Amplitude point-spread function measurement of high-NA microscope objectives by digital holographic microscopy

We present here a three-dimensional evaluation of the amplitude point-spread function (APSF) of a microscope objective (MO), based on a single holographic acquisition of its pupil wavefront. The aberration function is extracted from this pupil measurements and then inserted in a scalar model of diffraction, allowing one to calculate the distribution of the complex wavefront propagated around the focal point. The accuracy of the results is compared with a direct measurement of the APSF with a second holographic system located in the image plane of the MO. Measurements on a 100 x 1.3 NA MO are presented.     

Complexes of 3d(n) metal ions with thiosemicarbazones: synthesis and antimicrobial activity

The chelating behavior of the thiosemicarbazone derivatives of 2-hydroxy-8-R-tricyclo[7.3.1.0.(2,7)]tridecane-13-one (where R = H, CH3, C6H5) towards Co(II), Ni(II) and Cu(II) has been investigated by elemental analysis, molar conductivity measurements, UV-VIS, IR, ESR spectroscopy and thermal studies. It was deduced from the experiments performed that the ligands coordinate to metal ions in different ways--neutral bidentate or mononegative bidentate--depending on the nature of R. Also, if metal acetates are used instead of metal chlorides, the ligands coordinate in a mononegative bidentate fashion, regardless of the nature of R or the thiosemicarbazone type ligand. The antimicrobial activity of the ligands and of the complexes towards samples of Acinetobacter boumanii, Klebsiella pneumoniae, Escherichia coli, Staphylococcus aureus and Pseudomonas aeruginosa was determined.     

Lipase-catalyzed kinetic resolution of racemic 1-(10-alkyl-10H-phenothiazin-3-yl)ethanols and their butanoates

The synthesis of both enantiomers of 1-(10-alkyl-10H-phenothiazin-3-yl)ethanols and their butanoates by enantiomer-selective acylation of racemic alcohols with the lipase from Pseudomonas fluorescens (L-AK) or/and by methanolysis of the corresponding racemic esters with lipase B from Candida antarctica (CaL-B) is described. The absolute configuration of the enantiomerically pure enantiomers was determined by X-ray crystallography.     

Organoselenium(II) complexes containing organophosphorus ligands. Crystal and molecular structure of PhSeSP(S)Ph2, [2-{MeN(CH2CH2)2NCH2}C6H4]SeSP(S)R′2 (R′ = Ph,OPri) and [2-{O(CH2CH2)2NCH2}C6H4]SeSP(S)(OPri)2

Arylselenium(II) derivatives of dithiophosphorus ligands of type ArSeSP(S)R₂ [Ar = Ph, R = Ph (1), OPrⁱ (2); 2-[MeN(CH₂CH₂)₂NCH₂]C₆H₄, R = Ph (3), OPrⁱ (4); 2-[O(CH₂CH₂)₂NCH₂]C₆H₄, R = OPrⁱ (6)] were prepared by redistribution reactions between Ar₂Se₂ and [R₂P(S)S]₂. The derivative [2-{O(CH₂CH₂)₂NCH₂}C₆H₄]SeSP(S)Ph₂ (5) was obtained by the salt metathesis reaction between [2-{O(CH₂CH₂)₂NCH₂}C₆H₄]SeCl and NH₄S₂PPh₂. The compounds were investigated by multinuclear (¹H, ¹³C, ³¹P, ⁷⁷Se) NMR and infrared spectroscopy. The crystal and molecular structures of 1, 3, 4 and 6 were determined by single-crystal X-ray diffraction. In compounds 3, 4 and 6 the N(1) atom is intramolecularly coordinated to the selenium center, resulting in a T-shaped geometry (hypervalent 10-Se-3 species). The dithiophosphorus ligands act as anisobidentate in 1 and monodentate in 3, 4 and 6. Supramolecular architectures based on intermolecular S?H and N?H contacts between molecular units are formed in the hypervalent derivatives 3 and 4, while in the compounds 1 and 6 the molecules are associated into polymeric chains through either Se?S or O?H contacts, with no further inter-chain interactions.     

Reaction of Moore's ketene (tert-butylcyanoketene) with 1,3-cyclopentadiene and 1,3-cyclohexadiene. Is periselectivity controlled by the dynamic of trajectories at the bifurcation point?

The cycloaddition reaction of tert-butylcyanoketene (TBCK, Moore's ketene) with 1,3-cyclopentadiene yields the [2+2] product, namely cyclobutanone 9. TBCK and 1,3-cyclohexadiene provide the cyclobutanone 10 and some of the ether 11. Both reactions yielding the cyclobutanones (9 and 10, respectively) are reversible. Cyclobutanone 10 is converted thermally and irreversibly into the bicyclic ether 11 via a [3,3] sigmatropic rearrangement (oxo-Cope). The X-ray single crystal data for the ether 11 confirms that the CN and the ether oxygen are in a trans configuration. Data provided by density functional calculations at B3LYP/6-311++G(d,p) level mirror the X-ray data.Furthermore, the relative thermodynamic stabilities (ΔG calculated at 273 °C, 1 atm) of the most relevant isomers of 10 at mPWB1K/6-31+G(d,p) level of theory is provided. Details of the transition states that: (i) leads to cyclobutanone 10 from TBCK and 1,3-cyclohexadiene, and (ii) the oxo-Cope rearrangement of cyclobutanone 10 to produce ether 11 are provided.     

On the monodromy action on Milnor fibers of graphic arrangements

We analyze the monodromy action, over the rationals, on the first homology group of the Milnor fiber, for arbitrary subarrangements of Coxeter arrangements. We propose a combinatorial formula for the monodromy action, involving Aomoto complexes in positive characteristic. We verify the formula, in cases A, B and D.     

A new Fenchel dual problem in vector optimization

We introduce a new Fenchel dual for vector optimization problems inspired by the form of the Fenchel dual attached to the scalarized primal multiobjective problem. For the vector primal-dual pair we prove weak and strong duality. Furthermore, we recall two other Fenchel-type dual problems introduced in the past in the literature, in the vector case, and make a comparison among all three duals. Moreover, we show that their sets of maximal elements are equal.     

Quantifying brain tumor tissue abundance in HR‐MAS spectra using non‐negative blind source separation techniques

Given high‐resolution magic angle spinning (HR‐MAS) spectra from several glial tumor subjects, our goal is to differentiate between tumor tissue types by separating the different sources that contribute to the profile of each spectrum. Blind source separation techniques are applied for obtaining characteristic profiles for necrosis, highly cellular tumor and border tumor tissue and providing the contribution (abundance) of each of these tumor tissue types to the profile of each spectrum. The problem is formulated as a non‐negative source separation problem. Non‐negative matrix factorization, convex analysis of non‐negative sources and non‐negative independent component analysis methods are considered. The results are in agreement with the pathology obtained by the histopathological examination that succeeded the HR‐MAS measurements. Furthermore, an analysis to verify to which extent the dimension of the input space, the input features and the number of sources to be extracted from the HR‐MAS data could influence the performance of the source separation is presented. Copyright © 2012 John Wiley & Sons, Ltd.