John’s Ellipsoid and the Integral Ratio of a Log-Concave Function

We extend the notion of John’s ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the log-concave function maximizing the integral ratio. A reverse functional affine isoperimetric inequality will be given, written in terms of this integral ratio. This can be viewed as a stability version of the functional affine isoperimetric inequality.     

Fredholmness and invertibility of Toeplitz operators with matrix almost periodic symbols

We consider Toeplitz operators with symbols that are almost periodic matrix functions of several variables. It is shown that under certain conditions on the group generated by the Fourier support of the symbol, a Toeplitz operator is Fredholm if and only if it is invertible.

     

Modelling Unsaturated Moisture Transport in Heterogeneous Limestone

The influence of macro-scale heterogeneities on the imbibition process is investigated for Savonnières, a French layered limestone. Free uptake experiments are performed both parallel and perpendicular to the bedding. It is found that the position of the different layers, and the exact material properties inside each layer can significantly influence the imbibition process. The experimental results are compared with numerical simulations. For the flow simulations, moisture permeability of the different layers is obtained with the upscaling technique presented in Part 1. Good agreement between simulations and experiments validate the proposed upscaling from meso to macroscopic scale.     

Instabilities of micellar systems under homogeneous and non-homogeneous flow conditions

The rheological behavior of a cetylpyridinium chloride 100 mmol l^–1/sodium salicylate 60 mmol l^–1 aqueous solution was studied in this work under homogeneous (cone and plate) and non-homogeneous flow conditions (vane-bob and capillary rheometers), respectively. Instabilities consistent with non-monotonic flow curves were observed in all cases and the solution exhibited similar behavior under the different flow conditions. Hysteresis and the sigmoidal flow curve suggested as characteristic of systems that show constitutive instabilities were observed when running cycles of increasing and decreasing stress or shear rate, respectively. This information, together with a detailed determination of steady states at shear stresses close to the onset of the instabilities, allowed one to show unequivocally that "top and bottom jumping" are the mechanisms to trigger the instabilities in this micellar system. It is shown in addition that there is not a true plateau region in between the "top and bottom jumping". Finally, the flow behavior beyond the upturn seemed to be unstable and was found accompanied by an apparent violation of the no-slip boundary condition.     

Toward a Comparison of Classical and New Privacy Mechanism

In the last decades, the development of interconnectivity, pervasive systems, citizen sensors, and Big Data technologies allowed us to gather many data from different sources worldwide. This phenomenon has raised privacy concerns around the globe, compelling states to enforce data protection laws. In parallel, privacy-enhancing techniques have emerged to meet regulation requirements allowing companies and researchers to exploit individual data in a privacy-aware way. Thus, data curators need to find the most suitable algorithms to meet a required trade-off between utility and privacy. This crucial task could take a lot of time since there is a lack of benchmarks on privacy techniques. To fill this gap, we compare classical approaches of privacy techniques like Statistical Disclosure Control and Differential Privacy techniques to more recent techniques such as Generative Adversarial Networks and Machine Learning Copies using an entire commercial database in the current effort. The obtained results allow us to show the evolution of privacy techniques and depict new uses of the privacy-aware Machine Learning techniques.     

Two definitions of exponential dichotomy for skew-product semiflow in Banach spaces

In this paper we introduce a concept of exponential dichotomy for linear skew-product semiflows (LSPS) in infinite dimensional Banach spaces, which is an extension of the classical concept of exponential dichotomy for time dependent linear differential equations in Banach spaces. We prove that the concept of exponential dichotomy used by Sacker-Sell and Magalhães in recent years is stronger than this one, but they are equivalent under suitable conditions. Using this concept we where able to find a formula for all the bounded negative continuations. After that, we characterize the stable and unstable subbundles in terms of the boundedness of the corresponding projector along (forward/backward) the LSPS and in terms of the exponential decay of the semiflow. The linear theory presented here provides a foundation for studying the nonlinear theory. Also, this concept can be used to study the existence of exponential dichotomy and the roughness property for LSPS.

     

Stereochemical study of phosphonothioate cleavage by a metallomicelle

[reaction: see text] The copper metallomicellar hydrolysis of O-methyl O-4-nitrophenyl phenylphosphonothioate to O-methyl phenylphosphonothioic acid takes place with effectively complete inversion at phosphorus.     

Kinetische Untersuchungen über die Silicium—Aryl-Spaltung mit Bromwasserstoff

Rate constants of the cleavage reaction of silicon aryl linkages with HBr were estimated for various aryl derivatives by means of NMR. A row of substituents was obtained, dependent on the cleavage rates. Correlation with theHammett function shows the electrophilic character of the reaction. The different cleavage rates give the possibility for specific cleavages of aryl groups from silanes.