Magnetic anisotropy in the excited states of low symmetry lanthanide complexes

Ab initio investigation of multiplet spectrum of lanthanides in archetypal coordination geometries shows an unexpected regular structure consisting of (i) mirror symmetry of anisotropic magnetic properties of doublet states, (ii) high magnetic axiality of low-lying and high-lying doublets, comparable to complexes with ideal axial symmetry, and (iii) the strong rotation of the anisotropy axes of individual doublets. The obtained high axiality of the ground doublet states explains the SMM behaviour of low-symmetry lanthanide complexes.     

Supramolecular “Double‐Propeller” Dimers of Hexanuclear CuII/LnIII Complexes: A {Cu3Dy3}2 Single‐Molecule Magnet

Propelling magnetism : Supramolecular organization leads to a remarkable dodecanuclear {Cu₃Dy₃}₂ cluster with a “double–propeller” shape (see picture). The linkages of the CuDy units, both intramolecular and supramolecular, appear to be responsible for a drastic change in the single molecule magnetic behavior.

     

On exact 2-para Sasakian manifolds

Paracontact and para Sasakian manifoldsM carryingr(1<r≤dimM) Reed vector filds ξ _r have been especially studied by A. Bucki [2], [3], [4]. In the present paper, we consider a (2m+2)-dimensional para Sasakian manifoldM(ϕ, ξ _r , η ^r g), whose Reed convectors η ^r =ξ _r ^b are exact 1-forms and the covariant derivatives of ξ _r are given by ∇ξ _r =f _r dp ^⊺, wheredp ^⊤ means the horizontal component of the soldering formdp andf _r∈C^∞M satisfydf _r =cη ^r ,c=constant. It is proved that such a manifold may be viewed as the local Riemannian productM=M ^⊥×M^⊤, where

Inclusion of C60 into an adjustable porphyrin dimer generated by dynamic disulfide chemistry

A new, highly flexible porphyrin dimer was isolated in preparative scale from a dynamic disulfide library; this receptor adjusts to fit guests with a wide range of steric requirements and, whilst C60 proved to be an unsuitable template for this library, a new C60-porphyrin complex was isolated and characterised.     

Unified application of the coupling model to segmental, Rouse, and terminal dynamics of entangled polymers

The temperature dependence and relaxation function breadth of segmental dynamics (α-relaxation) for 1,2-polybutadiene and 1,4-polybutadiene are used to predict their respective temperature-dependent terminal relaxation times by unified application of the Ngai coupling model. Literature results for the terminal flow of near-monodisperse linear polybutadienes having widely varying molecular weights are successfully represented using the coupling model by variation of only a single parameter, C, which is the proportionality constant between the longest Rouse relaxation time and the primitive relaxation time which underlies the cooperative segmental process. The value of C varies with molecular weight (M) according to C ∝ M^b where b is found to range from 1.8 to 2.1, in close agreement with the expected exponent of 2. Contrary to experimental data and coupling model predictions, reptation theory predicts identical influences of temperature on Rouse and terminal relaxation processes; we suggest that invoking a temperature dependence for contour length fluctuations, and hence number of effective entanglements per chain, may resolve this deficiency of the tube model.     

Stability of the periodic motions of the vibro-impact systems

In many other papers a new direct method is developed for the study of vibro-impact system stability, a case in which the stability conditions are directly and rapidly obtained. This new method is stated and applied for systems with one or several degrees of freedom whose motion is analysed by Lagrange's equations. Thus, the equations in variations determined from the differential equations are considered, which by applying the boundary conditions lead by integration to the linearized equation in perturbations necessary to write the stability conditions. As example, is analysed in detail a particular case with one degree of freedom realised by the rod-crank mechanism. Also, a general system with two degrees of freedom is completely studied.     

Morse functions statistics

We answer a question of Arnold concerning the growth rate of the number of Morse functions on the two-sphere. This work was supported in part by the NSF (Grant No. DMS-0303601).     

A nonlocal convection-diffusion equation

In this paper we study a nonlocal equation that takes into account convective and diffusive effects, ut=J∗u−u+G∗(f(u))−f(u) in Rd, with J radially symmetric and G not necessarily symmetric. First, we prove existence, uniqueness and continuous dependence with respect to the initial condition of solutions. This problem is the nonlocal analogous to the usual local convection-diffusion equation ut=Δu+b⋅∇(f(u)). In fact, we prove that solutions of the nonlocal equation converge to the solution of the usual convection-diffusion equation when we rescale the convolution kernels J and G appropriately. Finally we study the asymptotic behaviour of solutions as t→∞ when f(u)=|u|^q−1u with q>1. We find the decay rate and the first-order term in the asymptotic regime.