Optimal Continuous Dependence Estimates for Fractional Degenerate Parabolic Equations

We derive continuous dependence estimates for weak entropy solutions of degenerate parabolic equations with nonlinear fractional diffusion. The diffusion term involves the fractional Laplace operator, \({\triangle^{\alpha/2}}\) for \({\alpha \in (0,2)}\) . Our results are quantitative and we exhibit an example for which they are optimal. We cover the dependence on the nonlinearities, and for the first time, the Lipschitz dependence on α in the BV-framework. The former estimate (dependence on nonlinearity) is robust in the sense that it is stable in the limits \({\alpha \downarrow 0}\) and \({\alpha \uparrow 2}\) . In the limit \({\alpha \uparrow 2}\) , \({\triangle^{\alpha/2}}\) converges to the usual Laplacian, and we show rigorously that we recover the optimal continuous dependence result of Cockburn and Gripenberg (J Differ Equ 151(2):231–251, 1999) for local degenerate parabolic equations (thus providing an alternative proof).     

Understanding the formation and evolution of ceria nanoparticles under hydrothermal conditions

Supercritical growth: The formation and evolution of ceria nanoparticles during hydrothermal synthesis was investigated by in?situ total scattering and powder diffraction. The nucleation of pristine crystalline ceria nanoparticles originated from previously unknown cerium dimer complexes. The nanoparticle growth was highly accelerated under supercritical conditions.     

A Nonlinear Parabolic Equation with Noise

In this paper we study a class of parabolic equations with a nonlinear gradient term. The system is disturbed by white noise in time. We show that the unique solution of this problem can be represented as the Wick product between a normalized random variable of exponential form and the solution of a nonlinear parabolic equation. We allow random initial data which might be anticipating. A relation between the Wick product with a normalized exponential and translation is proved in order to establish our results.     

Synthesis and biological evaluation of new dipicolylamine zinc chelators as metallo-β-lactamase inhibitors

Antibiotics are key drugs in modern healthcare, especially in hospitals, where multiresistant bacteria resides and is a potential threat to human health. In the present work, a new series of adjuvants working synergistically with the carbapenem meropenem, in which a selective zinc-chelating agent was covalently linked to the small bacterial peptide D-Ala-D-Ala, was synthesized and tested against VIM-2 and NDM-1 metallo-β-lactamases (MBLs). The nature of the linker was modified in a structure-activity relationship study. Compound 1i, having an ethyl piperidine linker, lowered the MIC of meropenem from 32 to 64?mg/L to 2 and 1–2?mg/L against VIM-2- and NDM-1-producing clinical isolates, respectively. The IC₅₀ value of 1i against VIM-2 was 9.8 and 2.2?μM after 5 and 20?min, respectively. Compound 1i also showed intrinsic toxicity against three eukaryotic human tumoral cell lines between 50 and 120?μM.     

Simulations of the PHOS detector in the ALICE experiment at CERN

In 2005 the ALICE experiment will start at the Large Hadron Collider at CERN. It will investigate hot and dense strongly interacting matter formed in heavy ion collisions. The photon spectrometer of the ALICE detector will be designed to identify direct photons. To optimize the detector, simulations will be carried out.     

Electronic structure of high-valent transition metal corrolazine complexes. The young and innocent?

This is a first quantum chemical study of corrolazine complexes. DFT calculations suggest that despite their extremely contracted central cavities, compared with porphyrins, a variety of corrolazine complexes may be expected to exist as stable compounds. The calculations also indicate that corrolazine complexes may be regarded as strongly electron-deficient analogues of corrole complexes. Thus, the calculated valence ionization potentials of P(V) and Cu(III) corrolazine derivatives are dramatically higher than those of analogous corrole derivatives. In addition, DFT calculations on Fe(IV) and Mn(IV) corrole and corrolazine derivatives suggest that compared with the often noninnocent corrole ligands, corrolazines are electronically more innocent and stabilize "purer" high-valent states of transition metal ions.     

Determination of homogeneity of standard materials by ion microscopy

Summary Secondary-ion microanalysis is used to investigate the homogeneity (at the microlevel) of a number of standard reference materials. High mass-resolution measurements are accomplished with a CAMECA IMS-300 ion microscope/ion microprobe equipped with an electrostatic analyser. By use of a 5.5-keV¹⁶O₂ ⁺ primary ion beam with approximately 1A intensity the following materials were investigated: NBS-SRM copper-base alloys, low-alloy steels and zinc-base alloys, and Aluminium Péchiney Al-Si-Cu, Al-Cu and Al-Mn alloys. The sampling-constant concept was applied in order to evaluate the applicability of the reference materials for micro-probe analysis, and other microanalytical techniques. The degree of heterogeneity was estimated and the number of replicate analyses required for achieving 5 and 10% precision were calculated. The results show that care must be taken when using these standards for calibration work in SIMS and other microsampling techniques, since heterogeneity on the microscale is proven for a number of elements. The technique was also applied to the determination of the homogeneity of standard samples of boron in zirconium metal from the Bureau of Reference Materials of the EEC.

---

Bestimmung der Homogenität von Standardproben durch Ionenmikroskopie

Zusammenfassung Sekundärionenmikroanalyse wurde zur Untersuchung der Homogenität einiger Standardreferenzmaterialien im Mikrobereich verwendet, wobei Messungen mit hoher Massenauflösung mittels einer CAMECA IMS-300 Ionenmikroskop/Ionenmikrosonde durchgeführt wurden, die mit einem elektrostatischen Sektor ausgestattet ist. Nachstehende Materialien wurden unter Verwendung eines 5,5 keV¹⁶O₂ ⁺-Primärionenstrahls mit etwa 1A Intensität untersucht: NBS-SRM Kupferlegierungen, NBS-SRM niedrig legierte Stähle, NBS-SRM Zinklegierungen und Aluminium Péchiney Al-Si-Cu-, Al-Cu- und Al-Mn-Legierungen.Zur Überprüfung der Verwendbarkeit der Referenzmaterialien für Mikrosondenanalysen und andere mikroanalytische Methoden wurde das Sampling-Constant-Konzept angewandt. Nach dem Abschätzen des He-terogenitätsgrades wird die Anzahl der Wiederholungen von Analysen berechnet, die für 5 und 10% Genauigkeit notwendig sind. Da Heterogenität im Mikrobereich für mehrere Elemente erwiesen ist, weisen die Resultate auf die anzuwendende Sorgfalt, soferne diese Standards für Eichungen in SIMS und anderen mikroanalytischen Methoden Verwendung finden sollen. Ebenso wird diese Technik für die Bestimmung der Homogenität von Bor in Standardproben des Bureau of Reference Materials des E. E. C. angewandt.

---

---

Presented at the 8th International Microchemical Symposium, Graz, August 25–30, 1980.     

Image processing in secondary ion mass spectrometry

The application of image processing in secondary ion mass spectrometry is discussed. The Cameca 4f SIMS uses a single microchannel plate and a highly sensitive camera in combination with an image processor with real time capabilities (Kontron IBAS). An automation procedure with image integration, extended dynamic range image acquisition and retro depth profiling is presented and illustrated with practical applications.     

On numerical density approximations of solutions of SDEs with unbounded coefficients

We study a numerical method to compute probability density functions of solutions of stochastic differential equations. The method is sometimes called the numerical path integration method and has been shown to be fast and accurate in application oriented fields. In this paper we provide a rigorous analysis of the method that covers systems of equations with unbounded coefficients. Working in a natural space for densities, L ¹, we obtain stability, consistency, and new convergence results for the method, new well-posedness and semigroup generation results for the related Fokker-Planck-Kolmogorov equation, and a new and rigorous connection to the corresponding probability density functions for both the approximate and the exact problems. To prove the results we combine semigroup and PDE arguments in a new way that should be of independent interest.     

Ornstein–Uhlenbeck processes in Hilbert space with non-Gaussian stochastic volatility

We propose a non-Gaussian operator-valued extension of the Barndorff-Nielsen and Shephard stochastic volatility dynamics, defined as the square-root of an operator-valued Ornstein–Uhlenbeck process with Lévy noise and bounded drift. We derive conditions for the positive definiteness of the Ornstein–Uhlenbeck process, where in particular we must restrict to operator-valued Lévy processes with “non-decreasing paths”. It turns out that the volatility model allows for an explicit calculation of its characteristic function, showing an affine structure. We introduce another Hilbert space-valued Ornstein–Uhlenbeck process with Wiener noise perturbed by this class of stochastic volatility dynamics. Under a strong commutativity condition between the covariance operator of the Wiener process and the stochastic volatility, we can derive an analytical expression for the characteristic functional of the Ornstein–Uhlenbeck process perturbed by stochastic volatility if the noises are independent. The case of operator-valued compound Poisson processes as driving noise in the volatility is discussed as a particular example of interest. We apply our results to futures prices in commodity markets, where we discuss our proposed stochastic volatility model in light of ambit fields.