phase transition from a low-coupling phase with equally spaced particles to a high-coupling phase with particles clustered into dipolar pairs. An exact expression for the partition function is developed. In zero applied field the zeros in the plane occupy the imaginary axis from –i to –i_c and i_c to i for some _c. They also occupy the diamond shape of four straight lines from ±i_c to _c and from ±i_c to –_c. The fugacity acts like a temperature or coupling variable. The symmetry-breaking field is the applied electric fieldE. A finite-size scaling representation for the partition in scaled coupling and scaled electric field is developed. It has standard mean field form. When the scaled coupling is real, the zeros in the scaled field lie on the imaginary axis and pinch the real scaled field axis as the scaled coupling increases. The scaled partition function considered as a function of two complex variables, scaled coupling and scaled field, has zeros on a two-dimensional surface in a domain of four real variables. A numerical discussion of some of the properties of this surface is presented.     

Novel aromatic carboxamides from dehydroabietylamine as potential fungicides: Design,synthesis and antifungal evaluation

The present study was carried out to design and synthesize a number of novel aromatic carboxamide derivatives of dehydroabietylamine. The preliminary antifungal assay indicated that most of title compounds displayed moderate to good antifungal activity toward the six fungal strains in vitro. Compounds 3i, 3q, 4b and 4d showed significant antifungal activity against Sclerotinia sclerotiorum, with EC₅₀ values ranging from 0.067 ～ 0.393 mg/L. Compounds 3i, 4b and 4d also showed pronounced mycelial growth inhibition activities against B. cinerea and A. solani. Furthermore, in the in vivo assay, compound 4b exhibited brilliant protective activity against S. sclerotiorum-infected rape leaves. Meanwhile, the in vivo bioassay on tomato plants infected by B. cinerea showed that compound 3i and 4d displayed excellent protective activity at 200 mg/L, which were near to boscalid. Primary mechanistic study revealed that 4b could inhibit sclerotia formation as well as reduce the exopolysaccharide level. SEM and TEM analysis indicated that 4b possessed a strong ability to destroy the surface morphology of mycelia, cell structure and seriously interfere with the growth of the fungal pathogen. In addition, 4b exhibited good inhibitory activity (IC₅₀ = 23.3 ± 1.6 μM) toward succinate dehydrogenase (SDH). Molecular modeling study confirmed the binding modes between compound 4b and SDH. The above antifungal results and fungicidal mechanism study revealed that this class of dehydroabietylamine derivatives could be potential SDH inhibitors and lead compounds for novel fungicides development.     

线性不对称损失时非正态分布过程均值优化

针对常见的两种非正态分布———梯形分布和三角分布，研究线性不对称质量损失时其过程均值的优化问题，建立了梯形分布在五种不同情况下线性不对称质量损失的数学模型，基于以上模型给出了线性不对称质量损失时梯形分布最优过程均值的确定方法；研究三角分布在四种不同情况下线性不对称质量损失的数学模型，并给出了线性不对称质量损失时三角分布最优过程均值的确定方法。最后，用实例验证本过程均值优化模型的有效性。实例表明，应用线性不对称损失函数，适当的改变过程均值，可以有效地降低产品的质量损失，通过调整工艺过程将获得最佳经济效益。     

再谈Minc-Sathre不等式的上下界

用调和平均值、均值不等式之间的关系及对数平均不等式,对Minc-Sathre不等式的上下界进行改进,使结论更精确.     

含中介值ξ-η-ζ等式的证明方法

介绍含三个中介值ξ-η-ζ等式的几种证明方法,并结合实例加以说明.