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.     

Use of RP-TLC to Investigate the Solubility in Water of Fatty Acids,Hydroxy Fatty Acids and their Esters

JPC – Journal of Planar Chromatography – Modern TLC - Long-chain fatty acids and hydroxy fatty acids and their esters have been separated by reversed-phase thin-layer chromatography...     

Polyester hydrogels with swelling properties controlled by the polymer architecture,molecular weight,and crosslinking agent

Hydrogels of poly(1,5‐dioxepan‐2‐one) and hydrogels of block copolymers of poly(1,5‐dioxepan‐2‐one) and poly(L ‐lactide) were synthesized. Both star‐shaped polymers and linear polymers were polymerized with ring‐opening polymerization and crosslinked in situ with a tetrafunctional acid chloride (1,2,3,4‐cyclopentane tetracarboxylic acid chloride) or a difunctional acid chloride (succinyl chloride). Different network architectures were synthesized in this way. The initial monomer concentrations and the molecular weights of the macromonomers were also altered. The networks were characterized with ¹H NMR and differential scanning calorimetry, and the swelling abilities of the different hydrogels were investigated in water and dichloromethane. The ratio of the monomer to the crosslinking agent was assessed by the quantification of the signal intensities in the ¹H NMR spectra of the swelled network and agreed with the theoretical crosslinking density. Both the homopolymers of 1,5‐dioxepan‐2‐one and the copolymers of 1,5‐dioxepan‐2‐one and L ‐lactide swelled to a high degree in water. The swelling properties of the materials could be varied over a broad range by changes in the architecture, molecular weight, and content of the precursor in the network. Star‐shaped poly(1,5‐dioxepan‐2‐one) crosslinked with a difunctional acid chloride had the highest degree of swelling among the different homopolymer hydrogels. This network also had the lowest glass‐transition temperature because of the flexible units in the structure. The same trends found for the homopolymer hydrogels were also seen in the hydrogels with block copolymers. The hydrogels swelled enormously in dichloromethane, and as in water, the star‐shaped copolymer crosslinked with a difunctional acid chloride had the highest degree of swelling. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 1296–1305, 2003     

Indistinguishable particles and hidden variables

An axiomatics for the indistinguishability of elementary particles in terms of hidden variables is presented in a manner which depart from the standard approaches usually given to hidden variables. Quantum distribution functions are also discussed and some possible related lines of work are suggested.     

Remarks on the r and Δ convolutions

In this paper we study the properties of the r–deformation introduced in [B1]. We observe that the associated convolution coming from the conditionally free convolution is associative only for r = 1 and r = 0. We give the realization of some r–Gaussian random variables and obtain Haagerup–Pisier–Buchholz type inequalities. We also study another convolution defined with the use of the r–deformation through a moment–cumulant formula [KY1] and show that it is associative and in general not positive. Partially sponsored with KBN grant no 2P03A00723 and RTN HPRN-CT-2002-00279.     

Spectrophotometric determination of olanzapine by its oxidation with N-bromosuccinimide and cerium(IV)sulfate.

Three simple spectrophotometric methods have been described for the assay of olanzapine in its pure and pharmaceutical formulations. The direct method (A) is based on the drug oxidation with excess of N-bromosuccinimide in acidic medium and the two indirect methods (B and C) are based on the oxidation of the drug with excess of N-bromosuccinimide and cerium(IV)sulfate, followed by the reaction of the unconsumed oxidants with celestine blue. The calibration graphs were linear over the range 10 - 120 microg mL(-1) (method A), 0.5 - 6.0 microg mL(-1) (method B) and 0.6 - 3.0 microg mL(-1) (method C). After validation, the proposed methods were successfully applied to assay of olanzapine in its commercial tablets with mean percentage recoveries of 101.23 +/- 0.10, 96 +/- 0.10 and 94 +/- 0.04%. The mechanism of olanzapine oxidation with N-bromosuccinimide was also proposed.