Quantum mechanical designs toward planar delocalized cyclooctatetraene: a new target for synthesis.

Ab initio and hybrid density functional quantum mechanical computation are applied to the structure and energetics of a series of annelated cyclooctatetraenes. Tetrakis-cyclobuteno, perfluorocyclobuteno or bicyclo[2.1.1]hexeno annelations result in planar structures with distinct exo and endo valence tautomers of the double bonded cycle. The contribution of each basic annelation to the exo/endo relative energy is estimated. An additivity scheme for approximating the energy of a mixed system is developed and compared to the quantum mechanical prediction. Bis bicyclic annelation to the a and d positions creates "valence tautomeric frustration" and strongly perturbs the molecular structure. This phenomenon leads to a general design for a planar cyclooctatetraenes where the "delocalized" diradicaloid state is the minimum energy form. These compounds are seen as excellent targets for chemical synthesis.     

Synthesis of oligopyridines and their metal complexes as precursors to topological stereoisomers

[structure: see text]. Palladium-based carbon-carbon coupling reactions in sequence with halogen-exchange chemistry on a series of heterocycles lead to an efficient synthetic strategy for oligopyridines that bind metal ions such as ruthenium to form coordination racks. The particular structures are designed to form terpyridine subunits for octahedral binding. Reaction of 4,6-diiodopyrimidine produces a "double-bay" terpyridine from which binuclear coordination complexes have been formed.     

Influence of surface effects on the performance of lead-niobium-germanate optical waveguides

Lead-niobium-germanate planar waveguides have been produced by pulsed laser deposition. The composition of the waveguides is found to be relatively weakly dependent on the laser fluence, while their surface morphology is affected dramatically. Smooth surfaces are obtained for a narrow fluence range centered at 2.0 J/cm², while particulates having typical diameters of <0.5 μm or droplets with typical diameters of <10 μm are observed at lower and higher fluences, respectively. The refractive index of the waveguides increases with fluence up to 2.1 at 2.0 J/cm², which is close to the value of the bulk glass, and remains constant at higher fluences. Propagation losses show instead a minimum (≈6.5 dB/cm) at 2.0 J/cm². The characteristics of the ablation process that leads to the ejection of solid particulates or molten droplets as well as the increase of the waveguides density on increasing the fluence are discussed to be responsible for the observed optical behavior.     

Deep subsurface optical waveguides produced by direct writing with femtosecond laser pulses in fused silica and phosphate glass

In the present work, we have analyzed the use of elliptical beam shaping along with low numerical aperture focusing optics in order to produce circular cross-section waveguides in different materials at large processing depths by direct femtosecond laser writing (100 fs, 800 nm, 1 kHz). A variable slit located before the focusing optics allows to generate a nearly elliptical beam shape and also to reduce the effective numerical aperture of the beam along the shat axis of the ellipse. The focusing optics allows to focus the beam deep inside the sample, which is translated at a constant speed transversely to the writing beam direction. The influence of several experimental parameters (energy per pulse, slit width, processing depth) on the properties of the produced waveguides has been analyzed. The influence of the intrinsic properties of the material (refractive index, composition) has been analyzed by comparing results obtained in fused silica and Er:Yb co-doped phosphate glass. The results obtained show that this approach leads to the successful production of deep subsurface (up to 7 mm) waveguides with circular cross-sections. Preliminary results using chirped pulses in the phosphate glass suggest that temporal pulse shaping can be used as an additional parameter to optimize the guided mode symmetry.     

Polymer surface patterning by laser scanning

Proposed work develops method of polymer surface patterning, suggested in our laboratory. Surface structures with different symmetry and shape are prepared on PMMA and photoresist (Su-8) surface. For surface modification, periodic laser scanning from confocal microscope was used. For optical response improvement meso tetraphenylporphyrine was added either in the polymer bulk or on the top of pristine polymer by vacuum evaporation method. Applications of vacuum deposition methods allow increasing applicability of the technique and preparation of more complex structure. Parameters of the created structures were studied with the aim to better understand the driving forces of the surface modification. Application of prepared structures in photonics as diffraction grating or light coupling elements is also given.     

An Isoperimetric Theorem in Plane Geometry

Abstract. Let P be a simple polygon. Let the vertices of P be mapped, according to a counterclockwise traversal of the boundary, into a strictly increasing sequence of real numbers in [0, 2π) . Let a ray be drawn from each vertex so that the angle formed by the ray and a horizontal line pointing to the right equals, in measure, the number mapped to the vertex. Whenever the rays from two consecutive vertices intersect, let them induce the triangular region with extreme points comprising the vertices and the intersection point. It is shown that there is a fixed α such that if all of the assigned angles are increased by α , the triangular regions induced by the redirected rays cover the interior of P . This covering implies the standard isoperimetric inequalities in two dimensions, as well as several new inequalities, and resolves a question posed by Yaglom and Boltanskii.     

Über Näherungswerte algebraischer Zahlen

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