Interval Reductions and Extensions of Orders: Bijections to Chains in Lattices

We discuss bijections that relate families of chains in lattices associated to an order P and families of interval orders defined on the ground set of P. Two bijections of this type have been known:(1) The bijection between maximal chains in the antichain lattice A(P) and the linear extensions of P.(2) The bijection between maximal chains in the lattice of maximal antichains A_M(P) and minimal interval extensions of P.We discuss two approaches to associate interval orders with chains in A(P). This leads to new bijections generalizing Bijections 1 and 2. As a consequence, we characterize the chains corresponding to weak-order extensions and minimal weak-order extensions of P.Seeking for a way of representing interval reductions of P by chains we came upon the separation lattice S(P). Chains in this lattice encode an interesting subclass of interval reductions of P. Let S_M(P) be the lattice of maximal separations in the separation lattice. Restricted to maximal separations, the above bijection specializes to a bijection which nicely complements 1 and 2.(3) A bijection between maximal chains in the lattice of maximal separations S_M(P) and minimal interval reductions of P.     

Experimental evaluation of nonlinearities of small-sized insertable gradient coils

A phase imaging technique is proposed to map out and quantify gradient nonlinearities of small-sized insertable gradient coils, assuming the whole-body system gradients are highly linear in the domain of interest. The theory is developed and simple equations are derived to allow quantification. It is applied to a 4-loop 18-cm diameter cylindrical gradient coil of optimal design. Experimental gradient nonlinearity maps are obtained for different fields of view. Gradient non-linearities are quantified locally and in regions of interest, showing close agreement with model data.     

The use of PDE centres in the local RBF Hermitian method for 3D convective-diffusion problems

In this work an extension is proposed to the Local Hermitian Interpolation (LHI) method; a meshless numerical method based on interpolation with small and heavily overlapping radial basis function (RBF) systems. This extension to the LHI method uses interpolation functions which themselves satisfy the partial differential equation (PDE) to be solved. In this way, a much improved reconstruction of partial derivatives can be obtained, resulting in significantly improved accuracy in many cases.     

A note on the structure of spaces of domino tilings

We study spaces of tilings, formed by tilings which are on a geodesic between two fixed tilings of the same domain (the distance is defined using local flips). We prove that each space of tilings is homeomorphic to an interval of tilings of a domain when flips are classically directed by height functions.     

Numerical modeling of coherent structures attendant on impurity propagation in the atmospheric boundary layer over a forest canopy

Three-dimensional large eddy simulation is used to solve the problem for a homogeneous forest canopy. The development of the Kelvin-Helmholtz instability above the canopy leads to the formation of coherent structures in the atmosphere flow, which are reproduced in the calculations. The statistical characteristics of the flow obtained from the numerical modeling are compared with experimental data. The passive admixture transfer from the canopy to the clean atmosphere is studied for two cases, namely, for constant and variable coupled concentration of the impurity in the canopy.     

Modeling [FeFe] hydrogenase: Synthesis and protonation of a diiron dithiolate complex containing a phosphine-N-heterocyclic-carbene ligand

The ligand exchange reaction of I_Me-(CH₂)₂-PPh₂ (I_Me = 1-methyimidazol-2-ylidene) and the hexacarbonyl complex [{Fe₂{μ-S(CH₂)₃S}(CO)₆] (1) resulted in the formation of the chelated complex [{Fe₂{μ-S(CH₂)₃S}(CO)₄(I_Me-(CH₂)₂-PPh₂)] (2). The molecular structure of 2 was confirmed by spectroscopic and X-ray analyses. This complex catalyzes proton reduction. Low temperature NMR studies on the protonation of 2 revealed the formation of a terminal hydride intermediate.     

Chemical vapor deposition and electric characterization of perovskite oxides LaMO3 (M=Co, Fe, Cr and Mn) thin films

Oxides with a perovskite structure are important functional materials often used for the development of modern devices. In view of extending their applicability, it is necessary to efficiently control their growth as thin films using technologically relevant synthesis methods. Pulsed spray evaporation CVD was used to grow several perovskite-type oxides on planar silicon substrates at temperatures ranging from 500 to 700 °C. The optimization of the process control parameters allows the attainment of the perovskite structure as a single phase. The electrical characterization using the temperature-dependent conductivity and thermopower indicates the p-type conduction of the grown films and shows a decreasing concentration of the charge carrier, mobility and band gap energy in the sequence LaCoO₃>LaMnO₃>LaCrO₃>LaFeO₃. The investigation of the electric properties of the obtained perovskite thin films shows the versatility of CVD as a method for the development of innovative devices.     

Heat‐Triggered Crystallization of Liquid Crystalline Macrocycles Allowing for Conductance Switching through Hysteretic Thermal Phase Transitions

A polymesomorphic thermal phase‐transition of a macrocyclic amphiphile consisting of aromatic groups and oligoethylene glycol (OEG) chains is reported. The macrocyclic amphiphile exists in a highly‐ordered liquid crystal (LC) phase at room temperature. Upon heating, this macrocycle shows phase‐transition from columnar‐lamellar to nematic LC phases followed by crystallization before melting. Spectroscopic studies suggest that the thermally induced crystallization is triggered by a conformational change at the OEG chains. Interestingly, while the macrocycle returns to the columnar‐lamellar phase after cooling from the isotropic liquid, it retains the crystallinity after cooling from the thermally‐induced crystal. Thanks to this bistability, conductance switching was successfully demonstrated. A different macrocyclic amphiphile also shows an analogous phase‐transition behavior, suggesting that this molecular design is universal for developing switchable and memorizable materials, by means of hysteretic phase‐transition processes.     

Algebraic K-Theory In Low Degree and The Novikov Assembly Map

We prove that the Novikov assembly map for a group factorizes,in ‘low homological degree’, through the algebraicK-theory of its integral group ring. In homological degree 2,this answers a question posed by N. Higson and P. Julg. As adirect application, we prove that if is torsion-free and satisfiesthe Baum-Connes conjecture, then the homology group H₁(; Z)injects in and in , for any ring A such that . If moreover B is of dimension lessthan or equal to 4, then we show that H₂(; Z) injects in and in , where A is as before, and ₂ is generated by the Steinberg symbols{,}, for . 2000 Mathematical Subject Classification: primary 19D55, 19Kxx,58J22; secondary: 19Cxx, 19D45, 43A20, 46L85.