Stratifiable Families of Extremals and Sufficient Conditions for Optimality in Optimal Control Problems

It is shown that, if a parametrized fämily of extremals F can be stratified in a way compatible with the flow map generated by F, then those trajectories of the family which realize the minimal values of the cost in F are indeed optimal in comparison with all trajectories which lie in the region R covered by the trajectories of F. It is not assumed that F is a field covering the state space injectively. As illustration, an optimal synthesis is constructed for a system where the flow of extremals exhibits a simple cusp singularity.     

Lattices contained in planar orders are planar

The covering graph of a lattice which is contained in an ordered set with a planar covering graph is itself planar.Presented by R. W. Quackenbush.     

Sufficient conditions for a strong relative minimum in an optimal control problem

In this paper, on the basis of Young's method (Ref. 1), sufficient conditions for a strong relative minimum in an optimal control problem are given. Young's method generalizes geodesic coverings and the simplest Hilbert integral from the standard variational calculus. This paper carries Young's method over to nonparametric problems.     

Multipeak distributions of first passage times in bistable dynamics in a model of a thermochemical system.

A master equation is used to study transitions between the stable limit cycle and stable focus in the two-variable bistable system. The distribution function of the mean first passage time between these attractors and the relative dispersion of the mean first return time from the stable focus to itself as a function of the intensity of fluctuations are calculated and discussed. A coherence resonance is observed for the return time from the focus to itself.     

The endomorphism spectrum of an ordered set

Theendomorphism spectrum of an ordered setP, spec(P)={|f(P)|:f End(P)} andspectrum number, sp(P)=max(spec(P)\{|P|}) are introduced. It is shown that |P|>(1/2)n(n – 1) ^{n – 1} implies spec(P) = {1, 2, ...,n} and that if a projective plane of ordern exists, then there is an ordered setP of size 2n ²+2n+2 with spec(P)={1, 2, ..., 2n+2, 2n+4}. Lettingh(n)=max{|P|: sp(P)n}, it follows thatc ₁ n ²h(n)c ₂ n ⁿ⁺¹ for somec ₁ andc ₂. The lower bound disproves the conjecture thath(n)2n. It is shown that if |P| – 1 spec(P) thenP has a retract of size |P| – 1 but that for all there is a bipartite ordered set with spec(P) = {|P| – 2, |P| – 4, ...} which has no proper retract of size|P| – . The case of reflexive graphs is also treated.Partially supported by a grant from the NSERC.Partially supported by a grant from the NSERC.     

On gauge invariance of Breit-Wigner propagators

We present an approach to bosonic (Z ^o,W ^±) as well as fermionic (top-quark) Breit-Wigner propagators which is consistent with gauge invariance arguments. In particular, for theZ ^o-boson propagator we extend previous analyses and show that the part proportional tok k _v /M ² must be modified near the resonance. We derive a mass shift which agrees with results obtained elsewhere by different methods. The modified form of a resonant heavy fermion propagator is also given.     

Morphology,surface roughness,electron inelastic and quasielastic scattering in elastic peak electron spectroscopy of polymers

In elastic peak electron spectroscopy (EPES), the nearest vicinity of elastic peak in the low kinetic energy region reflects electron inelastic and quasielastic processes. Incident electrons produce surface excitations, inducing surface plasmons, with the corresponding loss peaks separated by 1–20 eV energy from the elastic peak. In this work, X‐ray photoelectron spectroscopy (XPS) and helium pycnometry are applied for determining surface atomic composition and bulk density, whereas atomic force microscopy (AFM) is applied for determining surface morphology and roughness. The component due to electron recoil on hydrogen atoms can be observed in EPES spectra for selected primary electron energies. Simulations of EPES predict a larger contribution of the hydrogen component than observed experimentally, where hydrogen deficiency is observed. Elastic peak intensity is influenced more strongly by surface morphology (roughness and porosity) than by surface excitations and quasielastic scattering of electrons by hydrogen atoms. Copyright © 2007 John Wiley & Sons, Ltd.     

Fundamental Characterization,Photophysics and Photocatalysis of a Base Metal Iron(II)-Cobalt(III) Dyad

A new base metal iron-cobalt dyad has been obtained by connection between a heteroleptic tetra-NHC iron(II) photosensitizer combining a 2,6-bis[3-(2,6-diisopropylphenyl)imidazol-2-ylidene]pyridine with 2,6-bis(3-methyl-imidazol-2-ylidene)-4,4′-bipyridine ligand, and a cobaloxime catalyst. This novel iron(II)-cobalt(III) assembly has been extensively characterized by ground- and excited-state methods like X-ray crystallography, X-ray absorption spectroscopy, (spectro-)electrochemistry, and steady-state and time-resolved optical absorption spectroscopy, with a particular focus on the stability of the molecular assembly in solution and determination of the excited-state landscape. NMR and UV/Vis spectroscopy reveal dissociation of the dyad in acetonitrile at concentrations below 1 mM and high photostability. Transient absorption spectroscopy after excitation into the metal-to-ligand charge transfer absorption band suggests a relaxation cascade originating from hot singlet and triplet MLCT states, leading to the population of the ³MLCT state that exhibits the longest lifetime. Finally, decay into the ground state involves a ³MC state. Attachment of cobaloxime to the iron photosensitizer increases the ³MLCT lifetime at the iron centre. Together with the directing effect of the linker, this potentially makes the dyad more active in photocatalytic proton reduction experiments than the analogous two-component system, consisting of the iron photosensitizer and Co(dmgH)₂(py)Cl. This work thus sheds new light on the functionality of base metal dyads, which are important for more efficient and sustainable future proton reduction systems.