Lensmeter using a lateral shearing interferometer

The use of a laser shear interferometer for checking the collimation condition within a lensmeter is proposed. The interferometer consist of a wedged glass plate which produces a shear along the orthogonal direction to the wedge; when the fringes at the center of the pattern are parallel to the shear, the collimation condition is attained. The feasibility of the proposal for measuring the vertex power is experimentally shown and the accuracy of the method is under 5% of the measured value being an improvement to the commercial instruments based on the focusing of a reticule.     

Clocking ultrafast wave packet dynamics in molecules through UV-induced symmetry breaking

We investigate the use of UV-pump-UV-probe schemes to trace the evolution of nuclear wave packets in excited molecular states by analyzing the asymmetry of the electron angular distributions resulting from dissociative ionization. The asymmetry results from the coherent superposition of gerade and ungerade states of the remaining molecular ion in the region where the nuclear wave packet launched by the pump pulse in the neutral molecule is located. Hence, the variation of this asymmetry with the time delay between the pump and the probe pulses parallels that of the moving wave packet and, consequently, can be used to clock its field-free evolution. The performance of this method is illustrated for the H(2) molecule.     

Effects of the induced birefringence in photorefractive crystals on speckle optical vortices

In this work, we show that it is possible to change the properties of an optical vortex formed in a speckle pattern by the control of an external electric field applied to a sillenite-type photorefractive material in a non-holographic configuration. To show it, a scheme that allows the recovering of both, the polarization state and the phase distribution of an optical field was implemented. Changes in the polarization state of the light in the neighborhood of the vortex were observed with the application of an external electric field. Likewise, changes in the phase structure around the vortex and displacements of the vortices themselves were measured. These displacements have a fairly linear dependence on the applied field to the photorefractive crystal. Experimental results are qualitatively explained with the theoretical treatment of non-holographic recording in photorefractive crystals.     

Single-fiber diffuse optical time-of-flight spectroscopy

We demonstrate interstitial diffuse optical time-of-fight spectroscopy based on a single fiber for both light delivery and detection. Detector saturation due to the massive short-time reflection is avoided by ultrafast gating of a single photon avalanche diode. We show that the effects of scattering and absorption are separable and that absorption can be assessed independently of scattering. Measurements on calibrated liquid phantoms and subsequent Monte Carlo-based evaluation illustrate that absorption coefficients can be accurately assessed over a wide range of medically relevant optical properties. Our findings pave the way to simplified and less invasive interstitial in vivo spectroscopy.     

Semiexperimental equilibrium structures for the equatorial conformers of N-methylpiperidone and tropinone by the mixed estimation method

N-Methylpiperidone (MPIP) and tropinone, which contain a structural motif found in numerous alkaloids, are too large to determine an accurate equilibrium structure either by ab initio methods or by experiment. However, the ground state rotational constants of the parent species and of all isotopologues with a substituted heavy atom ((13)C, (15)N, (18)O) are known from microwave spectroscopy. These constants have been corrected for the rovibrational contribution calculated from an ab initio cubic force field. These semiexperimental equilibrium rotational constants have been supplemented by carefully chosen structural parameters from medium level ab initio calculations. The two sets of data have been used in a weighted least-squares fit to determine reliable equilibrium structures for both molecules. This work shows that it is possible to determine reliable equilibrium structures for large molecules (34 degrees of freedom in the case of tropinone) at a detailed level of accuracy, and the method could be applied without too much difficulty to still larger molecules.     

Diastereoselective indium-mediated allylation of N-tert-butanesulfinyl ketimines: easy access to asymmetric quaternary stereocenters bearing nitrogen atoms

Indium-mediated allylation of N-tert-butanesulfinyl ketimines afforded in high yields and diastereoselectivities homoallylic amine derivatives with the nitrogen atom bonded to a quaternary stereocenter.     

Experimental study of the influence of solvent and asphaltenes on liquid–solid phase behavior of paraffinic model systems by using DSC and FT-IR techniques

This experimental work presents the results of a study about the liquid–solid phase behavior of high molecular weight n-paraffins (C₂₄–C₂₈ mixture and C₃₆ pure) in aliphatic (n-decane and squalane) and aromatic (xylene and 1-phenyl dodecane) solvents. The effect of asphaltenes of different chemical nature over the liquid–solid behavior of heavy n-paraffins is also studied. Differential Scanning Calorimetry (DSC) was used to obtain the phase transitions onsets and enthalpies as well as the wax solubility curves. Crystallinity was studied by using both DSC and Infrared Spectroscopy (FT-IR) techniques. The results obtained and presented in this study showed that both, solvent and asphaltenes as well as their chemical nature have a significant effect on paraffin crystallization process.     

Syntheses of four new pyridinium phenolates with caged phenolate functionalities as chromophores for quadratic optics

Semi-empirical calculations as well as our preliminary studies indicate an increase of the nonlinear response of pyridinium phenolates with the raise of their interplanar angle. Unfortunately, the tendency of previously synthesized zwitterionic compounds to form aggregates prevents their use in electro-optical devices. In order to understand the process of aggregation and to circumvent it, the syntheses of new pyridinium phenolates bearing alkyl chains of various length, caging the phenolate functionality, have been achieved and are described herein.     

Matrix completion problems over integral domains: The case with a diagonal of prescribed blocks

Let $\mathfrak{R}$ be an arbitrary integral domain, let $\wedge =\{{\lambda }_1\text{,}\dots \text{,}{\lambda }_n\}$ be a multiset of elements of $\mathfrak{R}$, let $\sigma$ be a permutation of $\{1\text{,}\dots \text{,}k\}$ let $n_1\text{,}\dots \text{,}{n}_k$ be positive integers such that $n_1+?+n_k=n$, and for $r=1\text{,}\dots \text{,}k$ let $A_r\in {\mathfrak{R}}^{n_r\times n_{\sigma (r)}}$. We are interested in the problem of finding a block matrix $Q={\left[Q_{\mathit{rs}}\right]}_{r\text{,}s=1}^k\in {\mathfrak{R}}^{n\times n}$ with spectrum $\mathrm{\Lambda }$ and such that $Q_{r\sigma (r)}=A_r$ for $r=1\text{,}\dots \text{,}k$. Cravo and Silva completely characterized the existence of such a matrix when $\mathfrak{R}$ is a field. In this work we construct a solution matrix $Q$ that solves the problem when $\mathfrak{R}$ is an integral domain with two exceptions: (i) $k=2$; (ii) $k\ge 3$, $\sigma (r)=r$ and $n_r>n/2$ for some $r$.What makes this work quite unique in this area is that we consider the problem over the more general algebraic structure of integral domains, which includes the important case of integers. Furthermore, we provide an explicit and easy to implement finite step algorithm that constructs an specific solution matrix (we point out that Cravo and Silva’s proof is not constructive).     

The conservation relation for cuspidal representations

Let \({\pi \in Cusp ({\rm U}(V_n))}\) be a smooth cuspidal irreducible representation of a unitary group U(V _n ) of dimension n over a non-Archimedean locally compact field. Let \({W^\pm_m}\) be the two isomorphism classes of Hermitian spaces of dimension m, and the denote by \({\tau^+ \in Cusp ({\rm U}(W_{m^+}^+))}\) and \({\tau^- \in Cusp ({\rm U}(W_{m^-}^-))}\) the first non-zero theta lifts of π. In this article we prove that m ⁺ + m ^? = 2n + 2, which was conjectured in Harris et al. (J AMS 9:941–1004, 1996, Speculations 7.5 and 7.6). We prove similar equalities for the other dual pairs of type I: the symplectic-orthogonal dual pairs and the quaternionic dual pairs.