Synthesis and characterization of partially coherent beams with propagation-invariant transverse polarization pattern

Partially coherent beams, whose transverse polarization pattern remains invariant upon paraxial propagation, are synthesized and characterized. Synthesis is performed by imposing a spiral-like polarization profile to a rotationally symmetric partially coherent light source. Irradiance and polarization profiles of the propagated beam are detected at different transverse planes, both in the near and in the far zone, and are compared to the theoretical ones. Furthermore, overall parameters, measuring the circular, radial and azimuthal polarization contents across the beam profile, are used to characterize the generated beam from a global point of view.     

A Study on the Diastereoselective Synthesis of α‐Fluorinated β3‐Amino Acids by α‐Fluorination

The treatment of a β³‐amino acid methyl ester with 2.2 equiv. of lithium diisopropylamide (LDA), followed by reaction with 5 equiv. of N‐fluorobenzenesulfonimide (NFSI) at ?78° for 2.5 h and then 2 h at 0°, gives syn‐fluorination with high diastereoisomeric excess (de). The de and yield in these reactions are somewhat influenced by both the size of the amino acid side chain and the nature of the amine protecting group. In particular, fluorination of N‐Boc‐protected β³‐homophenylalanine, β³‐homoleucine, β³‐homovaline, and β³‐homoalanine methyl esters, 5 and 9 – 11 , respectively, all proceeded with high de (>86% of the syn‐isomer). However, fluorination of N‐Boc‐protected β³‐homophenylglycine methyl ester ( 16 ) occurred with a significantly reduced de. The use of a Cbz or Bz amine‐protecting group (see 3 and 15 ) did not improve the de of fluorination. However, an N‐Ac protecting group (see 17 ) gave a reduced de of 26%. Thus, a large N‐protecting group should be employed in order to maximize selectivity for the syn‐isomer in these fluorination reactions.     

Nine Diiron(II) Complexes of Three Bis-tetradentate Pyrimidine Based Ligands with NCE (E = S, Se, BH(3)) Coligands

Three bis-tetradentate acyclic amine ligands differing only in the arm length of the pyridine pendant arms attached to the 4,6-positions of the pyrimidine ring, namely, 4,6-bis[N,N-bis(2'-pyridylethyl)aminomethyl]-2-phenylpyrimidine (L(Et)), 4,6-bis[N,N-bis(2'-pyridylmethyl)aminomethyl]-2-phenylpyrimidine (L(Me)), and 4,6-[(2'-pyridylmethyl)-2'-pyridylethyl)aminomethyl]-2-phenylpyrimidine (L(Mix)) have been used to synthesize nine air-sensitive diiron(II) complexes: [Fe(II)(2)L(Et)(NCS)(4)]·MeOH·(3)/(4)H(2)O (1·MeOH·(3)/(4)H(2)O), [Fe(II)(2)L(Et)(NCSe)(4)]·H(2)O (2·H(2)O), [Fe(II)(2)L(Et)(NCBH(3))(4)]·(5)/(2)H(2)O (3·(5)/(2)H(2)O), [Fe(II)(2)L(Me)(NCS)(4)]·(1)/(2)H(2)O (4·(1)/(2)H(2)O), [Fe(II)(2)L(Me)(NCSe)(4)] (5), [Fe(II)(2)L(Me)(NCBH(3))(4)]·(3)/(2)H(2)O (6·(3)/(2)H(2)O), [Fe(II)(2)L(Mix)(NCS)(4)]·(1)/(2)H(2)O (7·(1)/(2)H(2)O), [Fe(II)(2)L(Mix)(NCSe)(4)]·(3)/(2)H(2)O (8·(3)/(2)H(2)O), and [Fe(II)(2)L(Mix)(NCBH(3))(4)]·(3)/(2)H(2)O (9·(3)/(2)H(2)O). Complexes 3·(5)/(2)H(2)O, 4·(1)/(2)H(2)O, 5, 6·(3)/(2)H(2)O, and 8·(3)/(2)H(2)O were structurally characterized by X-ray crystallography, revealing, in all cases, both of the iron(II) centers in an octahedral environment with two NCE (E = S, Se, or BH(3)) anions in a cis-position relative to one another. Variable temperature magnetic susceptibility measurements showed that all nine diiron(II) complexes are stabilized in the [HS-HS] state from 300 K to 4 K, and exhibit weak antiferromagnetic coupling. M?ssbauer spectroscopy confirmed the spin and oxidation states of eight of the nine complexes (the synthesis of air-sensitive complex 3 was not readily reproduced).     

Formylation of 4,7‐Dihydro‐1,2,4‐triazolo[1,5‐a]pyrimidines Using Vilsmeier–Haack Conditions

Formylation of 5‐methyl‐7‐phenyl‐4,7‐dihydro‐1,2,4‐triazolo[1,5‐a]pyrimidine 1a using Vilsmeier–Haack conditions yields 5‐methyl‐7‐phenyl‐4,7‐dihydro‐1,2,4‐triazolo[1,5‐a]pyrimidin‐6‐ylcarbaldehyde 3a . 5,7‐Diaryl‐4,7‐dihydro‐1,2,4‐triazolo[1,5‐a]pyrimidines 1b , 1c in this reaction apart from formylation undergo recyclization into 5‐aryl‐1,2,4‐triazolo[1,5‐a]pyrimidin‐6‐ylmethane derivatives 4b , 4c , 5b , 5c , and 6 . The structure of the synthesized compounds was determined on the basis of NMR, IR, and MS spectroscopic data and confirmed by the X‐ray analysis of the 6‐(ethoxy‐phenyl‐methyl)‐5‐phenyl‐[1,2,4]triazolo[1,5‐a]pyrimidine 6 , 5‐phenyl‐6‐(1‐phenyl‐vinyl)‐[1,2,4]triazolo[1,5‐a]pyrimidine 11 , and 7‐phenyl‐6‐(1‐phenyl‐vinyl)‐[1,2,4]triazolo[4,3‐a]pyrimidine 12 .     

Radical mechanism in the elimination of 2-arylsulfinyl esters

The mechanism of the dehydrosulfenylation of 2-arylsulfinyl esters was investigated. The reaction was found to follow a homolytic cleavage mechanism as verified by electrospray ionization tandem mass spectrometry and experimental work. Rearranged sulfoxides are obtained as byproduct during the elimination reaction.     

l-Proline-derived ligands to mimic the ‘2-His-1-carboxylate’ triad of the non-haem iron oxidase active site

Non-haem iron(II) oxidases (NHIOs) catalyse a variety of oxidative transformations in biology. The iron-binding environment of the NHIO active site typically incorporates a ‘2-His-1-carboxylate’ facial triad of amino acid side-chains, a motif that has emerged as a defining feature of the enzyme family. Towards the goal of biomimetic, iron-mediated C–H activation we have synthesized a series of peptidomimetic ligands from l-proline. By coupling l-proline to 2,6-bis(bromomethyl)pyridine, 2-(bromomethyl)-6-((tert-butyldimethylsilyloxy)methyl)pyridine and picolinic acid, we have generated several new ligand architectures designed to complex with iron(II) and mimic the NHIO active site. The resulting iron complexes promote modest levels of alkene dihydroxylation and allylic oxidation using hydrogen peroxide as oxidant.     

Inner models with large cardinal features usually obtained by forcing

We construct a variety of inner models exhibiting features usually obtained by forcing over universes with large cardinals. For example, if there is a supercompact cardinal, then there is an inner model with a Laver indestructible supercompact cardinal. If there is a supercompact cardinal, then there is an inner model with a supercompact cardinal κ for which 2 ^κ ?=?κ ⁺, another for which 2 ^κ ?=?κ ⁺⁺ and another in which the least strongly compact cardinal is supercompact. If there is a strongly compact cardinal, then there is an inner model with a strongly compact cardinal, for which the measurable cardinals are bounded below it and another inner model W with a strongly compact cardinal κ, such that ${H^{V}_{\kappa^+} \subseteq {\rm HOD}^W}$ . Similar facts hold for supercompact, measurable and strongly Ramsey cardinals. If a cardinal is supercompact up to a weakly iterable cardinal, then there is an inner model of the Proper Forcing Axiom and another inner model with a supercompact cardinal in which GCH?+?V?=?HOD holds. Under the same hypothesis, there is an inner model with level by level equivalence between strong compactness and supercompactness, and indeed, another in which there is level by level inequivalence between strong compactness and supercompactness. If a cardinal is strongly compact up to a weakly iterable cardinal, then there is an inner model in which the least measurable cardinal is strongly compact. If there is a weakly iterable limit δ of <δ-supercompact cardinals, then there is an inner model with a proper class of Laver-indestructible supercompact cardinals. We describe three general proof methods, which can be used to prove many similar results.     

Synthesis of isocyanate-based brush block copolymers and their rapid self-assembly to infrared-reflecting photonic crystals

The synthesis of rigid-rod, helical isocyanate-based macromonomers was achieved through the polymerization of hexyl isocyanate and 4-phenylbutyl isocyanate, initiated by an exo-norbornene functionalized half-titanocene complex. Sequential ruthenium-mediated ring-opening metathesis polymerization of these macromonomers readily afforded well-defined brush block copolymers, with precisely tunable molecular weights ranging from high (1512 kDa) to ultrahigh (7119 kDa), while maintaining narrow molecular weight distributions (PDI = 1.08-1.39). The self-assembly of these brush block copolymers to solid thin-films and their photonic properties were investigated. Due to the rigid architecture of these novel polymeric materials, they rapidly self-assemble through simple controlled evaporation to photonic crystal materials that reflect light from the ultra-violet, through the visible, to the near-infrared. The wavelength of reflectance is linearly related to the brush block copolymer molecular weight, allowing for predictable tuning of the band gap through synthetic control of the polymer molecular weight. A combination of scanning electron microscopy and optical modeling was employed to explain the origin of reflectivity.     

A hybrid method using wavelets for the numerical solution of boundary value problems on the interval

In this work, various aspects of wavelet-based methods for second order boundary value problems under Galerkin framework are investigated. Based on the B-spline multiresolution analysis (MRA) on the line we propose a hybrid method on the interval which combines different treatments for interior and boundary splines. By using this procedure, the MRA structure was conserved and hierarchical representations of the solution at different scales were obtained without much computational effort. Numerical examples are given to verify the effectiveness of the proposed method and the comparison with other techniques is presented.     

Unsupervised classification of children’s bodies using currents

Object classification according to their shape and size is of key importance in many scientific fields. This work focuses on the case where the size and shape of an object is characterized by a current. A current is a mathematical object which has been proved relevant to the modeling of geometrical data, like submanifolds, through integration of vector fields along them. As a consequence of the choice of a vector-valued reproducing kernel Hilbert space (RKHS) as a test space for integrating manifolds, it is possible to consider that shapes are embedded in this Hilbert Space. A vector-valued RKHS is a Hilbert space of vector fields; therefore, it is possible to compute a mean of shapes, or to calculate a distance between two manifolds. This embedding enables us to consider size-and-shape clustering algorithms. These algorithms are applied to a 3D database obtained from an anthropometric survey of the Spanish child population with a potential application to online sales of children’s wear.