Principles and calibration of collinear photofragmentation and atomic absorption spectroscopy

The kinetics of signal formation in collinear photofragmentation and atomic absorption spectroscopy (CPFAAS) are discussed, and theoretical equations describing the relation between the concentration of the target molecule and the detected atomic absorption in case of pure and impure samples are derived. The validity of the equation for pure samples is studied experimentally by comparing measured target molecule concentrations to concentrations determined using two other independent techniques. Our study shows that CPFAAS is capable of measuring target molecule concentrations from parts per billion (ppb) to hundreds of parts per million (ppm) in microsecond timescale. Moreover, the possibility to extend the dynamic range to cover eight orders of magnitude with a proper selection of fragmentation light source is discussed. The maximum deviation between the CPFAAS technique and a reference measurement technique is found to be less than 5 %. In this study, potassium chloride vapor and atomic potassium are used as a target molecule and a probed atom, respectively.     

Selective Demethylations in 2, 3, 4-Trimethoxyaryl Carbonyl Compounds

2, 3, 4-Trimethoxybenzaldehyde, -acetophenone and -benzoic acid give the corresponding 2, 3-dihydroxy-4-methoxy compounds in good yield on treatment with BCl₃.     

Perfect quantum excitation energy transport via single edge perturbation in a complete network

We consider quantum excitation energy transport (EET) in a network of two-state nodes in the Markovian approximation by employing the Lindblad formulation. We find that EET from an initial site, where the excitation is inserted to the sink, is generally inefficient due to the inhibition of transport by localization of the excitation wave packet in a symmetric, fully-connected network. We demonstrate that the EET efficiency can be significantly increased up to ≈100% by perturbing hopping transport between the initial node and the one connected directly to the sink, while the rate of energy transport is highest at a finite value of the hopping parameter. We also show that prohibiting hopping between the other nodes which are not directly linked to the sink does not improve the efficiency. We show that external dephasing noise in the network plays a constructive role for EET in the presence of localization in the network, while in the absence of localization it reduces the efficiency of EET. We also consider the influence of off-diagonal disorder in the hopping parameters of the network.     

Z→E Photoisomerization of Homoactivated Carbon Carbon Double Bonds

Z-configured 1,4-diene or β,γ-unsaturated carbonyl systems are readily available by the Wittig reaction. Isomerization required for access into the E-series can easily be accomplished by irradiation using an ordinary tungsten lamp and diphenyl disulphide sensitizer. There is very little formation of conjugated isomers (less than 1%).     

Packing dimension and Ahlfors regularity of porous sets in metric spaces

Let X be a metric measure space with an s-regular measure μ. We prove that if A ì X{A\subset X} is r{\varrho} -porous, then dim_p(A) ￡ s-cr^s{{\rm {dim}_p}(A)\le s-c\varrho^s} where dim_p is the packing dimension and c is a positive constant which depends on s and the structure constants of μ. This is an analogue of a well known asymptotically sharp result in Euclidean spaces. We illustrate by an example that the corresponding result is not valid if μ is a doubling measure. However, in the doubling case we find a fixed N ì X{N\subset X} with μ(N) = 0 such that dim_p(A) ￡ dim_p(X)-c(log\tfrac1r)^-1r^t{{\rm {dim}_p}(A)\le{\rm {dim}_p}(X)-c(\log \tfrac1\varrho)^{-1}\varrho^t} for all r{\varrho} -porous sets A ì X\ N{A \subset X{\setminus} N} . Here c and t are constants which depend on the structure constant of μ. Finally, we characterize uniformly porous sets in complete s-regular metric spaces in terms of regular sets by verifying that A is uniformly porous if and only if there is t < s and a t-regular set F such that A ì F{A\subset F} .     

Measurement and modeling of diffraction from an edge of a thin panel

The diffraction of sound from an edge of a thin chipboard panel was measured in an anechoic chamber, and compared to simulations based on the diffraction formulation developed by Svensson et al. [Svensson UP, Fred RI, Vanderkooy J. An analytic secondary source model of edge diffraction impulse responses. J Acoust Soc Am 1999;106(5):2331-44]. The measurements and simulations were performed for a line of receiver positions below the panel to include cases for which the direct sound had an unobstructed propagation path to the receivers, as well as cases for which the direct sound was occluded by the panel. Comparison of the measured and simulated responses is provided in both the time and frequency-domains, and shows that the differences between them are small over the entire audible frequency range. This case study verifies that the applied diffraction-modeling method gives accurate results, and that the assumptions of ideal source and wedge characteristics inherent in the method do not preclude its use in simulations of realistic scenarios.     

Some transformation techniques with applications in global optimization

In this paper some transformation techniques, based on power transformations, are discussed. The techniques can be applied to solve optimization problems including signomial functions to global optimality. Signomial terms can always be convexified and underestimated using power transformations on the individual variables in the terms. However, often not all variables need to be transformed. A method for minimizing the number of original variables involved in the transformations is, therefore, presented. In order to illustrate how the given method can be integrated into the transformation framework, some mixed integer optimization problems including signomial functions are finally solved to global optimality using the given techniques.     

Models for thermal dissociation of silane on a polysilicon surface

Simple models for the thermally activated dissociation reaction of silane and silicon growth on a polycrystalline silicon surface are presented. The models are fitted to recent experimental molecular beam scattering data for the low-pressure reactive sticking coefficient. Thermally activated few-step models fit the data reasonably well, and thus, we are able to explain the temperature and pressure dependencies of the observed deposition rate.     

New methods for calculating \alpha BB-type underestimators

Most branch-and-bound algorithms in global optimization depend on convex underestimators to calculate lower bounds of a minimization objective function. The $\alpha $ BB methodology produces such underestimators for sufficiently smooth functions by analyzing interval Hessian approximations. Several methods to rigorously determine the $\alpha $ BB parameters have been proposed, varying in tightness and computational complexity. We present new polynomial-time methods and compare their properties to existing approaches. The new methods are based on classical eigenvalue bounds from linear algebra and a more recent result on interval matrices. We show how parameters can be optimized with respect to the average underestimation error, in addition to the maximum error commonly used in $\alpha $ BB methods. Numerical comparisons are made, based on test functions and a set of randomly generated interval Hessians. The paper shows the relative strengths of the methods, and proves exact results where one method dominates another.     

Non-branching geodesics and optimal maps in strong CD(K,\infty )-spaces

We prove that in metric measure spaces where the entropy functional is \(K\) -convex along every Wasserstein geodesic any optimal transport between two absolutely continuous measures with finite second moments lives on a non-branching set of geodesics. As a corollary we obtain that in these spaces there exists only one optimal transport plan between any two absolutely continuous measures with finite second moments and this plan is given by a map. The results are applicable in metric measure spaces having Riemannian Ricci curvature bounded below, and in particular they hold also for Gromov-Hausdorff limits of Riemannian manifolds with Ricci curvature bounded from below by some constant.