About the synthesis of N-1-substituted 3-aminopyrroles. A comparison

A general method for the preparation of 3-amino-1-methylpyrroles in excellent yields is reported. The key step involves the N-methylation of the nitro derivatives 2 , under phase transfer catalysis conditions.     

Operator geometric stable laws

Operator geometric stable laws are the weak limits of operator normed and centered geometric random sums of independent, identically distributed random vectors. They generalize operator stable laws and geometric stable laws. In this work we characterize operator geometric stable distributions, their divisibility and domains of attraction, and present their application to finance. Operator geometric stable laws are useful for modeling financial portfolios where the cumulative price change vectors are sums of a random number of small random shocks with heavy tails, and each component has a different tail index.     

Hemivariational inequalities for stationary Navier-Stokes equations

In this paper we study a class of inequality problems for the stationary Navier-Stokes type operators related to the model of motion of a viscous incompressible fluid in a bounded domain. The equations are nonlinear Navier-Stokes ones for the velocity and pressure with nonstandard boundary conditions. We assume the nonslip boundary condition together with a Clarke subdifferential relation between the pressure and the normal components of the velocity. The existence and uniqueness of weak solutions to the model are proved by using a surjectivity result for pseudomonotone maps. We also establish a result on the dependence of the solution set with respect to a locally Lipschitz superpotential appearing in the boundary condition.     

Delayed minocycline inhibits ischemia-activated matrix metalloproteinases 2 and 9 after experimental stroke

Background  

Matrix metalloproteinases 2 and 9 (MMP-2 and MMP-9) are increased in the brain after experimental ischemic stroke in rats. These two proteases are involved with the degradation of the basal lamina and loss of stability of the blood brain barrier that occurs after ischemia and that is associated with thrombolytic therapy in ischemic stroke. Minocycline is a lipophilic tetracycline and is neuroprotective in several models of brain injury. Minocycline inhibits inflammation, apoptosis and extracellular matrix degradation. In this study we investigated whether delayed minocycline inhibits brain MMPs activated by ischemia in a model of temporary occlusion in Wistar rats.     

X-ray photoelectron spectroscopy studies on solid xanthates

Two commonly used xanthates, potassium ethyl xanthate (KEX) and sodium isopropyl xanthate (NaiPX) were characterized by comparing their bulk and surface composition. The XPS spectra were recorded using Al K and Mg K excitation and potential sources of contamination were accounted for. Sulfate and carbonate contaminations were identified, both in the bulk and on the surface of the KEX sample. NaiPX contained hydroxyl- and carbonyl-type contaminations. The earlier published XPS spectral data on xanthates were compiled and compared with the results of this work.     

Mixed Norm and Multidimensional Lorentz Spaces

In the last decade, the problem of characterizing the normability of the weighted Lorentz spaces has been completely solved ([16], [7]). However, the question for multidimensional Lorentz spaces is still open. In this paper, we consider weights of product type, and give necessary and sufficient conditions for the Lorentz spaces, defined with respect to the two-dimensional decreasing rearrangement, to be normable. To this end, it is also useful to study the mixed norm Lorentz spaces. Finally, we prove embeddings between all the classical, multidimensional, and mixed norm Lorentz spaces. Research partially supported by KAW 2000.0048 and STINT KU 2002-4025. Research partially supported by Grants MTM2004-02299, 2005SGR00556 and The Swedish Research Council no. 624-2003-571.     

Photoconductance of two-dimensional ballistic microstructures

We calculate the photoconductance of two-dimensional ballistic microstructures subject to a high-frequency electromagnetic field. First, we study a simple quantum point contact. Absorption of photons is due to electronic transitions between different modes. A transition between a propagating and a nonpropagating mode results effectively in a backscattering process, and gives a negative or positive contribution to the current, depending on the gate voltage; the total quantized conductance acquires an additional, quite pronounced step-structure. Then, we demonstrate a new effect where the electron-photon interaction in a structure of slightly more complex geometry plays the same role as impurity scattering does in a “dirty” system. All relevant photons of the external electromagnetic field are coherent and spatial interference effects in electron-photon scattering become possible in spite of the inelastic nature of the collisions. These interference effects can be controlled by the gate voltage or the frequency of the electromagnetic field. As an illustration we calculate the photoconductance of a double point-contact geometry.     

Simultaneous production and purification ofBacillus subtilis α-amylase

Production of α-amylase withB. subtilis CCM 2722 in an aqueous two-phase polyethylene glycol/dextran system integrated with product purification by affinity chromatography on crosslinked starch during cultivation was studied. The medium was drawn from the bioreactor to the external settler during fermentation. After phase separation in the settler the dextran-rich bottom phase with cells was returned to the bioreactor. The PEG-rich top phase was pumped to the column with crosslinked starch and returned to the bioreactor after α-amylase adsorption. The same volumetric productivities, 0.53 U/mL/h, were reached in both batch and described process, but total productivity of the latter method was much higher owing to shortening upstream and downstream processing time. The enzyme of 98% homogenity in 95% yield was obtained after its elution from the column.     

Rook numbers and the normal ordering problem

For an element w in the Weyl algebra generated by D and U with relation DU=UD+1, the normally ordered form is w=∑c_i,jUⁱD^j. We demonstrate that the normal order coefficients c_i,j of a word w are rook numbers on a Ferrers board. We use this interpretation to give a new proof of the rook factorization theorem, which we use to provide an explicit formula for the coefficients c_i,j. We calculate the Weyl binomial coefficients: normal order coefficients of the element (D+U)ⁿ in the Weyl algebra. We extend these results to the q-analogue of the Weyl algebra. We discuss further generalizations using i-rook numbers.