On the Komlós,Major and Tusnády strong approximation for some classes of random iterates

The famous results of Komlós, Major and Tusnády (see Komlós et al., 1976 [15] and Major, 1976 [17]) state that it is possible to approximate almost surely the partial sums of size $n$ of i.i.d. centered random variables in ${\mathbb{L}}^p$ ($p>2$) by a Wiener process with an error term of order $o\left(n^{1∕p}\right)$. Very recently, Berkes et al. (2014) extended this famous result to partial sums associated with functions of an i.i.d. sequence, provided a condition on a functional dependence measure in ${\mathbb{L}}_p$ is satisfied. In this paper, we adapt the method of Berkes, Liu and Wu to partial sums of functions of random iterates. Taking advantage of the Markovian setting, we shall give new dependent conditions, expressed in terms of a natural coupling (in ${\mathbb{L}}^{\infty }$ or in ${\mathbb{L}}^1$), under which the strong approximation result holds with rate $o\left(n^{1∕p}\right)$. As we shall see our conditions are well adapted to a large variety of models, including left random walks on $G{L}_d\left(\mathbb{R}\right)$, contracting iterated random functions, autoregressive Lipschitz processes, and some ergodic Markov chains. We also provide some examples showing that our ${\mathbb{L}}^1$-coupling condition is in some sense optimal.     

Die notentiometrische Titration des Zinns mit Kaliumbromat

Ohne Zusammenfassung     

Rigid Nanoporous Urea-Based Covalent Triazine Frameworks for C2/C1 and CO2/CH4 Gas Separation

C2/C1 hydrocarbon separation is an important industrial process that relies on energy-intensive cryogenic distillation methods. The use of porous adsorbents to selectively separate these gases is a viable alternative. Highly stable covalent triazine frameworks (urea-CTFs) have been synthesized using 1,3-bis(4-cyanophenyl)urea. Urea-CTFs exhibited gas uptakes of C₂H₂ (3.86 mmol/g) and C₂H₄ (2.92 mmol/g) at 273 K and 1 bar and is selective over CH₄. Breakthrough simulations show the potential of urea-CTFs for C2/C1 separation.     

Structural identification of new glycolipids based on cyclodextrin using high-resolution positive and negative electrospray ionization mass spectrometry

In the continuing challenge to increase the performance of cyclodextrins (CDs) for various applications, new phospholipidyl-cyclodextrin derivatives showing improved self-organization properties in water have been synthesized, as new carriers for drug vectorization, starting from natural beta-cyclodextrin. Due to the important chemical modifications of the original cyclic oligosaccharide molecules, simple nuclear magnetic resonance (NMR) experiments do not easily lead to both an unambiguous assignment of the structures and to a rapid evaluation of the purity of the final products. However, positive and negative ion electrospray ionization (ESI-MS) in combination with accurate mass measurements and tandem mass spectrometry (MS/MS) led to the positive structural identification of the first series of these new amphiphilic compounds.     

On a class of 3-dimensional contact metric manifolds

Let M³ be a 3-dimensional contact metric manifold with contact structure (, , , g), such that and =R(.,)) commute. Such a manifold is called 3--manifold. We prove that every 3--manifold with -parallel Weyl tensor is either flat or a Sasakian manifold with constant curvature 1.     

Opérations d''Adams en K-théorie algébrique (Adams Operations and Algebraic K-Theory)

Following Schechtman's work on deloopings of Adams operations, we show that rational Quillen K-theory of schemes defines a special ring for schemes which are quasi-projective over an affine regular base.     

Calibration system and analytical considerations for quantitative sesquiterpene measurements in air

Sesquiterpenes (C15H24, SQT) are semi-volatile organic compounds emitted from vegetation and are of interest for air quality considerations because of their suspected contribution to the formation of secondary aerosol. This article investigates the application of a capillary diffusion method for the generation of standard atmospheres of 16 SQT and four other related semi-volatile compounds. This instrument subsequently has been used in the testing of analytical materials, protocols and calibration of air sampling methods. SQT DB-1 retention indices, vapor pressures at 25 and 75 degrees C, and diffusion coefficients were determined. A quantitative, on-line GC method yielded improved results (median relative standard deviation of 5.0-6.1%) for the diffusion rate determination in comparison to a gravimetric approach (median relative standard deviation 18%). The GC method also allowed identifying errors in the gravimetric method stemming from residual solvent evaporation, impurities, and chemical analyte losses. Stainless steel, glass, nickel and PTFE tubing that were tested for transfer lines and a sampling loop had to be kept at temperatures in excess of approximately 110 degrees C in order to prevent significant analytical errors from the stickiness of SQT to these materials. In addition to SQT analysis, results from this research provide general guidelines for gas-phase analysis of related compounds in the C14-C16 volatility range.