Two-color approach for determination of thickness and dielectric constant of thin films using surface plasmon resonance spectroscopy

We report a real time, in situ non-perturbative all-optical approach for determining both the average thickness and the average dielectric constant of transparent thin films using surface plasmon resonance spectroscopy. While it is impossible to obtain both of these parameters from a single surface plasmon resonance spectroscopy experiment, we show both theoretically and experimentally that a two-color experiment allows unambiguous determination of both parameters. The approach is tested for organic thin films at the gold/solution interface which have thickness of a single monolayer.     

Products from furans. XXI Synthesis of novel oxygen containing heterocyclic isosteres of tyrosine derivatives

Novel oxygen containing heterocyclic isosteres of tyrosine and tyramine derivatives were synthesized. All new compounds contain the pyran ring as a consequence of their common route of preparation. Furthermore several methyl, ethyl, diethyl and isopropyl derivatives of the prepared amines were synthesized.     

On the solution of steady-state elastodynamic crack problems by using complex variable methods

Summary Solutions in a closed-form, or in a series-expansion form, are given, concerning steady-state elastodynamic crack problems. The configuration of the problems treated consists, either of an infinite body under plane extension, or a strip-like body under anti-plane shear. The loading mode consisted of constant stresses, acting on the crack faces and moving with the velocity of the crack tip. In the domain of elliptic wave-equations, viz. for subsonic crack velocities, the solution of the problems was reduced to a solution of a Dirichlet problem, whereas in the case of hyperbolic wave-equations, viz. for transonic crack velocities, a Riemann-Hilbert problem was formulated and solved.

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Résumé On donne des solutions sous forme explicite ou sous forme de séries infinies pour des problèmes de fissures stables elastodynamiques. La configuration des problèmes traités consiste soit en un corps infini soumis à une extension plane, soit en un corps en forme de bande soumis à un cisaillement anti-plan. Les plaques étaient soumises à un état plan de contraintes constantes, agissant sur les faces de la fissure et suivant l'extrémité de la fissure avec la même vitesse. On a montré que dans le cas où le problème peut être exprimé par des équations d'ondes elliptiques, c.à.d. pour des vitesses de propagation de la fissure d'ordre subsonique, la solution a été réduite à une solution d'un problème de Dirichlet, tandis que dans le cas des équations d'ondes hyperboliques, c.à.d. pour des vitesses transoniques, le problème a été formulé et résolu comme un problème de Riemann-Hilbert.

     

Products from furans. VII. A General Route for the Synthesis of α-(1,2-cis) and β-(1,2-trans) Glycoconjugates via 1-O-Acyl and 1-O-Ethoxycarbonyl-2-azido-2,3-dideoxyglycopyranosides

A methodology for the synthesis of 2,3,6-trideoxy- and 2,3-dideoxy-2-aminoglycosides is presented. 2,3-Dideoxyhex-2-enopyranos-4-uloses (named also as 2H-pyran-3(6H)-ones) were used for the synthesis of 1-O-acetyl, 1-O-ethyloxycarbonyl and 1-S-phenyl-2,3,6-trideoxy-(or 2,3-dideoxy)-2-azidoglycopyranosyl donors. Glycosidation of the above thio-ethers with a variety of alcohols in the presence of N-bromosuccinimide as activator yielded predominantly α-glycosides, while acetates afforded β-glycosides when TMSOTf was used as a promoter. The coupling of carbonates using tin tetrachloride or TMSOTf proved to be the most successful procedure, yielding the β-glycoside as the predominant product. Thus, glycoconjugates of aminosugars, steroids and aminoacids have been synthesized.     

Synthesis, structure, magnetic properties and aqueous solution characterization of p-hydroquinone and phenol iminodiacetate copper(II) complexes

The reaction of Cu2+ acetate monohydrate with 2-[N,N'-bis(carboxymethyl)aminomethyl]-4-carboxyphenol (H4cacp), 2-[N,N-bis(carboxymethyl)aminomethyl]hydroquinone (H4cah) and the dinucleating 2,5-bis[N,N-bis(carboxymethyl)aminomethyl]hydroquinone (H6bicah) in water results in the formation of several Cu2+ species, which are in dynamic equilibrium in aqueous solution and their stability is pH dependent. A systematic crystallographic study of these species was pursued, resulting in the characterization of most of the species. Additional techniques were employed to characterize the molecules in the solid state (infrared spectroscopy) and in solution (UV-vis spectroscopy and electrochemistry). These measurements show that the Cu2+ ions are ligated mainly to the iminodiacetate at pH < 6, exhibiting only weak interactions with the phenol oxygen. At pH > 6, the phenol oxygen was deprotonated and dinuclear-bridged species, from the phenolate oxygen complexes exhibiting a Cu2+ 2O2 core, were isolated. The coordination environment around the copper ions varies between trigonal bipyramidal, tetragonal pyramidal and distorted octahedral geometries. The two unpaired electrons of the Cu2+ ions are found to be antiferromagnetically coupled. A survey of the magnetic and structural properties of the dinuclear phenoxide bridged Cu2+ complexes shows that the strength of the antiferromagnetic coupling is linearly dependent on the Cu-Ophenolate bond lengths, at bond distances below 1.98 angstroms. The effect of the Cu-O-Cu angles on the magnetic properties of the complexes is also discussed.     

Polynuclear cobalt(II/III) sulfites: synthesis, structure, and magnetic properties of the octanuclear cluster (NH4)11(Li subset[Co4IICo4III(SO3)16(NH3)8]).10H2O encapsulating a lithium cation

Partial oxidation of an aqueous solution of CoIICl(2).6H2O with (NH4)6[Mo7VIO24].4H2O in the presence of (NH4)2SO3.H2O and LiCl, at pH approximately 5.3, leads to isolation of the octanuclear cluster (NH4)11(Li subset[Co4IICo4III(SO3)16(NH3)8].10H2O), 1. The structure of the anion of 1 consists of a central [Co4II], almost ideal square planar unit, and a pair of symmetry-related CoIII dimers above and below the Co4II plane grafting onto the tetramer by 16 bridging sulfite groups. The [Co8(SO3)16(NH3)8]12- cluster encapsulates a lithium cation which lies at the center of the Co4II square.     

A new property of a class of Jacobi polynomials

Polynomials whose coefficients are successive derivatives of a class of Jacobi polynomials evaluated at are stable. This yields a novel and short proof of the known result that the Bessel polynomials are stable polynomials. Stability-preserving linear operators are discussed. The paper concludes with three open problems involving the distribution of zeros of polynomials.

     

Product (α1, α2)-modulation spaces

We study fundamental properties of product (α₁, α₂)-modulation spaces built by (α₁, α₂)-coverings of ℝⁿ¹ × ℝⁿ². Precisely we prove embedding theorems between these spaces with different parameters and other classical spaces. Furthermore, we specify their duals. The characterization of product modulation spaces via the short time Fourier transform is also obtained. Families of tight frames are constructed and discrete representations in terms of corresponding sequence spaces are derived. Fourier multipliers are studied and as applications we extract lifting properties and the identification of our spaces with (fractional) Sobolev spaces with mixed smoothness.