Group IV complexes of a tetradentate amine mono(phenolate) ligand: a second side-arm donor stabilizes cationic species

An amine mono(phenolate) ligand bearing two side-arm donors led to octahedral trialkoxo and trialkyl group IV metal complexes, in which one of the donors was unbound, and to exceptionally stable cationic complexes in which the two side-arm donors were tightly bound.     

Geometrical and electronic structures of dinuclear complex ions {(mu-bpym)[Cu(EAr3)2]2}2+ with intramolecular "organic sandwich" formation (E = P or As; Ar = Aryl; bpym = 2,2'-bipyrimidine)

The compound {(mu-bpym)[Cu(AsPh3)2]2}(BF4)2 (1) has been prepared and studied in comparison with the triphenylphosphine analogue 2. Qualitatively, the structure of 1 with characteristically distorted copper(I) coordination caused by Ph/bpym/Ph sandwich interactions is similar to that of 2 and is approximately reproduced by DFT calculations for the model complex ions {(mu-bpym)[Cu(EMe2Ph)2]2}2+, E = P or As. In contrast, the dinuclear {(mu-bpym)[Cu(P(3-Me-C6H4)3)2]2}(BF4)2 (3) displays a distinctly less distorted metal coordination geometry due to the steric requirements of the methyl groups in the meta-tolyl substituents. The electrochemical reduction of 1 is less reversible than for the phosphine analogues; the one-electron-reduced form 1*- exhibits a broad, unresolved EPR signal at g = 2.0023. Resonance Raman spectroscopy of 1 shows the typical vibrations of the bpym ligand in agreement with the MLCT assignment of the long-wavelength transitions below 500 nm. All three dinuclear complexes exhibit luminescence at room temperature in the solid and in solution.     

Density functional theory calculations of selected Ru(II) two ring diimine complex dications

Geometry optimization for a series of ten, two-ring diimine Ru(II) complexes was effected using the Gaussian 98 protocol at density functional theory (DFT) B3LYP level with basis sets 3-21G*and 3-21G**. HOMO-LUMO energy difference values compared favorably to the experimental data from electrochemistry [Delta E(1/2) = (E(1/2ox) - E(1/2red))] and the lowest energy absorption maxima, which for these complexes correspond to the metal-to-ligand charge transfer (MLCT) band. The HOMO and LUMO distributions from DFT support the idea that the lowest energy transitions are metal-to-ligand charge transfer and that the lowest energy LUMO for the mixed ligand complexes is located on 2,2'-bipyrazine (bpz), followed by 2,2'-bipyrimidine (bpm) and then 2,2'-bipyridine (bpy).     

A novel approach for coincidence ion mass spectrometry

A novel approach is proposed for extracting a maximum of information from secondary ions ejected when surfaces are bombarded with keV mono or polyatomic ions. It is known that the event-by-event bombardment-detection mode allows identification of spatiotemporal relationships among individual secondary ions which in turn reveal surface composition within nanometric dimensions. We have devised a procedure for identifying spatiotemporal relationships among individual secondary ions without the requirement of pulsed sample interrogation (one single projectile at a time). The consequence of "mass separated time-of-flight mass spectrometry" is a much improved measurement duty cycle.     

A dynamical model of water recycling in a mine-processing enterprise

We consider a mine-processing enterprise, which runs a number of production plants. Each plant uses a considerable amount of water which is polluted during the production process. The aim is to determine the optimal amounts of water to be taken from a river or to be pumped back from a waste water reservoir. The problem is decomposed in two tasks. Task 1 is formulated as a time-discrete optimal control model and determines the amounts of water pumped in each period. The solution method used is dynamic programming. While Task 1 has an ecological objective (minimize environmental damage), in Task 2 the aim is to determine, by which pump configurations the desired quantities of water are most efficiently brought to reservoir (with least cost). Because of the special structure of this linear programming problem it can be solved simply by sorting with respect to unit costs.     

On Osgood theorem in Banach spaces

Let X be a real Banach space, ω : [0, +∞) → ? be an increasing continuous function such that ω(0) = 0 and ω(t + s) ≤ ω(t) + ω(s) for all t, s ∈ [0, +∞). According to the infinite dimensional analog of the Osgood theorem if ∫¹₀ (ω(t))^?1 dt = ∞, then for any (t₀, x₀) ∈ ?×X and any continuous map f : ?×X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all t ∈ ?, x, y ∈ X, the Cauchy problem (t) = f(t, x(t)), x(t₀) = x₀ has a unique solution in a neighborhood of t₀. We prove that if X has a complemented subspace with an unconditional Schauder basis and ∫¹₀ (ω(t))^?1 dt < ∞ then there exists a continuous map f : ? × X → X such that ∥f(t, x) – f(t, y)∥ ≤ ω(∥x – y∥) for all (t, x, y) ∈ ? × X × X and the Cauchy problem (t) = f(t, x(t)), x(t₀) = x₀ has no solutions in any interval of the real line.     

Ideas in the theory of random media

These lectures discuss the ideas of localization, intermittency, and random fluctuations in the theory of random media. These ideas are compared and contrasted with the older approach based on averaging. Within this framework, the topics discussed include: Anderson localization, turbulent diffusion and flows, periodic Schrödinger operators and averaging theory, longwave oscillations of elastic random media, stochastic differential equations, the spectral theory of Hamiltonians with (an infinite sequence of) wells, random Schrödinger operators, electrons in a random homogeneous field, influence of localization effects on the propagation of elastic waves, the Lyapunov spectrum (Lyapunov exponents), the Furstenberg and Oseledec theorems for ann-tuple of identically distributed unimodular matrices and their relation with the spectral theory of random Schrödinger or string operators, Rossby waves, averaging on random Schrödinger operators, percolation mechanisms, the moments method in the theory of sequences of random variables, the evolution of a magnetic field in the turbulent flow of a conducting fluid or plasma (the so-called kinematical dynamo problem), heat transmission in a randomly flowing fluid.