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

Electronic structure of linear thiophenolate-bridged heteronuclear complexes [LFeMFeL](n)(+) (M = Cr, Co, Fe; n = 1-3): a combination of kinetic exchange interaction and electron delocalization

The electronic properties of the isostructural series of heterotrinuclear thiophenolate-bridged complexes of the general formula [LFeMFeL](n)(+) with M = Cr, Co and Fe where L represents the trianionic form of the ligand 1,4,7-tris(4-tertbutyl-2-mercaptobenzyl)-1,4,7-triazacyclononane, synthesized and investigated by a number of experimental techniques in the previous work(1), are subjected now to a theoretical analysis. The low-lying electronic excitations in these compounds are described within a minimal model supported by experiment and quantum chemistry calculations. It was found indeed that various experimental data concerning the magnetism and electron delocalization in the lowest states of all seven compounds are completely reproduced within a model which includes the electron transfer between magnetic orbitals at different metal centers and the electron repulsion in these orbitals (the Hubbard model). Moreover, due to the trigonal symmetry of the complexes, only the electron transfer between nondegenerate orbital, a(1), originating from the t(2g) shell of each metal ion in a pseudo-octahedral coordination, is relevant for the lowest states. An essential feature resulting from quantum chemistry calculations, allowing to explain the unusual magnetic properties of these compounds, is the surprisingly large value and, especially, the negative sign of the electron transfer between terminal iron ions, beta'. According to their electronic properties the series of complexes can be divided as follows: (1). The complexes [LFeFeFeL](3+) and [LFeCrFeL](3+) show localized valences in the ground electronic configuration. The strong antiferromagnetic exchange interaction and the resulting spin 1/2 of the ground-state arise from large values of the transfer parameters. (2). In the complex [LFeCrFeL](+), due to a higher energy of the magnetic orbital on the central Cr ion than on the terminal Fe ones, the spin 3/2 and the single unpaired a(1) electron are almost localized at the chromium center in the ground state. (3). The complex [LFeCoFeL](3+) has one ground electronic configuration in which two unpaired electrons are localized at terminal iron ions. The ground-state spin S = 1 arises from a kinetic mechanism involving the electron transfer between terminal iron ions as one of the steps. Such a mechanism, leading to a strong ferromagnetic interaction between distant spins, apparently has not been discussed before. (4). The complex [LFeFeFeL](2+) is characterized by both spin and charge degrees of freedom in the ground manifold. The stabilization of the total spin zero or one of the itinerant electrons depends on beta', i.e., corresponds to the observed S = 1 for its negative sign. This behavior does not fit into the double exchange model. (5). In [LFeCrFeL](2+) the delocalization of two itinerant holes in a(1) orbitals takes place over the magnetic core of chromium ion. Although the origin of the ground-state spin S = 2 is the spin dependent delocalization, the spectrum of the low-lying electronic states is again not of a double exchange type. (6). Finally, the complex [LFeCoFeL](2+) has the ground configuration corresponding to the electron delocalization between terminal iron atoms. The estimated magnitude of the corresponding electron transfer is smaller than the relaxation energy of the nuclear distortions induced by the electron localization at one of the centers, leading to vibronic valence trapping observed in this compound.     

Synthesis, crystal structures and magnetic properties of cyanide- and phenolate-bridged [M(III)NiII]2 tetranuclear complexes (M=Fe and Cr)

The binuclear complex NiII2L(H2O)2(ClO4)2(1) and the neutral tetranuclear bimetallic compounds [{M(III)(phen)(CN)4}2{NiII2L(H2O)2}].2CH3CN with M=Fe (2) and Cr (3)[H2L=11,23-dimethyl-3,7,15,19-tetraazatricyclo[19.3.1.1(9,13)]hexacosa-2,7,9,11,13(26),14,19,21(25),22,24-decaene-25,26-diol] have been synthesized and the structures of and determined by single crystal X-ray diffraction. and are isostructural compounds whose structure is made up of centrosymmetric binuclear cations [Ni2(L)(H2O)2]2+ and two peripheral [M(phen)(CN)4]- anions [M=Fe (2) and Cr (3)] acting as monodentate ligands towards the nickel atoms through one of their four cyanide nitrogen atoms. The environment of the metal atoms in 2 and 3 is six-coordinated: two phen-nitrogen and four cyanide-carbon atoms at the iron and chromium atoms and a water molecule, one cyanide-nitrogen and two phenolate-oxygens and two imine-nitrogens from the binucleating ligand L2- at the nickel atom build distorted octahedral surroundings. The values of the FeNi and CrNi separations through the single cyanide bridge are 5.058(1) and 5.174(2)A respectively, whereas the Ni-Ni distances across the double phenolate bridge are 3.098(2)(2) and 3.101(1) A (3). The magnetic properties of have been investigated in the temperature range 1.9-290 K. The magnetic behaviour of corresponds to that of an antiferromagnetically coupled nickel(II) dimer with J=-61.0(1) cm-1, the Hamiltonian being defined as H=-J S(A).S(B). An overall antiferromagnetic behaviour is observed for and with a low-lying singlet spin state. The values of the intramolecular magnetic couplings are J(Fe-Ni)=+17.4(1) cm-1 and J(Ni-Ni(a))=-44.4(1) cm-1 for and J(Cr-Ni)=+11.8(1) cm-1 and J(Ni-Ni(a))=-44.6(1) cm-1 for [H=-J(M-Ni)(S(M).S(Ni)+S(Ma).S(Nia))-J(Ni-Nia)S(Ni)S(Nia)]. Theoretical calculations using methods based on density functional theory (DFT) have been employed on in order to analyze the efficiency of the exchange pathways involved and also to substantiate the exchange coupling parameters.     

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.     

Compact eye-safe laser sources based on OPOs with KTP or PPKTP crystals

We report on compact eye-safe nanosecond laser sources emitting in the 1.5 μm wavelength range based on non-critically phase-matched parametric interaction in optical parametric oscillators (OPOs) with KTP and periodically poled KTP (PPKTP) crystals, pumped by the fundamental frequency of Nd:YAG lasers. As much as 250 μJ signal pulse energy at 1.5 μm wavelength, 6.5 ns FWHM pulse-width, has been obtained in a PPKTP-OPO, extracavity pumped by a Nd:YAG microlaser oscillator–amplifier at 650 μJ pump pulse energy, 8 ns pulse-width. A single signal pulse of 2.7-mJ output energy at 1.57 μm wavelength, less than 5 ns pulse-width, was generated in a KTP-OPO, intracavity pumped by a passively Q-switched Nd:YAG laser.     

Three-dimensional noncollinear antiferromagnetic order in single-crystalline FeMn ultrathin films

We present experimental evidence for a three-dimensional noncollinear antiferromagnetic spin structure in ultrathin single-crystalline fcc Fe50Mn50 layers using magnetic circular dichroism photoelectron emission microscopy and x-ray magnetic linear dichroism. Layer-resolved as-grown domain images of epitaxial trilayers grown on Cu(001) in which FeMn is sandwiched between ferromagnetic layers with different easy axes reveal the presence of antiferromagnetic spin components in the film plane and normal to the film plane. An FeMn spin structure with no collinear order in the film plane is consistent with the absence of x-ray magnetic linear dichroism in Fe L3 absorption in FeMn/Co bilayers.