Sharp Lower Bounds for the Dimension of the Global Attractor of the Sabra Shell Model of Turbulence

In this work we derive lower bounds for the Hausdorff and fractal dimensions of the global attractor of the Sabra shell model of turbulence in different regimes of parameters. We show that for a particular choice of the forcing term and for sufficiently small viscosity term ν, the Sabra shell model has a global attractor of large Hausdorff and fractal dimensions proportional to log  ν ⁻¹ for all values of the governing parameter ε, except for ε =1. The obtained lower bounds are sharp, matching the upper bounds for the dimension of the global attractor obtained in our previous work. Moreover, the complexity of the dynamics of the shell model increases as the viscosity ν tends to zero, and we describe a precise scenario of successive bifurcations for different parameters regimes. In the “three-dimensional” regime of parameters this scenario changes when the parameter ε becomes sufficiently close to 0 or to 1. We also show that in the “two-dimensional” regime of parameters, for a certain non-zero forcing term, the long-term dynamics of the model becomes trivial for every value of the viscosity. AMS Subject Classifications: 76F20, 76D05, 35Q30     

Metabolic compartmentalization in the human cortex and hippocampus: evidence for a cell- and region-specific localization of lactate dehydrogenase 5 and pyruvate dehydrogenase

Background  

For a long time now, glucose has been thought to be the main, if not the sole substrate for brain energy metabolism. Recent data nevertheless suggest that other molecules, such as monocarboxylates (lactate and pyruvate mainly) could be suitable substrates. Although monocarboxylates poorly cross the blood brain barrier (BBB), such substrates could replace glucose if produced locally.     

A stochastic Lagrangian representation of the three‐dimensional incompressible Navier‐Stokes equations

In this paper we derive a probabilistic representation of the deterministic three‐dimensional Navier‐Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self‐contained proof of local existence for the nonlinear stochastic system and can be extended to formulate stochastic representations of related hydrodynamic‐type equations, including viscous Burgers equations and Lagrangian‐averaged Navier‐Stokes alpha models. © 2007 Wiley Periodicals, Inc.     

Synthesis, structure determination, and (radio-)fluorination of novel functionalized phosphanes suitable for the traceless Staudinger ligation

An elegant and efficient synthesis approach for the preparation of novel benzoate and nicotinate containing phosphanes is presented. This reaction path has a broad substrate scope. Thus, various functionalized phosphanes were obtained in high yields using an esterification procedure under Steglich conditions. A facile blocking of the phosphorus atom with BH₃ was carried out. BH₃ as easily insertable and removable protecting group enables a further derivatization of the benzoate residue. The prepared phosphane derivatives proved to be valuable labeling building blocks for the implementation of a bioorthogonal (radio-)fluorination strategy and were applied for labeling purposes using the traceless Staudinger ligation. For this purpose, a selection of azide-functionalized small organic and bioactive sample molecules was prepared. Furthermore, a mild and selective (radio-)fluorination of these derivatives is demonstrated adopting this bioorthogonal ligation method.     

Twisted equivariant K-theory with complex coefficients

Using a global version of the equivariant Chern character, wedescribe the complexified twisted equivariant K-theory of aspace with a compact Lie group action in terms of fixed-pointdata. We apply this to the case of a compact group acting onitself by conjugation and relate the result to the Verlindealgebra and to the Kac numerator at q=1. Verlinde's formulais also discussed in this context. Received February 28, 2007.     

A note on the second problem of Stokes for Maxwell fluids

New exact solutions corresponding to the second problem of Stokes for Maxwell fluids have been established by means of Laplace transforms. For large times, these solutions reduce to the well-known steady-state solutions which are periodic in time and independent of the initial conditions. Furthermore, the transient solutions are in accordance with the previous solutions obtained using the Fourier sine transform. The required time to get the steady-state is determined by graphical illustrations. This time decreases if the frequency of the velocity increases. The effects of the material parameters on the decay of the transients in time are also investigated by graphs.     

A multicriteria DSS for stock evaluation using fundamental analysis

The paper describes a multicriteria decision support system which aims at presenting an evaluation of the Athens Stock Exchange (ASE) stocks, on the basis of fundamental analysis. The system evaluates the stocks based on the method of fundamental analysis ratios, which is the most appropriate evaluation approach regarding investment decisions within a long term horizon. In addition to quantitative data deriving from fundamental analysis, the system uses qualitative data as well, in order to improve the reliability of the evaluation. The system introduced in this paper, utilises multicriteria analysis methodologies in order to rank the stocks by placing the best stock first and the worst last. Stock evaluation considers the specific characteristics of the potential investor, as well as his attitude towards undertaken risk. The final output of the system is four stock rankings which respond to four different criteria groups, depending on the type of accounting plan each listed company belongs to. The system incorporates a large volume of relevant information and operates in ‘real world conditions’ since its data are constantly updated. Finally, the system is intended for both institutional and private investors.