Infinite independent sets in distributive lattices

We show that a poset P contains a subset isomorphic to if and only if the poset J(P) consisting of ideals of P contains a subset isomorphic to the power set of κ. If P is a join-semilattice this amounts to the fact that P contains an independent set of size κ. We show that if κ := ω and P is a distributive lattice, then this amounts to the fact that P contains either or as sublattices, where Γ and Δ are two special meet-semilattices already considered by J. D. Lawson, M. Mislove and H. A. Priestley.Dedicated to the memory of Ivan RivalReceived April 22, 2003; accepted in final form July 11, 2004.This revised version was published online in August 2005 with a corrected cover date.     

Optoreflectometry Determination of the Resonance Properties of a Vocal Fold

A new method of measuring the resonance properties of a vocal fold using electromagnetic excitation and laser optoreflectometry for response monitoring is described. Two resonance peaks were experimentally identified with one magnet stuck on the vocal fold at frequencies F0(1m)=54.7 Hz and F0'(1m)=35.8 Hz. The addition of a second magnet allowed calculation of the actual viscoelastic properties of the vocal fold: F0=71.8 Hz; quality factor Q=8.03; mass m=0.057 g; stiffness k=11.6 Nm; and damping zeta=0.0032 Nm(-1). A numerical simulation of a two-layered model verified the experimental data.     

Electrochemical study of the thermodynamics and kinetics of hydrophilic ion transfers across water | <Emphasis Type="Italic">n</Emphasis>-octanol interface

Thermodynamics and kinetics of hydrophilic ion transfers across water|n-octanol (W|OCT) interface have been electrochemically studied by means of novel three-phase and thin-film electrodes. Three-phase electrodes used for thermodynamics measurements comprise edge plane pyrolytic graphite, the surface of which was partly modified with an ultrathin film of OCT, containing hydrophobic lutetium bis(tetra-tert-butylphthalocyaninato) (Lu[tBu₄Pc]₂) as a redox probe. The transfers of anions and cations from W to OCT were electrochemically driven by reversible redox transformations of Lu[tBu₄Pc]₂ to chemically stable lipophilic monovalent cation and anion , respectively. Upon reduction of Lu[tBu₄Pc]₂, the transfers of alkali metal cations from W to OCT have been studied for the first time, enabling estimation of their Gibbs transfer energies. For kinetic measurements, a thin-film electrode configuration has been used, consisting of the same electrode covered completely with a thin layer of OCT that contained the redox probe and a suitable electrolyte. Combining the fast and sensitive square-wave voltammetry with thin-film electrodes, the kinetics of , , and Cl⁻ transfers have been estimated. Dedicated to Professor Dr. Yakov I. Tur’yan on the occasion of his 85th birthday.     

An EPR/ENDOR study of the asymmetric hydrogen bond between the quinone electron acceptor and the protein backbone in Photosystem I

Hydrogen bonding to the photoaccumulated secondary acceptor radical anion A₁^√− in photosystem (PS) I has been studied using pulsed Q-band ENDOR spectroscopy. With deuterated quinone in protonated PS I particles it is demonstrated that the observed radical anion has only one hydrogen-bond hyperfine coupling (hfc) tensor with tensor components above the 2 MHz range. Below 2 MHz the protein matrix protons dominate and a second weak H-bond could not be detected. The spectral resolution of pulsed Q-band ENDOR is critically required to separate the signals of the H-bond proton from those of the primary chlorophyll acceptor, A₀^√−, which cannot be avoided to be formed to some extent in the photoaccumulation procedure. The determined H-bond hfc tensor of A₁^√− is found to be close to axial symmetry with a small isotropic component, as expected from a predominantly dipolar electron–proton spin interaction in a hydrogen-bond. The principal tensor components are A=(+)7.7, MHz A=(−)4.9 MHz, A_iso=(−)0.7 MHz. The magnitude of the dipolar tensor corresponds to an unusually short H-bond which can be estimated from the point-dipole approximation (1.5±0.1 Å). Based on previous studies with A- and B-branch specific site-directed mutants of the A₁ site of PS I and the chosen photoaccumulation protocol, the observed A₁^√− radical anion can be assigned to the Q_K–A site of the A-branch. The observed H-bond hfc tensor is compared to those determined for related quinone radical anions observed in frozen protic solution as well as in the Q_A site of type II bacterial reaction centers.     

Trifluoromethylated enaminones and their explorative coordination chemistry with Cu(II): synthesis, redox properties and structural characterization of the complexes

The syntheses of three original trifluoromethylated enaminones L1H-L3H, an unexplored type of ligand with possible multiple coordination centres, their redox properties and explorative coordination chemistry with copper(II) are presented. The ability of these ligands to coordinate copper(II) and then to form new mono- and dinuclear complexes is presented and discussed. The consequences of this metal coordination on redox properties are also explored.     

Femtosecond time-resolved photoelectron-photoion coincidence imaging of multiphoton multichannel photodynamics in NO2

The multiphoton multichannel photodynamics of NO(2) has been studied using femtosecond time-resolved coincidence imaging. A novel photoelectron-photoion coincidence imaging machine was developed at the laboratory in Amsterdam employing velocity map imaging and "slow" charged particle extraction using additional electron and ion optics. The NO(2) photodynamics was studied using a two color pump-probe scheme with femtosecond pulses at 400 and 266 nm. The multiphoton excitation produces both NO(2) (+) parent ions and NO(+) fragment ions. Here we mainly present the time dependent photoelectron images in coincidence with NO(2) (+) or NO(+) and the (NO(+),e) photoelectron versus fragment ion kinetic energy correlations. The coincidence photoelectron spectra and the correlated energy distributions make it possible to assign the different dissociation pathways involved. Nonadiabatic dynamics between the ground state and the A (2)B(2) state after absorption of a 400 nm photon is reflected in the transient photoelectron spectrum of the NO(2) (+) parent ion. Furthermore, Rydberg states are believed to be used as "stepping" states responsible for the rather narrow and well-separated photoelectron spectra in the NO(2) (+) parent ion. Slow statistical and fast direct fragmentation of NO(2) (+) after prompt photoelectron ejection is observed leading to formation of NO(+)+O. Fragmentation from both the ground state and the electronically excited a (3)B(2) and b (3)A(2) states of NO(2) (+) is observed. At short pump probe delay times, the dominant multiphoton pathway for NO(+) formation is a 3x400 nm+1x266 nm excitation. At long delay times (>500 fs) two multiphoton pathways are observed. The dominant pathway is a 1x400 nm+2x266 nm photon excitation giving rise to very slow electrons and ions. A second pathway is a 3x400 nm photon absorption to NO(2) Rydberg states followed by dissociation toward neutral electronically and vibrationally excited NO(A (2)Sigma,v=1) fragments, ionized by one 266 nm photon absorption. As is shown in the present study, even though the pump-probe transients are rather featureless the photoelectron-photoion coincidence images show a complex time varying dynamics in NO(2). We present the potential of our novel coincidence imaging machine to unravel in unprecedented detail the various competing pathways in femtosecond time-resolved multichannel multiphoton dynamics of molecules.