Constant locked inertia tensor trajectories for simple mechanical systems with symmetry

Saari’s Conjecture, generalized from its usual context of the N$N$-body problem to a simple mechanical system with symmetry, says roughly that a condition of constant locked inertia tensor (interpreted appropriately) along a solution curve should guarantee that the curve is a relative equilibrium. Using a local Lagrangian slice parametrization about a non-symmetric point in phase space, we offer the motion in the form of a reduced Euler–Poincaré–Lagrange system together with the reconstruction equation. We state necessary and sufficient conditions for the existence of relative equilibria in this parametrization. These conditions allow us to relate curves with constant locked inertia tensors to relative equilibria. We find a class of simple mechanical systems with symmetry for which Saari’s Conjecture is true. We also show that if a simple mechanical system with n$n$ degrees of freedom is symmetric under the free linear action of a k$k$-dimensional Lie group where k(k+1)/2≥(n−k)$k(k+1)/2\ge (n-k)$, then a version of Saari’s Conjecture holds except at specific isolated points. We apply our results to the three-dimensional three-body and four-body problems and to the n$n$-dimensional general relative two-body problem.     

Linear bounds for Calderón–Zygmund operators with even kernel on UMD spaces

It is well-known that several classical results about Calderón–Zygmund singular integral operators can be extended to X-valued functions if and only if the Banach space X has the UMD property. The dependence of the norm of an X-valued Calderón–Zygmund operator on the UMD constant of the space X is conjectured to be linear. We prove that this is indeed the case for sufficiently smooth Calderón–Zygmund operators with cancellation, associated to an even kernel. Our method uses the Bellman function technique to obtain the right estimates for the norm of dyadic Haar shift operators. We then apply the representation theorem of T. Hytönen to extend the result to general Calderón–Zygmund operators.     

Surface morphology and amide concentration depth profile of aminolyzed poly(ethylene terephthalate) films

Surface of biaxially oriented poly(ethylene terephthalate) films was chemically modified by exposure to ethylenediamine (EDA), triethylenetetramine (TETA), and tetraethylenepentamine (TEPA) for different treatment times. Variable angle attenuated total reflection Fourier transform infrared (ATR‐FTIR) spectroscopy was used in conjunction with weight loss measurements, scanning electron microscopy (SEM), and atomic force microscopy to establish the surface modification and to draw the depth profile of the newly created species, with emphasis on amide group. A clear differentiation was found between the effects of the three amines studied: EDA produces the highest amidation degree but, because of its deep penetration into the film, leads to delamination of rather thick layers, TETA reacts at and near surface and develops surface cracks without delamination, and TEPA is the mildest reactant, generating amide groups on the surface without visible deterioration of the sample. It was proved that the amide II absorption band became weaker with increasing analyzed depth, with a pronounced heterogeneity near the surface. SEM micrographs showed the development of cracks onto the surface at longer aminolysis time, which allowed a better understanding of ATR‐FTIR observations. Assuming an exponential decay for the depth profile spectrally obtained, the surface concentration of amide groups and the decay constant were determined for the amines and reaction times used. © 2010 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem, 2010     

A biotinylated intercalator for selective post-labeling of double-stranded DNA as a basis for high-sensitive DNA assays

For increasing the sensitivity of label-free DNA assays an amplification strategy is proposed based on the synthesis of a proflavine derivative which on the one hand retains its high affinity for double-stranded DNA (dsDNA) intercalation and on the other hand is functionalized via a flexible spacer with biotin moieties. By this, subsequent to the post-labeling of areas with dsDNA, reporter systems such as streptavidin/enzyme conjugates can be bound. Amplified DNA hybridization detection using an oligonucleotide model system, a biotinylated proflavine as intercalator and streptavidin/alkaline phosphatase is demonstrated.     

Hydrogen effects on the electric conductivity of a Pt/Al2O3 catalyst

Hydrogen desorption, hydrogen spillover and reduction processes have been evidenced using a new experimental strategy based on AC electric conductivity measurements during TPD and TPR experiments on a 0.5% Pt/Al₂O₃ catalyst.     

Determination of valuable elements in natural phosphates

Natural phosphates are used on large scale in the fertilizer industry. The usual process of the chemical attack is sulfuric (predominant) and nitric acids. The liquid phosphoric acid phase resulted contains dissolved valuable elements like: uranium and rare earths elements (REEs). Uranium and REEs are recovered in some technologies as valuable products. It is therefore important to know, uranium and REEs content in natural phosphates in view to decide on their recovery. In this paper determinations were carried out to find the uranium and REEs contents. The concentrations involved are low, therefore, it is difficult to find a classical reliable method without incurring important losses, i. e., errors. In this work uranium and REEs were determined by physical methods like: neutron activation analysis (NAA), emission spectroscopy, mass spark spectrometry and X-ray fluorescence. The results obtained were acceptable and intercomparison between various methods was carried out. It was found that most reliable results were given by mass spark spectrometry and activation analysis. The data resulted are in good agreement with uranium and REEs in the green cake (uranium tetrafluoride) and in the REEs concentrate obtained by solvent, extraction from phosphoric acid.