The essential Lagrangian-Grassmannian and the homotopy type of the Fredholm Lagrangian-Grassmannian

Let H be a separable infinite dimensional Hilbert space endowed with a symplectic structure and let L₀⊂H be a Lagrangian subspace. Using the results of [A. Abbondandolo, P. Majer, Infinite dimensional Grassmannians, math.AT/0307192], we show that the Fredholm Lagrangian-Grassmannian FL₀(Λ) has the homotopy type of Gc(L₀), the Grassmannian of all Lagrangian subspaces of H that are compact perturbations of L₀. It is well known that the latter has the homotopy type of the quotient U(∞)/O(∞). As a corollary, we recover a result by B. Booss-Bavnbek and K. Furutani (see [B. Booss-Bavnbek, K. Furutani, Symplectic functional analysis and spectral invariants, Contemp. Math. 242 (1999) 53-83; K. Furutani, Fredholm-Lagrangian-Grassmannian and the Maslov index, J. Geom. Phys. 51 (2004) 269-331]) that the L₀-Maslov index is an isomorphism between the fundamental group of FL₀(Λ) and the integers.     

Specific MARY spectrum from radical anion of pentafluorobenzene

The paper presents the first resolved experimental magnetically affected reaction yield (MARY) spectrum for a system with nonequivalent nuclei, radical anion of pentafluorobenzene. This observation dispels the common apprehension that because of a rather involved energy level layout a system with not all nuclei magnetically equivalent cannot produce resolved MARY lines in nonzero fields, and greatly, increases the practical scope of level-crossing techniques for studies of spin-correlated radical pairs. The experimental finding is supported by schemes of energy levels calculated for this system.     

Advances in constant-velocity Mössbauer instrumentation

A prototype of a programmable constant-velocity scaler is presented. This instrument allows the acquisition of partial Mössbauer spectra in selected energy regions using standard drivers and transducers. It can be fully operated by a remote application, thus data acquisition can be automated. The instrument consists of a programmable counter and a constant-velocity reference. The reference waveform generator is amplitude modulated with 13-bit resolution, and is programmable in a wide range of frequencies and waveforms in order to optimize the performance of the transducer. The counter is compatible with most standard SCA, and is configured as a rate-meter that provides counts per selectable time slice at the programmed velocity. As a demonstration of the instrument applications, a partial Mössbauer spectrum of a natural iron foil was taken. Only positive energies were studied in 512 channels, accumulating 20 s per channel. A line width of 0.20 mm/s was achieved, performing with an efficiency of 80%.     

Epimerization, diastereoselectivity and hemilability in dicationic chiral ruthenium complexes with bidentate (PS) bisphosphine monosulfide ligands

The binding of heterobidentate P^∧S ligands introduces metal-centered chirality to the planar chiral parent complex Ru(η⁶:η¹-NMe₂C₆H₄C₆H₄PCy₂)Cl₂. Observed diastereomeric ratios for the kinetic product vary dramatically depending upon ring size of the chelate formed with the P^∧S ligand. The complexes epimerize very slowly to thermodynamic product ratios that are substantially different from the kinetic product ratios.     

Some remarks on Newton–Sabatier methods

It is shown how Newton–Sabatier methods (arising in inverse scattering at fixed energy) can be related to spectral measures and typically when they correspond to regular potentials. A number of spectral formulae for various transmutation kernels are also given in terms of general Kontorovi?–Lebedev theory and connections to generating functions, generalized orthogonal polynomials, etc. are indicated.     

Determination of cyanuric acid in swimming pool water by differential pulse polarography

A reliable differential pulse polarographic method is described for the determination of cyanuric acid (1,3,5-triazine-2,4,6-triol) in pool water. Cyanuric acid in the range 10^?5–10^?3 M is determined by means of the peak at ca. –60 mV (vs. Ag/AgCl/3 M NAcl). The high sensitivity of the polarographic technique allows ten-fold dilution of samples, thus avoiding matrix effects. It it shown that the peak can be attributed to formation of insoluble mercury(I) cyanurate, Hg₂(HC₃N₃O₃), at the mercury electrode.     

On perfectly normal dense subspaces of products

Let M be a separable metric space consisting of more than one point. We construct perfectly normal dense subspaces Z⊂Mc² and (under additional set-theoretic assumption) Y⊂Mc which are not collectionwise Hausdorff.