A cyclic hexacopper(II) fluoro complex that encapsulates two fluoride anions

The complex [[Cu3(HpztBu)4(mu-pztBu)2(mu-F)2(mu 3-F)]2]F2 (HpztBu = 3[5]-tert-butylpyrazole) has a cyclic, C2v-symmetric hexacopper core. The two non-coordinated F- anions are encapsulated within cavities formed by three HpztBu ligands.     

Phase-object analysis with a speckle interferometer

We describe the characteristics of a double-exposure specklegram obtained through a double-aperture system, by introduction of a wedge in front of one aperture in one exposure. It is assumed that a uniform displacement of the diffuser is produced between exposures. The average intensity distribution and visibility of the interferometric fringes in the Fourier plane are analyzed. An alternative interferometric technique for phase-object detection is proposed.     

A correction algorithm for undersampled images using dynamic segmentation and entropy based focus criterion

A post-processing technique is presented for correcting images undersampled in k-space. The method works by taking advantage of the image's background zeros (dynamically segmented through the application of a threshold) to extrapolate the missing k-space samples. The algorithm can produce good quality images from a small set of k-space frequencies with only a few iterations of simple matrix operations, using the image entropy as the focus criterion. It does not require any special patient preparation, extra pulse sequences, complex gradient programming or specialized hardware. This makes it a good candidate for any application that requires short scan times or where only few frequencies can be sampled.     

Noise- and inertia-induced inhomogeneity in the distribution of small particles in fluid flows

The dynamics of small spherical neutrally buoyant particulate impurities immersed in a two-dimensional fluid flow are known to lead to particle accumulation in the regions of the flow in which vorticity dominates over strain, provided that the Stokes number of the particles is sufficiently small. If the flow is viewed as a Hamiltonian dynamical system, it can be seen that the accumulations occur in the nonchaotic parts of the phase space: the Kolmogorov-Arnold-Moser tori. This has suggested a generalization of these dynamics to Hamiltonian maps, dubbed a bailout embedding. In this paper we use a bailout embedding of the standard map to mimic the dynamics of neutrally buoyant impurities subject not only to drag but also to fluctuating forces modeled as white noise. We find that the generation of inhomogeneities associated with the separation of particle from fluid trajectories is enhanced by the presence of noise, so that they appear in much broader ranges of the Stokes number than those allowing spontaneous separation. (c) 2002 American Institute of Physics.     

Imaging the neural circuitry and chemical control of aggressive motivation

Background  

With the advent of functional magnetic resonance imaging (fMRI) in awake animals it is possible to resolve patterns of neuronal activity across the entire brain with high spatial and temporal resolution. Synchronized changes in neuronal activity across multiple brain areas can be viewed as functional neuroanatomical circuits coordinating the thoughts, memories and emotions for particular behaviors. To this end, fMRI in conscious rats combined with 3D computational analysis was used to identifying the putative distributed neural circuit involved in aggressive motivation and how this circuit is affected by drugs that block aggressive behavior.     

A Semigroup Crossed Product Arising in Number Theory

Recently Bost and Connes have studied an interesting C*-algebraicHecke algebra arising in number theory. Here it is shown thatthis algebra can be realised as a semigroup crossed product,and be profitably studied using methods developed by the authorsfor analysing Toeplitz algebras. One main result is a characterisationof faithful representations of the Hecke algebra.     

A Bernstein type theorem on a Randers space

We consider Finsler spaces with a Randers metric F=+, on the three-dimensional real vector space, where is the Euclidean metric and is a 1-form with norm b,0 b1. By using the notion of mean curvature for immersions in Finsler spaces, introduced by Z. Shen, we obtain the partial differential equation that characterizes the minimal surfaces which are graphs of functions. For each b, 0 b1/, we prove that it is an elliptic equation of mean curvature type. Then the Bernstein type theorem and other properties, such as the nonexistence of isolated singularities, of the solutions of this equation follow from the theory developped by L. Simon. For b 1/, the differential equation is not elliptic. Moreover, for every b, 1/b1 we provide solutions, which describe minimal cones, with an isolated singularity at the origin.Partially supported by CAPES/PROCAD.Partially supported by NSF grant DMS-0072242.Partially supported by CNPq and CAPES/PROCAD.     

Existence and asymptotic stability for evolution problems on manifolds with damping and source terms

One considers the nonlinear evolution equation with source and damping terms

     

Liquid-vapor isotherm in a closed single-component system with droplets or bubbles in smooth crevices

A thermodynamic model in order to study a single-component system where droplets or bubbles are inside smooth crevices is presented. Liquid-vapor interface curvature radius can change its sign as the droplet or bubble volume change. The results suggest that there is always dispersed phase inside smooth crevices of microscopic dimensions, even in the expected single-phase region. Thus, the occurrence of an anti-ripening phenomenon is predicted from a microscopic point of view; meanwhile the occurrence of a ripening phenomenon is energetically favorable at a macroscopic scale. The relevance of these results on the heterogeneous nucleation process is analyzed.     

From Endomorphisms to Automorphisms and Back: Dilations and Full Corners

When S is a discrete subsemigroup of a discrete group G suchthat G = S^–1S, it is possible to extend circle-valuedmultipliers from S to G, to dilate (projective) isometric representationsof S to (projective) unitary representations of G, and to dilate/extendactions of S by injective endomorphisms of a C*-algebra to actionsof G by automorphisms of a larger C*-algebra. These dilationsare unique provided they satisfy a minimality condition. The(twisted) semigroup crossed product corresponding to an actionof S is isomorphic to a full corner in the (twisted) crossedproduct by the dilated action of G. This shows that crossedproducts by semigroup actions are Morita equivalent to crossedproducts by group actions, making powerful tools available tostudy their ideal structure and representation theory. The dilationof the system giving the Bost–Connes Hecke C*-algebrafrom number theory is constructed explicitly as an application:it is the crossed product C₀(A_f)Q*₊, corresponding to the multiplicativeaction of the positive rationals on the additive group A_f offinite adeles.