Convolution Operators with Fractional Measures Associated to Holomorphic Functions

Let be an open set in the complex plane and let be a holomorphic function on . Let K be a compact subset of with nonempty interior such that 0 K. Let be the Borel measure of R ⁴ C ² given by(E = _K E(z, (z))|z|^–2 d(z)where 0 < 2 and d(x ₁ + ix ₂) = dx ₁ dx ₂ denotes the Lebesgue measure on C. Let T be the convolution operator T f = * f. In this paper we characterize the type set E associated to T .     

New Functional Polyolefins: Towards a Bridge Between Catalytic and RAFT Polymerizations?

Summary: Di‐polyethylenyl magnesium compounds, obtained by a transition metal catalyzed chain growth reaction on butyloctyl magnesium, are reacted with a range of disulfides of thiocarbonylated compounds (RC(S)SSC(S)R). Xanthate, dithiocarbamate, dithioester, and trithiocarbonate‐functionalized polyethylenes are thus obtained and characterized by ¹H NMR and IR spectroscopy, and MALDI TOF mass spectrometry. These macroRAFT agents may serve as building blocks for the synthesis of block copolymers based on polyolefins and polar segments.

Thio thiocarbonylate‐terminated polyethylene chains are easily prepared in high yield by a two step reaction and analyzed by MALDI‐TOF mass spectrometry.     

Quantitative analysis of essential oils in perfume using multivariate curve resolution combined with comprehensive two-dimensional gas chromatography

The use of multivariate curve resolution (MCR) to build multivariate quantitative models using data obtained from comprehensive two-dimensional gas chromatography with flame ionization detection (GC × GC-FID) is presented and evaluated. The MCR algorithm presents some important features, such as second order advantage and the recovery of the instrumental response for each pure component after optimization by an alternating least squares (ALS) procedure. A model to quantify the essential oil of rosemary was built using a calibration set containing only known concentrations of the essential oil and cereal alcohol as solvent. A calibration curve correlating the concentration of the essential oil of rosemary and the instrumental response obtained from the MCR-ALS algorithm was obtained, and this calibration model was applied to predict the concentration of the oil in complex samples (mixtures of the essential oil, pineapple essence and commercial perfume). The values of the root mean square error of prediction (RMSEP) and of the root mean square error of the percentage deviation (RMSPD) obtained were 0.4% (v/v) and 7.2%, respectively. Additionally, a second model was built and used to evaluate the accuracy of the method. A model to quantify the essential oil of lemon grass was built and its concentration was predicted in the validation set and real perfume samples. The RMSEP and RMSPD obtained were 0.5% (v/v) and 6.9%, respectively, and the concentration of the essential oil of lemon grass in perfume agreed to the value informed by the manufacturer. The result indicates that the MCR algorithm is adequate to resolve the target chromatogram from the complex sample and to build multivariate models of GC × GC-FID data.     

A versatile series of nickel(II) complexes derived from tetradentate imine/pyridyl ligands and various pseudohalides: azide and cyanate compared

The chemical reactions of a family of tetradentate pyridyl/imine ligands, L1, L2, and L3 (L1=[ N, N'-bis(2-pyridinylmethylene)]ethane-1,2-diamine; L2=[ N, N'-bis(pyridin-2-yl)benzylidene]ethane-1,2-diamine; L3=[ N, N'-bis(2-pyridinylmethylene)]propane-1,3-diamine), with Ni (II) in the presence of various pseudohalides (N3(-), SCN(-), and NCO(-)) have served to prepare six different complexes, [Ni 2(L1)2(N3)2](ClO4)2.H2O (1), [Ni 2(L2)2(N3)2](ClO4)2 (2), [Ni2(L2)2(NCS)4] (3), [Ni2(L2)2(NCO) 2](ClO4)2 (4), [Ni2(L3)2(NCO)2](ClO4)2 (5), and [Ni(L3)(N 3)2] (6), which have been characterized by X-ray crystallography. Interestingly, four of these complexes are dinuclear and exhibit end-on (EO) pseudohalide bridges (1, 2, 4, and 5), one is dinuclear and bridged exclusively by the tetradentate ligand (3), and one is mononuclear (6). The bulk magnetization of the complexes bridged by EO pseudohalides has been studied, revealing these ligands to mediate ferromagnetic coupling between the Ni(II) ions, with modeled coupling constants, J, of +31.62 (1), +28.42 (2), +2.81 (4), and +1.72 (5) cm(-1) (where the convention H=-2JS1S2 was used). The striking difference in the coupling intensity between N3(-) and NCO(-) has prompted an investigation by means of density functional theory calculations, which has confirmed the experimental results and provided insight into the reasons for this observation.     

Self-assembly of an azido-bridged [NiII6] cluster featuring four fused defective cubanes

The cluster [Ni6(H2L)2(HL1)2(N3)8].2C2H5OH.2H2O [1.2C2H5OH.2H2O], featuring four fused defective cubanes, has been obtained via azido-bridge-driven dimerization of two phenolate-centered trinuclear Ni3 fragments.     

Coordination complexes exhibiting anion...pi interactions: synthesis, structure, and theoretical studies

The polydentate ligand 2,4,6-tris(dipyridin-2-ylamino)-1,3,5-triazine (dpyatriz) in combination with the Cu(ClO 4) 2/CuX 2 salt mixtures (X (-) = Cl (-), Br (-), or N 3 (-)) leads to the formation of molecular coordination aggregates with formulas [Cu 3Cl 3(dpyatriz) 2](ClO 4) 3 ( 2), [Cu 3Br 3(dpyatriz) 2](ClO 4) 3 ( 3), and [Cu 4(N 3) 4(dpyatriz) 2(DMF) 4(ClO 4) 2](ClO 4) 2 ( 4). These complexes consist of two dpyatriz ligands bridged via coordination to Cu (II) and disposed either face-to-face in an eclipsed manner ( 2 and 3) or parallel and mutually shifted in one direction. The copper ions complete their coordination positions with Cl (-) ( 2), Br (-) ( 3), or N 3 (-), ClO 4 (-), and N, N-dimethylformamide (DMF) ( 4) ligands. All complexes crystallize together with noncoordinate ClO 4 (-) groups that display anion...pi interactions with the triazine rings. These interactions have been studied by means of high level ab initio calculations and the MIPp partition scheme. These calculations have proven the ClO 4 (-)...[C 3N 3] interactions to be favorable and have revealed a synergistic effect from the combined occurrence of pi-pi stacking of triazine rings and the interaction of these moieties with perchlorate ions, as observed in the experimental systems.     

Neuro-genetic multioptimization of the determination of polychlorinated biphenyl congeners in human milk by headspace solid phase microextraction coupled to gas chromatography with electron capture detection

Polychlorinated biphenyls (PCB) can eventually contaminate breast milk, which is a serious issue to the newborn due to their high vulnerability. Solid phase microextraction (SPME) can be a very convenient technique for their isolation and pre-concentration prior chromatographic analysis. Here, a simultaneous multioptimization strategy based on a neuro-genetic approach was applied to a headspace SPME method for determination of 12 PCB in human milk. Gas chromatography with electron capture detection (ECD) was adopted for the separation and detection of the analytes. Experiments according to a Doehlert design were carried out with varied extraction time and temperature, media ionic strength and concentration of the methanol (co-solvent). To find the best model that simultaneously correlate all PCB peak areas and SPME extraction conditions, a multivariate calibration method based on a Bayesian Neural Network (BNN) was applied. The net output from the neural network was used as input in a genetic algorithm (GA) optimization operation (neuro-genetic approach). The GA pointed out that the best values of the overall SPME operational conditions were the saturation of the media with NaCl, extraction temperature of 95 °C, extraction time of 60 min and addition of 5% (v/v) methanol to the media. These optimized parameters resulted in the decrease of the detection limits and increase on the sensitivity for all tested analytes, showing that the use of neuro-genetic approach can be a promising way for optimization of SPME methods.