Hydroquinone-bridged dinuclear Cu(II) complexes and single-crystalline Cu(II) coordination polymers

Cationic dinuclear Cu(II) complexes 3 and 4 have been prepared using the novel hydroquinone-based imine chelators 2,5-((i)Pr(2)NCH(2)CH(2)N[double bond, length as m-dash]CH)(2)-1,4-(OH)(2)-C(6)H(2) (1) and 2,5-(pyCH(2)CH(2)N[double bond, length as m-dash]CH)(2)-1,4-(OH)(2)-C(6)H(2) (2), respectively (py = 2-pyridyl). X-Ray quality crystals of both complexes were grown from their DMF solutions. The sterically more encumbered compound crystallizes in the form of discrete dinuclear entities with Cu(II) centres in a distorted square-planar ligand environment (one coordination site is occupied by a DMF molecule). The pyridyl derivative 4 features dinuclear hydroquinone-bridged subunits similar to 3. However, the Cu(II) ions are now six-coordinate with two DMF molecules at an axial and an equatorial position of a Jahn-Teller-distorted octahedron. Moreover, the dinuclear subunits are no longer isolated but linked with each other via bridging hydroquinone oxygen atoms which occupy the second apical position of each octahedron. The structure suggests that the magnetic properties of the resulting coordination polymer of 4 could be described by a model valid for dimerized spin chains. As a result of this analysis the antiferromagnetic coupling constants J(1)/k(B) = 9.9 K (intradimer) and J(2)/k(B) = 0.9 K (interdimer) are obtained. Both in 3 and in 4, the hydroquinone --> semiquinone transition of the central bridging unit (E degrees ' = + 0.57 V, 3; E degrees ' = + 0.51 V, 4; DMF; vs. SCE) displays features of chemical reversibility. In the case of , reduction of Cu(II) centres requires a peak potential of E(p) = - 0.42 V.     

On some sharp weighted norm inequalities

Given a weight ω, we consider the space which coincides with when ω∈A_p. Sharp weighted norm inequalities on for the Calderón-Zygmund and Littlewood-Paley operators are obtained in terms of the A_p characteristic of ω for any 1<p<∞.     

基于惩罚与补贴的再制造闭环供应链网络均衡模型

为研究我国废旧电子产品(WEEE)立法的问题,分析了供应商、制造商、零售商、需求市场及回收商的行为,分别建立了变分不等式模型,并在此基础上建立了五级再制造闭环供应链网络均衡模型。模型考虑了政府对于制造商的惩罚政策与对于回收商的补贴政策。通过修正投影算法求解算例,仿真分析了旧材料转化率、回收率、惩罚及补贴政策对闭环供应链网络均衡结果的影响。结果表明,随着政府对于回收商的补贴的增加,不但回收商的回收量提高,闭环供应链的新材料需求量、旧材料需求量、销售量均增加;相反,随着政府对于制造商未完成的回收量的罚款增加,回收量、新材料需求量、旧材料需求量、销售量均降低;追求高回收率的政策并不总是有效的;而提高WEEE的旧材料转化率对于闭环供应链有利。     

On an estimate of Calderón-Zygmund operators by dyadic positive operators

Given a general dyadic grid D and a sparse family of cubes S = {Q _j ^k ∈ D, define a dyadic positive operator A _D,S by $${A_{D,S}}f(x) = \sum\limits_{j,k} {{f_{Q_j^k}}{\chi _{Q_j^k}}} (x)$$ . Given a Banach function space X(? ⁿ ) and the maximal Calderón-Zygmund operator ${T_\natural }$ , we show that $${\left\| {{T_\natural}f} \right\|_X} \leqslant c(T,n)\mathop {\sup }\limits_{D,S} {\left\| {{A_{D,S}}|f|} \right\|_X}$$ This result is applied to weighted inequalities. In particular, it implies (i) the “twoweight conjecture” by D. Cruz-Uribe and C. Pérez in full generality; (ii) a simplification of the proof of the “A ₂ conjecture”; (iii) an extension of certain mixed A _p ?A _r estimates to general Calderón-Zygmund operators; (iv) an extension of sharp A ₁ estimates (known for T ) to the maximal Calderón-Zygmund operator $\natural $ .     

Spectral and phase space analysis of the linearized non-cutoff Kac collision operator

The non-cutoff Kac operator is a kinetic model for the non-cutoff radially symmetric Boltzmann operator. For Maxwellian molecules, the linearization of the non-cutoff Kac operator around a Maxwellian distribution is shown to be a function of the harmonic oscillator, to be diagonal in the Hermite basis and to be essentially a fractional power of the harmonic oscillator. This linearized operator is a pseudodifferential operator, and we provide a complete asymptotic expansion for its symbol in a class enjoying a nice symbolic calculus. Related results for the linearized non-cutoff radially symmetric Boltzmann operator are also proven.     

The Twinned Crystal Structure of Zinc(II) Acetylacetonate Trimer

Abstract  The crystal structure of the title compound, C₃₀H₄₂O₁₂Zn₃, originally determined from untwinned crystals (Bennett et al. Acta Cryst B 24:904, 1968) has been redetermined from twinned crystals. The effect of the twinning is that additional reflections appear in the diffraction pattern leading to a unit cell with a too long c-axis in which the structure cannot be solved. Thus, for a successful structure solution the correct unit cell has to be found and for refinement the twinning has to be taken into account. The central Zn atom is located on a twofold rotation axis. It is hexacoordinated in a distorted octahedral mode, whereas the coordination geometry of the two terminal Zn atoms is distorted trigonal bipyramidal. Index Abstract  The crystal structure of the title compound, Zinc(II) acetylacetonate trimer, has been redetermined from twinned crystals. For a successful structure solution the correct unit cell had to be found and for refinement the twinning had to be taken into account. The central Zn atom is located on a twofold rotation axis. It is hexacoordinated in a distorted octahedral mode, whereas the coordination geometry of the two terminal Zn atoms is distorted trigonal bipyramidal. An erratum to this article can be found at