GA-ACE: Alternating conditional expectations regression with selection of significant predictors by genetic algorithms

The non-linear regression technique known as alternating conditional expectations (ACE) method is only applicable when the number of objects available for calibration is considerably greater than the number of considered predictors. Alternating conditional expectations regression with selection of significant predictors by genetic algorithms (GA-ACE), the non-linear regression technique presented here, is based on the ACE algorithm but introducing several modifications to resolve the applicability limitations of the original ACE method, thus facilitating the practical implementation of a very interesting calibration tool. In order to overcome the lack of reliability displayed by the original ACE algorithm when working on data sets characterized by a too large number of variables and prior to the development of the non-linear regression model, GA-ACE applies genetic algorithms as a variable selection technique to select a reduced subset of significant predictors able to accurately model and predict a considered variable response. Furthermore, GA-ACE actually provides two alternative application approaches, since it allows either the performance of prior data compression computing a number of principal components to be subsequently subjected to GA-selection, or working directly on original variables.In this study, GA-ACE was applied to two real calibration problems, with a very low observation/variable ratio (NIR data), and the results were compared with those obtained by several linear regression techniques usually employed. When using the GA-ACE non-linear method, notably improved regression models were developed for the two response variables modeled, with root mean square errors of the residuals in external prediction (RMSEP) equal to 11.51 and 6.03% for moisture and lipid contents of roasted coffee samples, respectively. The improvement achieved by applying the new non-linear method introduced is even more remarkable taking into account the results obtained with the best performance linear method (IPW-PLS) applied to predict the studied responses (14.61 and 7.74% RMSEP, respectively).     

The determination of the efficiency of energy dispersive X-ray spectrometers by a new reference material.

A calibration procedure for the detection efficiency of energy dispersive X-ray spectrometers (EDS) used in combination with scanning electron microscopy (SEM) for standardless electron probe microanalysis (EPMA) is presented. The procedure is based on the comparison of X-ray spectra from a reference material (RM) measured with the EDS to be calibrated and a reference EDS. The RM is certified by the line intensities in the X-ray spectrum recorded with a reference EDS and by its composition. The calibration of the reference EDS is performed using synchrotron radiation at the radiometry laboratory of the Physikalisch-Technische Bundesanstalt. Measurement of RM spectra and comparison of the specified line intensities enables a rapid efficiency calibration on most SEMs. The article reports on studies to prepare such a RM and on EDS calibration and proposes a methodology that could be implemented in current spectrometer software to enable the calibration with a minimum of operator assistance.     

Nicke(II) halide complexes with hypoxanthine and xanthine

Summary Ni(LH)₃LX complexes (LH=hypoxanthine or xanthine; X=Cl, Br or I) are formed by boiling under reflux 2:1 molar mixtures of LH and hydrated NiX₂ in HC(OEt)₃–MeCO₂Et. The new complexes appear to be linear chain-like polymers, characterized by bidentate monoanionic L^– ligands singly bidging between adjacent Ni²⁺ ions. A coordination number six is attained by the presence of three terminal unidentate LH and one X ligand in the first coordination sphere of each Ni²⁺ ion. The neutral LH and monoanionic L^– ligands bind exclusivelyvia ring nitrogens to Ni^II. The probable binding sites of the uni- and bi-dentate hypoxanthine and ligands in the new complexes are discussed.Presented in part at the 3rd Chem. Congress of North America (LH=xanthine) and the XXVI ICCC (LH=hypoxanthine), see refs. 1 and 2, respectively.     

Experimental observation of spin delocalisation onto the aryl-alkynyl ligand in the complexes [Mo(C≡CAr)(Ph2PCH2CH2PPh2)(η-C7H7)]+ (Ar = C6H5, C6H4-4-F; C7H7 = cycloheptatrienyl): an EPR and ENDOR investigation

The paramagnetic aryl-alkynyl complexes [Mo(C≡CAr)(dppe)(η-C(7)H(7))](+) (dppe = Ph(2)PCH(2)CH(2)PPh(2); Ar = C(6)H(5), [1](+); C(6)D(5), [2](+); C(6)H(4)-4-F, [3](+); C(6)H(4)-4-Me, [5](+)) and [Mo(C≡CBu(t))(dppe)(η-C(7)H(7))](+) [4](+), have been investigated in a combined EPR and ENDOR study. Direct experimental evidence for the delocalisation of unpaired spin density over the framework of an aryl-alkynyl ligand has been obtained. The X-band solution EPR spectrum of the 4-fluoro derivative, [3](+), exhibits resolved hyperfine coupling to the remote para position of the aryl group [a(iso)((19)F) = 4.5 MHz, (1.6 G)] in addition to couplings attributable to (95/97)Mo, (31)P and (1)H of the C(7)H(7) ring. A full analysis of the (1)H ENDOR spectra is restricted by the low g anisotropy of the system which prevents the use of orientation selection. However, inter-comparison of the (1)H cw-ENDOR frozen solution spectra of [1](+), [2](+), [4](+) and [5](+), combined with spectral simulation informed by calculated values derived from DFT investigations, has facilitated estimation of the experimental a(iso)((1)H) hyperfine couplings of [1](+) including the ortho, ±3.7 MHz (±1.3 G) and para, ±3.9 MHz (±1.4 G) positions of the C(6)H(5) substituent of the aryl-alkynyl ligand.     

Trialkylammonium salt degradation: implications for methylation and cross-coupling

Trialkylammonium (most notably N,N,N-trimethylanilinium) salts are known to display dual reactivity through both the aryl group and the N-methyl groups. These salts have thus been widely applied in cross-coupling, aryl etherification, fluorine radiolabelling, phase-transfer catalysis, supramolecular recognition, polymer design, and (more recently) methylation. However, their application as electrophilic methylating reagents remains somewhat underexplored, and an understanding of their arylation versus methylation reactivities is lacking. This study presents a mechanistic degradation analysis of N,N,N-trimethylanilinium salts and highlights the implications for synthetic applications of this important class of salts. Kinetic degradation studies, in both solid and solution phases, have delivered insights into the physical and chemical parameters affecting anilinium salt stability. ¹H NMR kinetic analysis of salt degradation has evidenced thermal degradation to methyl iodide and the parent aniline, consistent with a closed-shell S_N2-centred degradative pathway, and methyl iodide being the key reactive species in applied methylation procedures. Furthermore, the effect of halide and non-nucleophilic counterions on salt degradation has been investigated, along with deuterium isotope and solvent effects. New mechanistic insights have enabled the investigation of the use of trimethylanilinium salts in O-methylation and in improved cross-coupling strategies. Finally, detailed computational studies have helped highlight limitations in the current state-of-the-art of solvation modelling of reaction in which the bulk medium undergoes experimentally observable changes over the reaction timecourse.

The dual reactivity of N,N,N-trimethylanilinium salts towards arylation and methylation is decoupled in this mechanistic investigation to enable more strategic application of these salts in either reaction class.     

A direct method to find solutions of some type of coupled Korteweg-de Vries equations using hyperelliptic functions of genus two

We suggest how one can obtain exact solutions of some type of coupled Korteweg-de Vries equations by means of hyperelliptic functions of genus two.     

Kähler manifolds of quasi-constant holomorphic sectional curvature

In correspondence with the manifolds of quasi-constant sectional curvature defined (cf [5], [9]) in the Riemannian context, we introduce in the K?hlerian framework the geometric notion of quasi-constant holomorphic sectional curvature. Some characterizations and properties are given. We obtain necessary and sufficient conditions for these manifolds to be locally symmetric, Ricci or Bochner flat, K?hler η-Einstein or K?hler-Einstein, etc. The characteristic classes are studied at the end and some examples are provided throughout.      

On the structural stability of thermoelastic model of porous media

In the present paper we study the structural stability of the mathematical model of the linear thermoelastic materials with voids. We prove that the solutions of problems depend continuously on the constitutive quantities, which may be subjected to error or perturbations in the mathematical modelling process. Thus, we assume to have changes in the various coupling coefficients of the model and then we establish estimates of continuous dependence of solutions. We have to outline that such estimates play a central role in obtaining approximations to these kinds of problems. To derive a priori estimates for a solution we first establish appropriate bounds for the solutions of certain auxiliary problems. These are achieved by means of so‐called Rellich‐like identities. We also investigate how the solution in the coupled model behaves as some coupling coefficients tend to zero. Copyright © 2007 John Wiley & Sons, Ltd.     

Photocatalytic titania based surfaces: Environmental benefits

The use of photocatalytic titania nanoparticles in the development of self-cleaning and de-polluting paints and microbiological surfaces is demonstrated. In the former case surface erosion and sensitised photooxidation is shown to be controlled by the use of catalytic grades of anatase nanoparticles. For environmental applications in the development of coatings and cementitious materials for destroying atmospheric pollutants such as nitrogen oxides (NOX) stable substrates are also illustrated with photocatalytic nanoparticles. Here porosity of the coatings through calcium carbonate doping is shown to be crucial in the control of the effective destruction of atmospheric NOX gases. Good environmental stability of the coatings is also crucial for long-term durability and this aspect is examined for a variety of material substrates. For the development of microbiological substrates for the destruction of harmful bacteria/fungi effective nanoparticle anatase titania is shown to be important with hydrated high surface area particles giving the greatest activity. Data from commercial pilot studies is used to signify the important practicalities of this type of new technology.     

Rate of Convergence in Trotter’s Approximation Theorem

We give a quantitative estimate of the convergence in Trotter’s approximation theorem on the convergence of iterates of linear operators to an assigned semigroup. An application is given concerning the classical Bernstein operator on the d-dimensional simplex.