Boundedness and Dissipativity of Truncated Rotations on Uniform Planar Lattices

The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated.     

Fractional iteration and a generalised abel's equation in two variables

Aequationes mathematicae -     

Uniqueness,Extinction and Explosivity of Generalised Markov Branching Processes with Pairwise Interaction

We examine basic properties regarding uniqueness, extinction, and explosivity for the generalised Markov branching processes with pairwise interaction. First we establish uniqueness criteria, proving that in the essentially-explosive case the process is honest if and only if the mean death rate is greater than or equal to the mean birth rate, while in the sub-explosive case the process is dishonest only in exceptional circumstances. Explicit expressions are then obtained for the extinction probabilities, the mean extinction times and the conditional mean extinction times. Explosivity is also investigated and an explicit expression for mean explosion time is established.     

A stochastic functional equation

Aequationes mathematicae -     

Toward Best Approximation of Nonlinear Systems: A Case of Models with Memory

The problem of nonlinear dynamical system modeling, considered in this paper, is motivated by restrictions arising in real-world tasks. The restrictions are that first, a system input cannot be entirely observed for one trial. Second, the system model must be subjected to the causality principle. Third, the input is corrupted by noise so that no relationship between the reference input and noise is known. Fourth, the model should have some degrees of freedom so that the associated accuracy can be regulated by a variation of these freedom degrees. We propose and justify new procedures for the nonlinear system modeling that are initialized by these motivations. The models are nonlinear and given by so called r-degree operators that can be reduced to a matrix form presentation. To satisfy the restrictions above, the matrices have special structures that we call the lower p-band matrices. The degree r of the models is the required degree of freedom. The rigorous analysis of errors associated with the presented techniques is given. Numerical experiments with real data demonstrate the efficiency of the proposed approach.     

A Novel Route to the Fused Maleic Anhydride Moiety of CP Molecules

A seven‐step cascade reaction —in which selective mesylation, epoxide formation, epoxide lysis, cyclization, reiterative oxidation, and nitrogen–oxygen exchange occur sequentially—facilitates the construction of the maleic anhydride moiety of CP molecules 1 and 2 (>93% yield per step). Unstable intermediates of this reaction sequence were detected, providing evidence for the proposed mechanism and resulting in the discovery of a new chemical entity.     

Effects of degassing on the long-range attractive force between hydrophobic surfaces in water

The long-ranged attractions between hydrophobic amorphous fluoropolymer surfaces are measured in water with and without dissolved air. An atomic force microscope is used to obtain more than 500 measured jump-in distances, which yields statistically reliable results. It is found that the range of the attraction and its variability is generally significantly decreased in deaerated water as compared to normal, aerated water. However, the range and strength of the attraction in deaerated water remain significantly greater than the van der Waals attraction for this system. The experimental observations are consistent with (1) nanobubbles being primarily responsible for the long-ranged attraction in normal water, (2) nanobubbles not being present in deaerated water when the surfaces are not in contact, and (3) the attraction in the absence of nanobubbles being most probably due to the approach to the separation-induced spinodal cavitation of the type identified by Bérard et al. [J. Chem. Phys. 1993, 98, 7236]. It is argued that the measurements in deaerated water reveal the bare or pristine hydrophobic attraction unobscured by nanobubbles.     

Surface tension of a Lennard-Jones liquid under supersaturation

A formally exact Kirkwood-Buff virial formula for the surface tension of a supersaturated interface is derived. A modified Gibbs ensemble method is given that allows the creation of interacting supersaturated phases of equal chemical potential, and which enables the Kirkwood-Buff formula to be applied. The methods are tested by Monte Carlo simulation of a supersaturated Lennard-Jones fluid with a planar liquid-vapor interface. The Kirkwood-Buff results for the supersaturated surface tension are found to be in reasonable agreement with new results obtained here using the recently developed, formally exact, ghost interface method, [M. P. Moody and P. Attard, J. Chem. Phys., 2002, 117, 6705]. The surface tension is obtained as a function of supersaturation at four temperatures, and it is found to decrease with increasing supersaturation, and to vanish at the vapor spinodal. The relevance of the present results to the nucleation of droplets in a supersaturated vapor is discussed.     

New Homoleptic Rare‐Earth Metal Complexes Comprising the Unsymmetrically Substituted Amidinate Ligand [MeC(NEt)(NtBu)]–

New homoleptic complexes of selected rare‐earth elements containing the unsymmetrically substituted amidinate ligand [MeC(NEt)(NtBu)]^– [= (L)^–] were synthesized and fully characterized. Treatment of in situ‐prepared Li(L) ( 1 ) with anhydrous lanthanide(III) chlorides, LnCl₃ (Ln = Sc, La, Ce, Ho), afforded three different types of amidinate complexes depending on the ionic radius of the central metal atom. The large La³⁺ formed the octa‐coordinate DME solvate La(L)₃(DME) ( 2 ). Using Ce³⁺, the octa‐coordinate “ate” complex Li(THF)[Ce(L)₄] ( 3 ) was formed. Depending on the crystallization conditions, compound 3 could be crystallized in two modifications differing in the coordination environment around Li. In the case of the smaller Sc³⁺ and Ho³⁺ ions, six‐coordinate homoleptic Sc(L)₃ ( 4 ) and Ho(L)₃ ( 5 ) were isolated. The title compounds were fully characterized by spectroscopic and analytical methods as well as single‐crystal X‐ray diffraction. With Ln = La and Ce, several by‐products incorporating lithium, chlorine and/or oxygen were also isolated and structurally characterized.     

Effect of hydrothermal aging on NOx reduction performance for Sb–V–CeO2/TiO2 catalyst

Research on Chemical Intermediates - Herein, we investigated the NOx reduction performance of Sb–V–CeO2/TiO2 (SbVCT) catalyst subjected to hydrothermal aging, where 6 vol% of H2O was...