The effects of conjugation path variation on electron delocalization in phenoxyl-based systems

A number of persistent 2,6-di-tert-butylphenoxyl based radicals were synthesized as models for unpaired spin delocalization as a function of conjugation pathway, and were investigated by ESR and UV-vis spectroscopy. Phenoxyl spin delocalizes significantly onto a para-phenyl ring, but further delocalization through a meta-vinyl or meta-carbonyl linkage is not detectable by ESR hyperfine coupling. UV- vis spectra do show a red shift of the longest wavelength transition for a carbonyl-type substituent by comparison to a vinyl substituent in the meta-position of a para-phenyl group. By comparison, a para-styryl substituent on the phenoxyl causes very large spin delocalization from the phenoxyl unit, with the largest hyperfine coupling being found on the ethenyl unit of the assemblage. This large delocalization accounts for the reactivity of radicals that incorporate such units.     

Mappings of finite distortion: Removable singularities

We derive sufficiently sharp local dimension-free estimates for volumes of sublevel sets of analytic functions in the unit ball of ℂ ⁿ The research was partially supported by the United States-Israel Binational Science Foundation.     

Galerkin Approximations for the Linear Parabolic Equation with the Third Boundary Condition

We solve a linear parabolic equation in ^d , d 1, with the third nonhomogeneous boundary condition using the finite element method for discretization in space, and the -method for discretization in time. The convergence of both, the semidiscrete approximations and the fully discretized ones, is analysed. The proofs are based on a generalization of the idea of the elliptic projection. The rate of convergence is derived also for variable time step-sizes.     

Acoustic detection and classification of river boats

We present a robust algorithm to detect the arrival of a boat of a certain type when other background noises are present. It is done via the analysis of its acoustic signature against an existing database of recorded and processed acoustic signals. We characterize the signals by the distribution of their energies among blocks of wavelet packet coefficients. To derive the acoustic signature of the boat of interest, we use the Best Discriminant Basis method. The decision is made by combining the answers from the Linear Discriminant Analysis (LDA) classifier and from the Classification and Regression Trees (CART) that is also accompanied with an additional unit, called Aisles, that reduces false alarms rate. The proposed algorithm is a generic solution for process control that is based on a learning phase (training) followed by an automatic real time detection while minimizing the false alarms rate.     

Relativity and the lead-acid battery

The energies of the solid reactants in the lead-acid battery are calculated ab?initio using two different basis sets at nonrelativistic, scalar-relativistic, and fully relativistic levels, and using several exchange-correlation potentials. The average calculated standard voltage is 2.13?V, compared with the experimental value of 2.11?V. All calculations agree in that 1.7-1.8?V of this standard voltage arise from relativistic effects, mainly from PbO2 but also from PbSO4.     

The structure of Cu{100}-p(2 × 6)-2mg-Sn studied by DFT and LEED

Low Energy Electron Diffraction (LEED) and Density Functional Theory (DFT) have been used to analyse the structure of Cu{100}-p(2 × 6)-2mg-Sn at room temperature. In this work we found that the favoured geometry for this 0.33 ML Cu{100}-Sn phase is a combination of an overlayer structure and a surface alloy; two Sn atoms are alloyed in to the first copper layer and the other two Sn atoms adsorb at off symmetry hollow sites. In order to relieve the stress in the alloyed layer, the alloyed Sn atoms are buckled 0.59/0.45 ± 0.2 Å (DFT/LEED) above the centre of mass of the first layer copper atoms.     

The analytic hierarchy process with stochastic judgements

The analytic hierarchy process (AHP) is a widely-used method for multicriteria decision support based on the hierarchical decomposition of objectives, evaluation of preferences through pairwise comparisons, and a subsequent aggregation into global evaluations. The current paper integrates the AHP with stochastic multicriteria acceptability analysis (SMAA), an inverse-preference method, to allow the pairwise comparisons to be uncertain. A simulation experiment is used to assess how the consistency of judgements and the ability of the SMAA-AHP model to discern the best alternative deteriorates as uncertainty increases. Across a range of simulated problems results indicate that, according to conventional benchmarks, judgements are likely to remain consistent unless uncertainty is severe, but that the presence of uncertainty in almost any degree is sufficient to make the choice of best alternative unclear.     

On the notion of coexistence in quantum mechanics

The notion of coexistence of quantum observables was introduced to describe the possibility of measuring two or more observables together. Here we survey the various different formalisations of this notion and their connections. We review examples illustrating the necessary degrees of unsharpness for two noncommuting observables to be jointly measurable (in one sense of the phrase). We demonstrate the possibility of measuring together (in another sense of the phrase) noncoexistent observables. This leads us to a reconsideration of the connection between joint measurability and noncommutativity of observables and of the statistical and individual aspects of quantum measurements.     

Mappings of finite distortion: the degree of regularity

This paper investigates the self-improving integrability properties of the so-called mappings of finite distortion. Let K(x)1 be a measurable function defined on a domain ΩRⁿ, n2, and such that exp(βK(x))L_loc¹(Ω), β>0. We show that there exist two universal constants c₁(n),c₂(n) with the following property: Let f be a mapping in W_loc^1,1(Ω,Rⁿ) with |Df(x)|ⁿK(x)J(x,f) for a.e. xΩ and such that the Jacobian determinant J(x,f) is locally in L¹ log^−c₁(n)βL. Then automatically J(x,f) is locally in L¹ log^c₂(n)βL(Ω). This result constitutes the appropriate analog for the self-improving regularity of quasiregular mappings and clarifies many other interesting properties of mappings of finite distortion. Namely, we obtain novel results on the size of removable singularities for bounded mappings of finite distortion, and on the area distortion under this class of mappings.