Solvable Subgroups of Out(F n ) are Virtually Abelian

Let F _n be the free group of rank n, let Aut(F _n ) be its automorphism group and let Out(F _n ) be its outer automorphism group. We show that every solvable subgroup of Out(F _n ) has a finite index subgroup that is finitely generated and free Abelian. We also show that every Abelian subgroup of Out(F _n ) has a finite index subgroup that lifts to Aut(F _n ).     

Improved predictability of two-dimensional turbulent flows using wavelet packet compression

We propose to use new orthonormal wavelet packet bases, more efficient than the Fourier basis, to compress two-dimensional turbulent flows. We define the “best basis” of wavelet packets as the one which, for a given enstrophy density, condenses the L² norm into a minimum number of non-negligible wavelet packet coefficients. Coefficients below a threshold are discarded, reducing the number of degrees of freedom. We then compare the predictability of the original flow evolution with several such reductions, varying the number of retained coefficients, either from a Fourier basis, or from the best-basis of wavelet packets. We show that for a compression ratio of 1/2, we still have a deterministic predictability using the wavelet packet best-basis, while it is lost when using the Fourier basis. Likewise, for compression ratios of 1/20 and 1/200 we still have statistical predictability using the wavelet packet best-basis, while it is lost when using the Fourier basis. In fact, the significant wavelet packet coefficients in the best-basis appear to correspond to coherent structures. The weak coefficients correspond to vorticity filaments, which are only passively advected by the coherent structures. In conclusion, the wavelet packet best-basis seems to distinguish the low-dimensional dynamically active part of the flow from the high-dimensional passive components. It gives us some hope of drastically reducing the number of degrees of freedom necessary to the computation of two-dimensional turbulent flows.     

Hemichrome Determination by Thermal Lensing with Polyethylene Glycols for Signal Enhancement in Aqueous Solutions

The thermal lens technique is proposed for the determination of total hemoglobin in the form of reversible hemichrome. The conditions were optimized (concentration of sodium dodecyl sulfate, 2?mM) to attain the maximum sensitivity with the use of polyethylene glycols as signal enhancers. For polyethylene glycols with molecular weights 1500–35000 Da in a concentration range of 5–15% w/w (5–25?mM), the influence on thermal lens signal enhancement was estimated. It is shown that the use of 5% w/w polyethylene glycol 2000 provides the maximum increase in the thermal lens enhancement factor (by 40%) in comparison with unmodified aqueous solutions. The detection limit of iron(II) tris(1,10-phenanthrolinate) as a model system is 60?nM. Under these conditions, the thermal lens detection limit of hemichrome is 10?nM, which shows a 15-fold enhancement compared to spectrophotometry. Modification of the medium with polyethylene glycols decreases the limit of detection of hemichrome determination by 15% in comparison with unmodified aqueous solutions due to better reproducibility for the range of concentrations from 0.02 to 0.9?µM.     

A novel bis-phenanthridine triamine with pH controlled binding to nucleotides and nucleic acids

The new bis-phenanthridine triamine is characterised by three pK(a) values: 3.65; 6.0 and >7.5. A significant difference in the protonation state of at pH = 5 (four positive charges) and at pH = 7 (less than two positive charges) accounts for the strong dependence of -nucleotide binding constants on nucleotide charge under acidic conditions, whereas at neutral pH all -nucleotide complexes are of comparable stability. All experimental data point at intercalation as the dominant binding mode of to polynucleotides. However, there is no indication of bis-intercalation of the two phenanthridine subunits in binding to double stranded polynucleotides, the respective complexes being most likely mono-intercalative. Thermal stabilisation of calf thymus DNA (ct-DNA) and poly A-poly U duplexes upon addition of is significantly higher at pH = 5 than at neutral conditions. This is not the case with poly dA-poly dT, indicating that the specific secondary structure of the latter, most likely the shape of the minor groove, plays a key role in complex stability. At pH = 5 acts as a fluorimetric probe for poly G (emission quenching) as opposed to other ss-polynucleotides (emission increase), while at neutral conditions this specificity is lost. One order of magnitude higher cytotoxicity of compared to its "monomer" can be accounted for by cooperative action of two phenanthridinium units and the charged triamine linker. The results presented here are of interest to the development of e.g. sequence-selective cytostatic drugs, and in particular for the possibility to control the drug activity properties over binding to DNA and/or RNA by variation of the pH of its surrounding.     

The Influence of Heat Pre-Treatment on the Sorption of Water Vapour on Bentonite

Sorption isotherms of water vapour on bentonite from the Rokle locality of northwest Bohemia in the Czech Republic were measured and analysed after being treated with heat. Protracted sorption measurements were performed at 30∘C in the range of water vapour relative pressures between 0.12 and 0.94. Prior to sorption measurements, the bentonite samples were exposed to flowing dry nitrogen for 18 hours at 115, 220 and 300∘C. Compared to the sample heated at 115∘C, the bentonite samples that were treated at 220 and 300∘C exhibited a decrease in water vapour sorption capacity. This decrease in sorption capacity was accompanied by structural changes that were confirmed by X-ray diffraction analysis.     

Regioselective Transformations of 2′,3′-Seconucleosides into Anhydro Structures and Chiral Crown Ethers

Intramolecular cyclisation of properly protected and activated derivatives of 2′,3′-secouridine ( = 1-{2-hydroxy-1-[2-hydroxy-1-(hydroxymethyl)ethoxy]-ethyl}uracil; 1 ) provided access to the 2,2′-, 2,3′-, 2,5′-, 2′,5′-, 3′,5′-, and 2′,3′-anhydro-2′,3′-secouridines 5, 16, 17, 26, 28 , and 31 , respectively (Schemes 1–3). Reaction of 2′,5′-anhydro-3′-O-(methylsulfonyl)- ( 25 ) and 2′,3′-anhydro-5′-O-(methylsulfonyl)-2′,3′-secouridine ( 32 ) with CH₂CI₂ in the presence of 1,8-diazabicyclo[5.4.0]undec-7-ene generated the N(3)-methylene-bridged bis-uridine structure 37 and 36 , respectively (Scheme 3). Novel chiral 18-crown-6 ethers 40 and 44 , containing a hydroxymethyl and a uracil-1-yl or adenin-9-yl as the pendant groups in a 1,3-cis relationship, were synthesized from 5′-O-(triphenylmethyl)-2′,3′-secouridine ( 2 ) and 5′-O,N⁶-bis(triphenylmethyl)-2′,3′-secoadenosine ( 41 ) on reaction with 3,6,9-trioxaundecane-1,11-diyl bis(4-toluenesulfonate) and detritylation of the thus obtained (triphenylmethoxy) methylcompound 39 and 43 , respectively (Scheme 4).     

Synthesis, structure, and biological evaluation of C-2 sulfonamido pyrimidine nucleosides

The C-2 sulfonamido pyrimidine nucleosides were prepared by opening the 2,2′- or 2,3′-bond in anhydronucleosides under nucleophilic attack of sulfonamide anions. Reaction of the sodium salt of p-toluenesulfonamide or 2-(aminosulfonyl)-N,N-dimethylnicotinamide with 2,2′-anhydro-1-(β-d-arabinofuranosyl)cytosine gave the C-2 sulfonamido derivatives in excellent yields. Ring opening of the less reactive 2,2′-anhydrouridine and 2,3′-anhydrothymidine could be accomplished with DBU/CH₃CN activation of p-toluenesulfonamide, giving moderate yields for C-2 sulfonamido derivatives. The action of acetic acid or ZnBr₂/CH₂Cl₂ on 5-methyl-N²-tosyl-1-(2-deoxy-5-O-trityl-β-d-threo-pentofuranosyl)isocytosine led to the cleavage of both the protection group and the nucleoside bond, yielding 5-methyl-N²-tosylisocytosine as the major product. Structures of the prepared C-2 sulfonamido nucleosides were confirmed by the 1D and 2D NMR experiments, and X-ray structural analysis of 4-imino-N²-tosylamino-1-(β-d-arabinofuranosyl)pyrimidine. Both methods confirmed β-configuration and anti-conformation of the 2-sulfonamido nucleosides. The investigated compounds displayed moderate inhibition of tumor cell growth in vitro, as determined by the MTT assay using six different human tumor cell lines.     

THE EFFECT OF DIFFERENTIATION ON PHOTOSENSITIZER UPTAKE BY HL60 CELLS

The capability of human promyelocytic leukemia cells HL60 to be induced to differentiate to various stages along the monocytic or myelocytic pathway was exploited for investigation of the uptake of selected photo-sensitizers by diverse types of cells of the same origin. The results showed that there was no substantial difference in photofrin uptake between noninduced HL60 cells, immature monocytes, immature neutrophils and cells differentiated along the eosinophilic pathway. In contrast, HL60 cells differentiated into macrophages (HL609) exhibited markedly increased photofrin uptake, which was further enhanced by their pretreatment with bacterial lipopolysaccharide. Similar results were obtained with other photosensitizers tested: di-and tetrasulfonated aluminum phthalocyanines (AIPcS₂ and AIPcS₄), tetrasulfonated zinc phthalocyanine (ZnPcS₄), tetraphenylporphine tetrasulfonate (TPPS₄) and benzoporphyrin derivative monoacid (BPD). Despite marked differences in the state of self-aggregation and other chemical properties of these compounds, the degree of their preferential uptake by HL60 PH cells showed very little variation. In a typical experiment, the uptake of these photosensitizers by HL60 PH cells was four to five times higher than the uptake by noninduced HL60 cells. In addition to the fluorometric assay employed in most of the experiments, cellular concentration of AlPcS₄ was determined by measurement of elementary aluminum using atomic absorption spectroscopy.     

Coherence for closed categories with biproducts

A coherence result for symmetric monoidal closed categories with biproducts is shown in this paper. It is also explained how to prove coherence for compact closed categories with biproducts and for dagger compact closed categories with dagger biproducts by using the same technique.