Fractional Kinetics in Kac–Zwanzig Heat Bath Models

We study a variant of the Kac–Zwanzig model of a particle in a heat bath. The heat bath consists of n particles which interact with a distinguished particle via springs and have random initial data. As n → ∞ the trajectories of the distinguished particle weakly converge to the solution of a stochastic integro-differential equation—a generalized Langevin equation (GLE) with power-law memory kernel and driven by 1/f ^α -noise. The limiting process exhibits fractional sub-diffusive behaviour. We further consider the approximation of non-Markovian processes by higher-dimensional Markovian processes via the introduction of auxiliary variables and use this method to approximate the limiting GLE. In contrast, we show the inadequacy of a so-called fractional Fokker–Planck equation in the present context. All results are supported by direct numerical experiments.     

Collisional quenching of resonance states of rare gases

We report an experimental study of Xe(³P₁) → Xe(³P₂) electronic quenching by Ar in Xe/Ar mixtures optically excited by the 1470 Å line of Xe. The quenching process was monitored by the observation of the Xe^*₂ second emission continuum at low Xe pressures.     

Perturbations of molecular extravalence excitations by rare-gas fluids

In this paper we report the results of an experimental study of the vacuum ultraviolet absorption spectra of molecular impurity states of methyl iodide in Ar (density range ? = 0–1.4 g cm^?3) and in Kr (? = 0–2.3 g cm^?3), of carbon disulphide in Ar (? = 0–1.4 g cm^?3) and of formaldehyde in Ar (? = 0–1.25 g cm^?3). The experimental results provide new information regarding medium perturbations of intravalenc transitions, of the lowest extravalence transitions and of transitions to mixed valence—Rydberg configurations, which serve as a diagnostic tool to distinguish between different types of electronic excitations. All the lowest extravalence molecular excitations exhibit appreciable blue spectral shifts at moderate and at high fluid densities, intravalence transitions are practically insensitive to medium effects, while excitations to mixed valence—Rydberg configurations are characterized by a moderate blue spectral shift. New information has been obtained concerning the energetics of molecular ionization processes in a dense fluid. The high n = 2–5 Rydberg states of CH₃l exhibit a large red shift at moderate (? = 0–0.5 cm^?3) Ar densities. The ionization potential E_g and the effective Rydberg constant G for CH₃I in Ar was found to decrease from G = 13.6 eV and E_g = 9.55 eV at ? = 0 and E_g = 9.08 eV and constant G for CH₃l in Ar was found to decrease from G = 13.6 eV and E_g = 9.55eV at ? = 0 and E_g = 9.08 eV and G ≈ 7.15 eV at ? = 0.5 g cm^?3. Experimental evidence was obtained for the identification of n = 2 molecular Wannier impurity states of CH₃I and of CH₂O in liquid Ar. These spectroscopic data result in E_g ≈ 8.6 eV for CH₃I in liquid Ar and E_g ≈ 10.2 eV for CH₂O in liquid Ar.     

Aerobic Iron‐Based Cross‐Dehydrogenative Coupling Enables Efficient Diversity‐Oriented Synthesis of Coumestrol‐Based Selective Estrogen Receptor Modulators

An iron‐based cross‐dehydrogenative coupling (CDC) approach was applied for the diversity‐oriented synthesis of coumestrol‐based selective estrogen receptor modulators (SERMs), representing the first application of CDC chemistry in natural product synthesis. The first stage of the two‐step synthesis of coumestrol involved a modified aerobic oxidative cross‐coupling between ethyl 2‐(2,4‐dimethoxybenzoyl)acetate and 3‐methoxyphenol, with FeCl₃ (10 mol %) as the catalyst. The benzofuran coupling product was then subjected to sequential deprotection and lactonization steps, affording the natural product in 59 % overall yield. Based on this new methodology other coumestrol analogues were prepared, and their effects on the proliferation of the estrogen receptor (ER)‐dependent MCF‐7 and of the ER‐independent MDA‐MB‐231 breast cancer cells were tested. As a result, new types of estrogen receptor ligands having an acetamide group instead of the 9‐hydroxyl group of coumestrol were discovered. Both 9‐acetamido‐coumestrol and 8‐acetamidocoumestrol were found more active than the natural product against estrogen‐dependent MCF‐7 breast cancer cells, with IC₅₀ values of 30 and 9 nM , respectively.     

Electrical properties study of multi-walled carbon nanotubes/hybrid-glass nanocomposites

Electrical properties of multi-walled carbon nanotubes (MWNTs)/hybrid-glass nanocomposites prepared by the fast-sol–gel reaction were investigated in light of percolation theory. A good correlation was found between the experimental results and the theory. We obtained a percolation threshold ? _c  = 0.22 wt%, and a critical exponent of t = 1.73. These values are reported for the first time for a silica-based system. The highest conductivity measured on the MWNT/hybrid-glass nanocomposites was σ ≈ 10^?3(Ω cm)^?1 for 2 wt% carbon nanotube (CNT) loading. The electrical conductivity was at least 12 orders of magnitude higher than that of pure silica. Electrostatic force microscopy and conductive-mode atomic force microscopy studies demonstrated conductivity at the micro-level, which was attributed to the CNT dispersed in the matrix. It appears that the dispersion in our MWNT/hybrid-glass system yields a particularly low percolation threshold compared with that of a MWNT/silica-glass system. Materials with electrical conductivities described in this work can be exploited for anti-static coating.     

Lower Bounds on the Distortion of Embedding Finite Metric Spaces in Graphs

The main question discussed in this paper is how well a finite metric space of size n can be embedded into a graph with certain topological restrictions. The existing constructions of graph spanners imply that any n -point metric space can be represented by a (weighted) graph with n vertices and n ^{1 +O(1/r)} edges, with distances distorted by at most r . We show that this tradeoff between the number of edges and the distortion cannot be improved, and that it holds in a much more general setting. The main technical lemma claims that the metric space induced by an unweighted graph H of girth g cannot be embedded in a graph G (even if it is weighted) of smaller Euler characteristic, with distortion less than g/4 - 3/2 . In the special case when |V(G)| =|V(H)| and G has strictly less edges than H , an improved bound of g/3 - 1 is shown. In addition, we discuss the case χ(G) < χ(H) - 1 , as well as some interesting higher-dimensional analogues. The proofs employ basic techniques of algebraic topology. Received September 26, 1995, and in revised form March 18, 1996.     

Microscopic visualization of alamethicin incorporation into model membrane monolayers

Lipid interactions and cooperative assembly properties are fundamental determinants for the action of antimicrobial membrane-active peptides. Here we analyze the interactions and aggregation properties of alamethicin, an antimicrobial pore-forming peptide, with films formed at the air/water interface. Surface-area/pressure isotherms, Brewster angle microscopy, and fluorescence-confocal microscopy provided detailed information on the morphologies and structural properties of the peptide and its effect on the film components. The pressure-area analysis and microscopy experiments facilitated unprecedented visualization of the structural consequences of alamethicin association at the air/water interface, with pure phospholipid films, and within mixed phospholipid/polydiacetylene (PDA) films. The analysis exposed the kinetic features and the interplay between the peptide aggregates and film constituents. In particular, the results demonstrate the use of phospholipid/PDA film assemblies for studying membrane-peptide association and interactions within two-dimensional films.     

Approximating CVP to Within Almost-Polynomial Factors is NP-Hard

This paper shows the problem of nding the closest vector in an n-dimensional lattice to be NP-hard to approximate to within factor n ^{c/log log n} for some constant c > 0.