On the applicability of the HSAB principle through the use of improved computational schemes for chemical hardness evaluation

Finite difference schemes, named Compact Finite Difference Schemes with Spectral-like Resolution, have been used for a less crude approximation of the analytical hardness definition as the second-order derivative of the energy with respect to the electron number. The improved computational schemes, at different levels of theory, have been used to calculate global hardness values of some probe bases, traditionally classified as hard and soft on the basis of their chemical behavior, and to investigate the quantitative applicability of the HSAB principle. Exchange acid-base reactions have been used to test the HSAB principle assuming the reaction energies as a measure of the stabilization of product adducts.     

A linearized compact difference scheme for a class of nonlinear delay partial differential equations

A linearized compact difference scheme is presented for a class of nonlinear delay partial differential equations with initial and Dirichlet boundary conditions. The unique solvability, unconditional convergence and stability of the scheme are proved. The convergence order is O(τ²+h⁴)$O({\tau }^2+h^4)$ in _L∞$L_{\infty }$ norm. Finally, a numerical example is given to support the theoretical results.     

A meshless method for Burgers’ equation using MQ-RBF and high-order temporal approximation

In this paper, a new numerical method is proposed to solve one-dimensional Burgers’ equation using multiquadric (MQ) radial basis function (RBF) for spatial approximation and a second-order compact finite difference scheme for temporal approximation. The numerical results obtained by this way for different Reynolds number have been compared with the existing numerical schemes to show the accuracy and efficiency of the approach. To show the superiority of this meshless method, numerical experiments with non-uniform MQ interpolation node distribution are also performed.     

Cone Length for DG Modules and Global Dimension of DG Algebras

As the definition of free class of differential modules over a commutative ring in [1 Avramov , L. L. , Buchweitz , R.-O. , Iyengar , S. ( 2007 ). Class and rank of differential modules . Invent. Math. 169 : 1 – 35 .[Crossref], [Web of Science ®] , [Google Scholar]], we define DG free class for semifree DG modules over an Adams connected DG algebra A. For any DG A-modules M, we define its cone length as the least DG free classes of all semifree resolutions of M. The cone length of a DG A-module plays a similar role as projective dimension of a module over a ring does in homological ring theory. The left (resp., right) global dimension of an Adams connected DG algebra A is defined as the supremum of the set of cone lengths of all DG A-modules (resp., A ^op -modules). It is proved that the definition is a generalization of that of graded algebras. Some relations between the global dimension of H(A) and the left (resp. right) global dimension of A are discovered. When A is homologically smooth, we prove that the left (right) global dimension of A is finite and the dimension of D(A) and D ^c (A) are not bigger than the DG free class of a minimal semifree resolution X of the DG A ^e -module A.     

A Note on Compactly Generated Co-t-Structures

The idea of a co-t-structure is almost ‘dual’ to that of a t-structure, but with some important differences. This note establishes co-t-structure analogues of Beligiannis and Reiten's corresponding results on compactly generated t-structures.     

Quantum double constructions for compact quantum group

For a non-degenerate pair of compact quantum groups, we first construct the quantum double as an algebraic compact quantum group in an algebraic framework. Then by adopting some completion procedure, we give the universal and reduced quantum double constructions in the correspondence C＊-algebraic settings, which generalize Drinfeld＇s quantum double construction and yield new C＊-algebraic compact quantum groups.     

不可压磁流体力学方程组的高精度数值解法

为数值求解低雷诺数下不可压流体在电磁场作用下的流动,提出一种四阶紧致差分方法.由二维原始变量的MHD方程组出发,推导出具有较少未知量的电流密度-涡量-流函数形式MHD方程组.建立了求解二维非定常不可压MHD方程组的电流密度-涡量-流函数形式的四阶精度紧致差分格式.为验证本文提出的高精度紧致差分方法的精确性和可靠性,对有...     

Determination of Hg and Pb in compact fluorescent lamp by slurry sampling inductively coupled plasma optical emission spectrometry

Mercury and lead were determined in an extraction solution applied to compact fluorescent lamps by axial view inductively coupled plasma optical emission spectrometry (ICP OES). The solution contained 50% v/v HNO₃ and 10% v/v H₂O₂. The compact fluorescent lamps were treated by removing the socket and breaking the rest of the lamp inside the solution, followed by placing the mixture in an ultrasonic bath for 1 h. The mixture was filtrated in a coarse paper filter and the resulting extraction slurry was analyzed. The determination of Pb in the slurry required calibration by the analyte addition technique, while for Hg, external calibration was adequate. The quantification limits (10 s, n = 7), for Hg (194.164 nm) and Pb (220.353 nm) were, respectively, 10 and 30 µg per lamp. Analysis of spiked samples demonstrated reasonable accuracy of the method, with recoveries in the range from 99 to 120% for Hg and from 91 to 107% for Pb. Fifteen analyzed samples showed Hg masses per lamp in the range from 1.6 to 27 mg, and six samples were above the limit allowed by the European Community that is 5 mg per compact lamp. The values for Pb were between 0.07 and 0.75 mg per lamp. By filtrating the slurry in a membrane filter, and analyzing the resulting solution, it was found that all Hg was extracted to the liquid phase of the slurry, while a fraction of about 40% m/v of Pb is retained in the solid particles. The lamp cover glass, after extraction of the phosphor layer, was also analyzed for Hg and Pb. The concentration of Hg in the glass is quite low; however, the Pb content is high.     

Quasi‐convexly dense and suitable sets in the arc component of a compact group

Let G be an abelian topological group. The symbol $\widehat{G}Let G be an abelian topological group. The symbol $\widehat{G}$ denotes the group of all continuous characters $\chi :G\rightarrow {\mathbb T}$ endowed with the compact open topology. A subset E of G is said to be qc‐dense in G provided that χ(E)?φ([? 1/4, 1/4]) holds only for the trivial character $\chi \in \widehat{G}$, where $\varphi : {\mathbb R}\rightarrow {\mathbb T}={\mathbb R}/{\mathbb Z}$ is the canonical homomorphism. A super‐sequence is a non‐empty compact Hausdorff space S with at most one non‐isolated point (to which S converges). We prove that an infinite compact abelian group G is connected if and only if its arc component G_a contains a super‐sequence converging to 0 that is qc‐dense in G. This gives as a corollary a recent theorem of Außenhofer: For a connected locally compact abelian group G, the restriction homomorphism $r:\widehat{G}\rightarrow \widehat{G}_a$ defined by $r(\chi )=\chi \upharpoonright _{G_a}$ for $\chi \in \widehat{G}$, is a topological isomorphism. We show that an infinite compact group G is connected if and only if its arc component G_a contains a super‐sequence converging to the identity that is qc‐dense in G and generates a dense subgroup of G. We also offer a short alternative proof of the result of Hofmann and Morris on the existence of suitable sets of minimal size in the arc component of a compact connected group.