Acoustooptic extension of the frequency tunability of CW CO2 lasers: New FIR lasers emissions from CH3OH and13CH3OH

We have increased the frequency tunability of our CW waveguide CO₂ lasers by means of an acoustooptic amplitude modulator, operating at the fixed frequency of 90 MHz. The up-shifted, or down-shifted, laser optical sideband can be generated independently by adjusting the orientation of the modulator. The efficiency is larger than 50%. The frequency tunability of the CO₂ laser around each laser line is thus increased by 180 MHz. To demonstrate the possibilities of this method, a source composed of the above modulator and of a CW, 300 MHz tunable waveguide CO₂ laser has been used for the search of new large offset FIR laser lines from optically pumped CH₃OH and¹³CH₃OH molecules. As a result 15 and 10 new large offset laser lines were discovered respectively. New assignments of some laser lines are also proposed. We have also measured the Stark effect, the offset, and the polarization of other already known lines. In particular a Stark effect frequency tuning of about 1 GHz is demonstrated for a laser line at 208.399 m.     

A perturbed martingale approach to global optimization

A new global stochastic search, guided mainly through derivative-free directional information computable from the sample statistical moments of the design variables within a Monte Carlo setup, is proposed. The search is aided by imparting to the directional update term additional layers of random perturbations referred to as ‘coalescence’ and ‘scrambling’. A selection step, constituting yet another avenue for random perturbation, completes the global search. The direction-driven nature of the search is manifest in the local extremization and coalescence components, which are posed as martingale problems that yield gain-like update terms upon discretization. As anticipated and numerically demonstrated, to a limited extent, against the problem of parameter recovery given the chaotic response histories of a couple of nonlinear oscillators, the proposed method appears to offer a more rational, more accurate and faster alternative to most available evolutionary schemes, prominently the particle swarm optimization.     

Synthesis,structural characterization and in vitro cytotoxic activity of novel polymeric triorganotin(IV) complexes of urocanic acid

Two novel triorganotin carboxylate complexes of the biologically active urocanic acid have been synthesized and characterized. Elemental analysis, melting point, spectroscopic techniques – IR, ¹H, ¹³C and ¹¹⁹Sn NMR – mass spectrometry and X‐ray diffraction studies have been used for structural characterization. Crystal structures of the tin(IV) derivatives show that urocanic acid acts as a bridging bidentate ligand through its imidazole nitrogen atom and its carboxylic group, producing a polymeric one‐dimensional chain. The molecular structures of the complexes, catena‐poly‐tri(n‐butyl)tin(IV) 3‐(3H‐imidazol‐4‐yl)prop‐2‐enoate (1) and catena‐poly‐triphenyltin(IV) 3‐(3H‐imidazol‐4‐yl)prop‐2‐enoate (2), present a distorted trigonal–bipyramidal configuration. This is further confirmed by ¹¹⁹Sn NMR in the solid state. The tin(IV) derivatives form double‐stranded ribbons via N―H^…O―H bonds. Nevertheless, the compounds are essentially monomeric in solution, with a tetrahedral configuration as observed by ¹¹⁹Sn NMR in solution. The cytotoxic activity of the titled compounds has been tested against six human cell lines and the corresponding IC₅₀ values are reported. Both tin(IV) compounds have a high to very high in vitro cytotoxic activity against the tumor cell lines K562, HCT‐15 and MCF‐7. Compound 1 is 86 times more active than cisplatin in the HTC‐15 cell line. Copyright © 2012 John Wiley & Sons, Ltd.     

On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

Poisson discretizations of Wiener functionals and Malliavin operators with Wasserstein estimates

This article proposes a global, chaos-based procedure for the discretization of functionals of Brownian motion into functionals of a Poisson process with intensity $\lambda >0$. Under this discretization we study the weak convergence, as the intensity of the underlying Poisson process goes to infinity, of Poisson functionals and their corresponding Malliavin-type derivatives to their Wiener counterparts. In addition, we derive a convergence rate of $O\left({\lambda }^{?1∕4}\right)$ for the Poisson discretization of Wiener functionals by combining the multivariate Chen–Stein method with the Malliavin calculus. Our proposed sufficient condition for establishing the mentioned convergence rate involves the kernel functions in the Wiener chaos, yet we provide examples, especially the discretization of some common path dependent Wiener functionals, to which our results apply without committing the explicit computations of such kernels. To the best our knowledge, these are the first results in the literature on the universal convergence rate of a global discretization of general Wiener functionals.     

Synthesis and cytotoxicity of new 2-oxo-7-phenyl-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid amides

Abstract

The synthesis and anticancer activity evaluation of new thiazolo[4,5-b]pyridine-5-carboxylic acid amides is described. The structures of the synthesized compounds were confirmed by spectroscopic data and a single crystal X-ray diffraction analysis for 2.4. The synthesized compounds were screened for their in vitro anticancer activity according to US NCI protocols. The most active 7-(4-fluorophenyl)-2-oxo-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid (4-chlorophenyl)amide 2.2 and 7-(4-chlorophenyl)-2-oxo-2,3-dihydrothiazolo[4,5-b]pyridine-5-carboxylic acid (4-chlorophenyl)amide 2.5 were screened for their cytotoxicity effects on C6 Rat glioma cells and U373 Human glioblastoma astrocytoma cells which revealed promising results comparable to temozolamide as reference control according MTT assay data.     

Peculiarities of wave dynamics in media with oscillating inclusions

The article is concerned with mathematical models for media with oscillating inclusions. These models consist of mutually connected equations, one of which is the wave equation for carrying medium and others are equations of motion for partial oscillators. To close these models, we use cubic and nonlocal equations of state for the carrying medium. Travelling wave solutions to these models are studied in detail. Using qualitative analysis methods, the phase space is shown to contain periodic, homo- and heteroclinic trajectories. Moreover, in the case of nonlocal models we observe the creation of quasiperiodic and chaotic regimes. Bifurcations of localized regimes are studied via the Poincaré section technique.     

Super-symmetric informationally complete measurements

Symmetric informationally complete measurements (SICs in short) are highly symmetric structures in the Hilbert space. They possess many nice properties which render them an ideal candidate for fiducial measurements. The symmetry of SICs is intimately connected with the geometry of the quantum state space and also has profound implications for foundational studies. Here we explore those SICs that are most symmetric according to a natural criterion and show that all of them are covariant with respect to the Heisenberg–Weyl groups, which are characterized by the discrete analog of the canonical commutation relation. Moreover, their symmetry groups are subgroups of the Clifford groups. In particular, we prove that the SIC in dimension 2, the Hesse SIC in dimension 3, and the set of Hoggar lines in dimension 8 are the only three SICs up to unitary equivalence whose symmetry groups act transitively on pairs of SIC projectors. Our work not only provides valuable insight about SICs, Heisenberg–Weyl groups, and Clifford groups, but also offers a new approach and perspective for studying many other discrete symmetric structures behind finite state quantum mechanics, such as mutually unbiased bases and discrete Wigner functions.     

A conformal mapping approach for investigating the free-boundary seepage from symmetric channels

We present a new method to investigate the two-dimensional free-boundary groundwater seepage from symmetric soil channels into a homogeneous isotropic porous medium. We use Levi–Civitá’s function to construct an integral representation for the conformal mapping of the complex potential domain onto the physical flow domain. A genetic algorithm (GA) is used to calculate the coefficients of the Maclaurin series expansion of Levi–Civitá’s function. The coordinates of the points from the channel contour, calculated by means of the integral representation, must satisfy the analytic equation of the contour. We use this condition to define the objective function of the genetic algorithm. Levi–Civitá’s function is afterwards used to calculate the seepage loss, the free lines, the streamlines, the equipotential lines, the isobars and the velocity field. Some examples illustrate the method.     

Formation of Glyco-Functionalized Platinum Complexes by Cross-Metathesis and Evaluation of Their Efficacy in Inhibition of Lung Tumor Cell Lines

Syntheses of carbohydrate-functionalized platinum complexes resembling presently employed cytostatics were performed. Mono-allylated sugar substrates obtained in two steps from glucose and galactose were connected with 2-allyl diethyl malonate by cross-metathesis. Following hydrogenation and acidic cleavage of the ester and alkylidene functionalities gave dicarboxylated glycoconjugates, which were transformed into their diammine platinum complexes. The antitumor activities of these platinum complexes were checked by sensitivity testing with 11 lung cancer cell lines. The novel glucose-platinum complex proved to be comparable to the drug carboplatin.