Regulating the slow magnetic relaxation behavior of two different shapes Dy4 clusters with in situ formed penta- and heptadentate Schiff base ligands

The design and synthesis of clusters possessing the same number of cores but different connection methods and properties have always been difficult. Herein, we used 2-pyridinaldehyde, 1,3-diamino-2-propanol, and Dy (ClO₄)₃·6H₂O at room temperature (RT) to obtain the cluster [Dy₄(L¹)₄(μ₂-OH)₄]·4ClO₄⁻ ( 1 , HL¹ = 2-pyridinecarboxaldehyde-1,3-diamino-2-propanol) with square Dy₄O₈ cluster cores. Cluster 1 consisted of four Schiff base ligands (L¹)⁻, four Dy(III) ions, four bridged (μ₂-OH)⁻, and four free ClO₄⁻. The ligand HL¹ was formed by in situ Schiff base reaction with 2-pyridinecarbaldehyde and 1,3-diamino-2-propanol in the presence of Dy(III) ions. 2-Aldehyde-8-hydroxyquinoline, 1,3-diamino-2-propanol, and Dy (NO₃)₃·6H₂O reacted at RT to yield a tetranuclear Dy(III) cluster [Dy₄(L²)₂(μ₃-OH)₂(NO₃)₄(EtOH)₂]·2CH₃CN ( 2 , H₃L² = 2-aldehyde-8-hydroxyquinoline-1,3-diamino-2-propanol) with butterfly-shaped Dy₄O₆ cluster core. Cluster 2 consisted of two ligands (L²)³⁻, four Dy(III) ions, two bridged μ₃-OH, two end-group-coordinated ethanol molecules, and four bidentate-chelated NO₃⁻. The in situ reaction of 2-aldehyde-8-hydroxyquinoline and 1,3-diamino-2-propanol under Dy(III) ion-assisted catalytic conditions provided the ligand H₃L². It is worth noting that the magnetic test showed that 1 is a typical single-molecule magnet (SMM), whereas 2 only showed a significant frequency dependence behavior. We considered Orbach and Raman processes (τ⁻¹ = τ₀⁻¹ exp(−U_eff/k_BT) + CTⁿ) to fit 1 and 2 in the high-temperature range and obtained U_eff = 7.01 and 5.43 K and τ₀ = 1.18 × 10⁻⁴ and 4.14 × 10⁻⁵ s, respectively.     

Interval analysis of nonlinear frames with uncertain connection properties

Semi-rigid connections can often be a more economical solution for a framing system than one with either fully fixed connections or fully pinned ones. In view of the fact that the properties of such ductile and partial-strength connections are not known accurately, this paper presents a method for the obtention of both upper and lower bound responses of semi-rigid frames for possible variations in their moment-rotation properties. The latter are thus assumed to be known within some key upper and lower bound values, namely a constitutive law that is still deterministic but is described in terms of a so-called “interval” model. A mathematical programming approach is used to formulate and solve the problem. In particular, for each load level, a pair of nonstandard optimization problems known as interval mathematical programs with equilibrium constraints (or interval MPECs) are solved to provide the required bounds. A number of examples are provided to highlight the important effects of considering uncertainties in semi-rigid connection properties.     

板柱节点抗冲切性能分析的力学转化模型

提出了一种基于力学转化模型的钢筋混凝土板柱节点抗冲切性能分析方法,该方法能够将传统弹性力学的研究问题用结构力学模型解决. 通过OpenSees (Open System for Earthquake Engineering Simulation)计算平台进行建模,根据数值分析和试验结果的对比,确定和验证模型中的关键参数. 结果表明,该数值模型能够很好模拟板柱节点的抗冲切性能,包括载荷-变形响应、刚度变化规律及变形分布规律等,为全面认识板柱节点的工作机理、受力特征及内力分布规律提供新的研究途径,同时为工程设计与实践提供理论指导.     

The Balian–Low theorem and noncommutative tori

We point out a link between the theorem of Balian and Low on the non-existence of well-localized Gabor–Riesz bases and a constant curvature connection on projective modules over noncommutative tori.     

Einstein Gravity in Almost Kähler Variables and Stability of Gravity with Nonholonomic Distributions and Nonsymmetric Metrics

We argue that the Einstein gravity theory can be reformulated in almost Kähler (nonsymmetric) variables with effective symplectic form and compatible linear connection uniquely defined by a (pseudo) Riemannian metric. A class of nonsymmetric theories of gravitation on manifolds enabled with nonholonomic distributions is considered. We prove that, for certain types of nonholonomic constraints, there are modelled effective Lagrangians which do not develop instabilities. It is also elaborated a linearization formalism for anholonomic noncommutative gravity theories models and analyzed the stability of stationary ellipsoidal solutions defining some nonholonomic and/or nonsymmetric deformations of the Schwarzschild metric. We show how to construct nonholonomic distributions which remove instabilities in nonsymmetric gravity theories. It is concluded that instabilities do not consist a general feature of theories of gravity with nonsymmetric metrics but a particular property of some models and/or unconstrained solutions.     

Nonholonomic Ricci Flows, Exact Solutions in Gravity, and?Symmetric and Nonsymmetric Metrics

We provide a proof that nonholonomically constrained Ricci flows of (pseudo) Riemannian metrics positively result into nonsymmetric metrics (as explicit examples, we consider flows of some physically valuable exact solutions in general relativity). There are constructed and analyzed three classes of solutions of Ricci flow evolution equations defining nonholonomic deformations of Taub NUT, Schwarzschild, solitonic and pp-wave symmetric metrics into nonsymmetric ones.     

Addendum to: “Ricci-flat holonomy: A classification” [J. Geom. Phys. 57 (6) 1457–1475]: The case of spin(10)

This note fills a hole in the author’s previous paper “Ricci-flat holonomy: A classification”, by dealing with irreducible holonomy algebras that are subalgebras or real forms of C⊕spin(10,C)$\mathbb{C}\oplus \mathfrak{s}\mathfrak{p}\mathfrak{i}\mathfrak{n}(10,\mathbb{C})$. These all turn out to be of Ricci type.     

Connections with prescribed first Pontrjagin form

Let be a principal bundle over a manifold of dimension . If , then we prove that every differential 4-form representing the first Pontrjagin class of is the Pontrjagin form of some connection on .