When random proportional subspaces are also random quotients

We discuss when a generic subspace of some fixed proportional dimension of a finite-dimensional normed space can be isomorphic to a generic quotient of some proportional dimension of another space. We show (in Theorem 4.1) that if this happens (for some natural random structures) then for any proportion arbitrarily close to 1, the first space has a lot of Euclidean subspaces and the second space has a lot of Euclidean quotients.     

Controlling the water content of never dried and reswollen bacterial cellulose by the addition of water-soluble polymers to the culture medium

For the modification of medically useful biomaterials from bacterially synthesized cellulose, fleeces of Acetobacter xylinum have been produced in the presence of 0.5, 1.0, and 2.0% (m/v) carboxymethylcellulose (CMC), methylcellulose (MC), and poly(vinyl alcohol) (PVA), respectively, in the Hestrin-Schramm culture medium. The incorporation of the water-soluble polymers into cellulose and their influence on the structure, crystal modifications, and material properties are described. With IR and solid-state ¹³C NMR spectroscopy of the fleeces, the presence of the cellulose ethers and an increase in the amorphous parts of the cellulose modifications (NMR results) have been detected. The incorporation is represented by a higher product yield, too. As demonstrated by scanning electron microscopy, a porelike cellulose network structure forms in the presence of CMC and MC. This modified structure increases the water retention ability (expressed as the water content), the ion absorption capacity, and the remaining nitrogen-containing residues from the culture medium or bacteria cells. The water content of bacterial cellulose (BC) in the never dried state and the freeze-dried, reswollen state can be controlled by the CMC concentration in the culture solution. The freeze-dried, reswollen BC-CMC (2.0%) contains 96% water after centrifugation, whereas standard BC has only 73%. About 98% water is included in a BC-MC composite in the wet state, and about 93% is included in the reswollen state synthesized in the presence of 0.5, 1.0, or 2.0% MC. These biomaterial composites can be stored in the dried state and reswollen before use, reaching a higher water absorption than pure, never dried BC. The copper ion capacity of BC-CMC composites increases proportionally with the added amount of CMC. BC-CMC (0.5%) can absorb 3 times more copper ions than original BC. In the case of 0.5 and 1.0% PVA additions to the culture solution, this polymer cannot be detected in the cellulose fleeces after they are washed. Nevertheless the presence of PVA in the culture medium effects a decreased product yield, a retention of nitrogen-containing residues in the material during purification, a reduced water absorption ability, and a slightly higher copper ion capacity in comparison with original BC. The water content of freeze-dried, reswollen BC-PVA (0.5%) is only 62%. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 463–470, 2004     

Generic Transport Aft-body Drag Reduction using Active Flow Control

Active flow-separation control is an effective and efficient mean for drag reduction and unsteady load alleviation resulting from locally or massively separated flow. Such a situation occurs in configurations where the aerodynamic performance is of secondary importance to functionality. The performance of heavy transport helicopters and aeroplanes, having a large, and almost flat, aft loading ramp suffer from the poor aerodynamics of the aft body. Hence, a combined experimental and numerical investigation was undertaken on a generic transport aeroplane/helicopter configuration. The experimental study provided surface pressures, direct drag measurements, surface and smoke flow visualization. The baseline flow was numerically analyzed, using finite volume solutions of the RANS equations. The baseline flow around the model was insensitive to the Reynolds number in the range it was tested. The flow separating from the aft body was characterized by two main sources of drag and unsteadiness. The first is a separation bubble residing at the lower ramp corner and the second is a pair of vortex systems developing and separating from the sides of the ramp. As the model incidence is decreased, the pair of vortex systems also penetrates deeper towards the centerline of the ramp, decreasing the pressure and increasing the drag. As expected, the ramp lower corner bubble was highly receptive to periodic excitation introduced from four addressable piezo-fluidic actuators situated at the ramp lower corner. Total drag was reduced by 3–11%, depending on the model incidence. There are indications that the flow in the wake of the model is also significantly steadier when the bubble at the lower ramp corner is eliminated. The vortex system is tighter and steadier when the ramp-corner bubble is eliminated.     

Conjecture de Franchetta forte

Sans résumé     

The ternary system CsCl−NaCl−LaCl3

The ternary system CsCl?NaCl?LaCl₃ was investigated by means of differential thermal analysis and X-ray powder diffraction analysis. There exists one congruently melting compound, Cs₂NaLaCl₆, crystallizing with the cubic elpasolite structure. No quasi-binary section exists for the whole system, however three binaries range from the ternary compound Cs₂NaLaCl₆ to NaCl, CsLa₂Cl₇ and Cs₃LaCl₆ resp., dividing the system in three areas of composition: one triangle, Cs₃LaCl₆?Cs₂NaLaCl₆?CsLa₂Cl₇, containing additionally a compound Cs₂LaCl₅ below 510°C, and the two areas CsCl?NaCl?Cs₂NaLaCl₆?Cs₃LaCl₆ and Cs₂NaLaCl₆?NaCl?LaCl₃?CsLa₂Cl₇, containing a mixed crystal range between LaCl₃ and Na₃La₅Cl₁₈. These areas could be further divided in five triangles, so that the whole system contains six Alkemade triangles.     

1.2 Anorganische analyse

Ohne Zusammenfassung     

BIOLOGICAL ACTIVITIES OF PHTHALOCYANINES-X. SYNTHESES AND ANALYSES OF SULFONATED PHTHALOCYANINES

Abstract— Synthetic methods to obtain selectively sulfonated metallo phthalocyanines are compared. Both condensation and direct sulfonation procedures lead to mixtures of mono- to tetrasulfonated products which are resolved by reverse phase liquid chromatography in buffered aqueous-methanol. The proportion of sulfonated derivatives is examined as a function of the starting reagents in the case of the condensation method, and as a function of the temperature and reaction time in the case of the direct sulfonation procedure. The number of sulfonate groups per phthalocyanine molecule is determined by oxidative degradation of the phthalocyanine ring followed by quantitative chromatographic analysis of the sulfophthalamide and phthalamide fragments.     

Analysis of aromatic compounds in gasoline with flow-switching comprehensive two-dimensional gas chromatography

A comprehensive two-dimensional gas chromatography (GC x GC) instrument has been created by coupling a flow-switching modulator and a standard gas chromatograph. The instrument was used to characterize the aromatic composition of gasoline. The high-resolution separation produced by flow-switching GC x GC allowed gasoline aromatics to be fully resolved from saturated components. The aromatic compounds were further separated into groups having the same carbon number. A standard gasoline sample was analyzed to evaluate the quantitative accuracy and precision of this technique. The data show that flow-switching GC x GC produces results that are comparable to gas chromatography-mass spectrometry (GC-MS) and thermal modulation GC x GC. The simple, low-cost, and robust nature of flow-switching GC x GC makes it an ideal technique for the routine analysis of aromatic compounds in gasoline.     

Voltammetric sizing of a sphere.

The size of a glass sphere positioned in the center of a microdisk electrode is determined by using a simple electrochemical procedure and is confirmed, additionally, by a microscopical measurement of the sphere at the time of the electrochemical measurement. The cyclic voltammetric response of the naked electrode and of the electrode with the sphere positioned in its center is recorded over a wide range of scan rates (0.002-1.5 V s(-1)). The size of the sphere is then determined by comparison of the experimental voltammogram with simulations for each individual scan rate.