Guest diffusion in interpenetrating networks of micro- and mesopores

Pulsed field gradient NMR is applied for monitoring the diffusion properties of guest molecules in hierarchical pore systems after pressure variation in the external atmosphere. Following previous studies with purely mesoporous solids, also in the material containing both micro- and mesopores (activated carbon MA2), the diffusivity of the guest molecules (cyclohexane) is found to be most decisively determined by the sample "history": at a given external pressure, diffusivities are always found to be larger if they are measured after pressure decrease (i.e., on the "desorption" branch) rather than after pressure increase (adsorption branch). Simple model consideration reproduces the order of magnitude of the measured diffusivities as well as the tendencies in their relation to each other and their concentration dependence.     

s-Representations for involutions¶on affine Kac–Moody algebras are polar

Let denote the eigenspace decomposition of a twisted affine Kac–Moody algebra with respect to an involution , where is a twisted loop algebra, is the center and d is the scaling element of . We endow with the standard bilinear symmetrical form.Then with and carries a Lorentzian signature. Let denote the group that corresponds to , then the adjoint representation of on can be restricted to and this submanifold is isometrical to the Hilbert space E _ε, where is the decomposition of the twisted loop algebra with respect to the induced involutionρ₀.We thus obtain an affine representation on E _ε and we show that this representation is polar, i. e., there exists a submanifold that intersects all orbits, and intersects them orthogonally. Received: 16 February 2000 RID=" ID="Supported by a DFG grant.     

SEM-EDS and XPS Studies of the High Temperature Oxidation Behaviour of Inconel 718

 The oxidation in air under isothermal conditions of Inconel 718 has been investigated at 900 °C. We have studied the firsts stages of the high temperature oxidation mechanism. The oxidised samples were examined using a number of surface analytical techniques including XPS and SEM-EDS. The results have shown that minor alloying elements strongly influence the oxidation behaviour of the alloy: Previous studies had shown that the rate of the external oxide scale growth and the intergranular oxide penetration during oxidation of Inconel 718 at 900 °C in air are lower than those of Inconel X or Incoloy 800. We suggest that the formation of a quasi continuous scale of the intermetallic phase Ni₃Nb at the oxide-alloy interface could have an important contribution to the good oxidation resistance of Inconel 718.     

Study of Thin Films of High Temperature Superconductors Based on YBaCuO by EPMA

 An analytical model of an effective atomic number, Z _eff, for simultaneous calculation of composition and thickness of films on substrates that allows for backscattering processes is presented. Comparison of dependencies of ϕ(ρz) parameters for film elements on electron beam energy, on atomic numbers of a film and a substrate and on film thickness was done. The errors inherent in EPMA have been determined by comparing experimental data obtained on YBa₂Cu₃O_7−x bulk crystals with model calculations. Possibility of EPMA as an effective technique for investigation of spatially inhomogeneous objects was demonstrated by studying the correlation between composition and local superconducting properties (values of critical temperature and critical current) of these films.     

Independent Directed Triangles in a Directed Graph

If D is a directed graph of order n≥3 with , then D contains independent directed triangles. Moreover, the condition on the minimum degree is sharp in general. Revised: April 19, 1999     

Zur Methodik der Konzentrationsmessungen an Polymerl?sungen bei den Adsorptionsuntersuchungen

Ohne Zusammenfassung     

Background gradient suppression in stimulated echo NMR diffusion studies using magic pulsed field gradient ratios

By evaluating the spin echo attenuation for a generalized 13-interval PFG NMR sequence consisting of pulsed field gradients with four different effective intensities (F(p/r) and G(p/r)), magic pulsed field gradient (MPFG) ratios for the prepare (G(p)/F(p)) and the read (G(r)/F(r)) interval are derived, which suppress the cross term between background field gradients and the pulsed field gradients even in the cases where the background field gradients may change during the z-store interval of the pulse sequence. These MPFG ratios depend only on the timing of the pulsed gradients in the pulse sequence and allow a convenient experimental approach to background gradient suppression in NMR diffusion studies with heterogeneous systems, where the local properties of the (internal) background gradients are often unknown. If the pulsed field gradients are centered in the tau-intervals between the pi and pi/2 rf pulses, these two MPFG ratios coincide to eta=G(p/r)/F(p/r)=1-8/[1+(1/3)(delta/tau)(2)]. Since the width of the pulsed field gradients (delta) is bounded by 0< or =delta< or =tau, eta can only be in the range of 5< or =-eta< or =7. The predicted suppression of the unwanted cross terms is demonstrated experimentally using time-dependent external gradients which are controlled in the NMR experiment as well as spatially dependent internal background gradients generated by the magnetic properties of the sample itself. The theoretical and experimental results confirm and extend the approach of Sun et al. (J. Magn. Reson. 161 (2003) 168), who recently introduced a 13-interval type PFG NMR sequence with two asymmetric pulsed magnetic field gradients suitable to suppress unwanted cross terms with spatially dependent background field gradients.     

The Stability of Magnetic VorticesRID="*"ID="*"Research on this paper was supported by NSERC under grant N7901

We study the linearized stability of n-vortex (n∈ℤ) solutions of the magnetic Ginzburg–Landau (or Abelian Higgs) equations. We prove that the fundamental vortices (n = ± 1) are stable for all values of the coupling constant, λ, and we prove that the higher-degree vortices (|n|≥ 2) are stable for λ < 1, and unstable for λ > 1. This resolves a long-standing conjecture (see, eg, [JT]). Received: 16 November 1998 / Accepted: 3 January 2000 RID="*" ID="*"Research on this paper was supported by NSERC under grant N7901 RID="**" ID="**"Present address: Courant Institute, 251 Mercer St., New York, NY 10012, USA.&para;E-mail: gustaf&commat;cims.nyu.edu     

$$L^p$$-Fourier asymptotics,Hardy-type inequality and fractal measures

Suppose \(\mu \) is an \(\alpha \)-dimensional fractal measure for some \(0<\alpha <n\). Inspired by the results proved by Strichartz (J Funct Anal 89:154–187, 1990), we discuss the \(L^p\)-asymptotics of the Fourier transform of \(fd\mu \) by estimating bounds of

$$\begin{aligned} \underset{L\rightarrow \infty }{\liminf }\ \frac{1}{L^k} \int _{|\xi |\le L}\ |\widehat{fd\mu }(\xi )|^pd\xi , \end{aligned}$$

for \(f\in L^p(d\mu )\) and \(2<p<2n/\alpha \). In a different direction, we prove a Hardy type inequality, that is,

$$\begin{aligned} \int \frac{|f(x)|^p}{(\mu (E_x))^{2-p}}d\mu (x)\le C\ \underset{L\rightarrow \infty }{\liminf }\frac{1}{L^{n-\alpha }} \int _{B_L(0)}|\widehat{fd\mu }(\xi )|^pd\xi \end{aligned}$$

where \(1\le p\le 2\) and \(E_x=E\cap (-\infty ,x_1]\times (-\infty ,x_2]\ldots (-\infty ,x_n]\) for \(x=(x_1,\ldots x_n)\in {\mathbb R}^n\) generalizing the one dimensional results by Hudson and Leckband (J Funct Anal 108:133–160, 1992).