Synthesis of tertiary benzamides via Pd-catalyzed coupling of arylboronic esters and carbamoyl chlorides

Ortho-substituted arylboronic esters are efficiently coupled with carbamoyl chlorides under Pd-catalysis to give tertiary benzamides.     

Photonic crystal fiber based evanescent-wave sensor for detection of biomolecules in aqueous solutions

We demonstrate highly efficient evanescent-wave detection of fluorophore-labeled biomolecules in aqueous solutions positioned in the air holes of the microstructured part of a photonic crystal fiber. The air-suspended silica structures located between three neighboring air holes in the cladding crystal guide light with a large fraction of the optical field penetrating into the sample even at wavelengths in the visible range. An effective interaction length of several centimeters is obtained when a sample volume of less than 1 microL is used.     

Microscopic structure of a vortex line in a dilute superfluid fermi gas

The microscopic properties of a single vortex in a dilute superfluid Fermi gas at zero temperature are examined within the framework of self-consistent Bogoliubov-de Gennes theory. Using only physical parameters as input, we study the pair potential, the density, the energy, and the current distribution. Comparison of the numerical results with analytical expressions clearly indicates that the energy of the vortex is governed by the zero-temperature BCS coherence length.     

Doped photonic bandgap fibers for short-wavelength nonlinear devices

Microstructured photonic bandgap fibers with a doped honeycomb cladding structure and the guiding defect defined by the absence of doping are proposed as nonlinear optical fibers for short wavelengths. It is shown that zero-dispersion wavelengths below 500 nm and corresponding effective areas of 1-2 microm2 can be obtained if structures with interhole distances near 600 nm can be fabricated. The cutoff wavelength for guidance of second-order modes can be controlled by variation of the radius and index contrast of the doped regions.     

Cr(N)Cl4]2-: a simple nitrido complex synthesized by nitrogen-atom transfer

A new general route to nitrido complexes of Cr(V) based on nitrogen-atom transfer from Mn(N)(salen) to labile CrCl3(THF)3 is presented. By this approach, the simplest nitrido complex of a first row transition metal, [Cr(N)Cl4]2-, has been synthesized and isolated. [[N(CH3)4]2[Cr(N)Cl4].H2O crystallizes in the cubic space group Fm-3m with disordered anions. Cr-N is 1.555(19) A, Cr-Cl is 2.2912(16) A, and N-Cr-Cl is 101.24(4) degrees . The orbital splitting scheme of [Cr(N)Cl4]2- is extreme with the dx2-y2 orbital 10 000 cm-1 lower in energy than the degenerate {dzx, dyz} set of orbitals destabilized by pi-bonding with the nitrido ligand. Hydrolysis of [Cr(N)Cl4]2 preserves the {CrN}2+ moiety.     

On the measuring of diffusion coefficients of solid materials

Instead of a circular cylindric sample of the material, which is used in a common method of measuring diffusion coefficients of solid materials, we propose to use a box shaped sample. The associated diffusion problem is solvable by means of conformal mapping. The solution is given.

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Zusammenfassung Statt einer zirkulärzylindrischen Stoffprobe, die bei einem Verfahren zur Messung von Diffusionskoeffizienten der Feststoffe verwendet wird, schlagen wir die Anwendung einer rechteckigen Parallelepipedon vor. Die assoziierten Diffusionsprobleme sind mittels konformer Abbildung lösbar. Die Lösung wird gegeben.

     

Equivariant embeddings of principal Z-bundles into complex vector bundles

Let π: E→X be a principal $\text{Z}$_n-bundle and p:V→X an m-dimensional complex vector bundle over, say, a connected CW-complex X. An equivariant embedding of π into p is an embedding h:E → V commuting with projections such that h(e · z)=zh(e) for all eεE and $\text{zε}\text{Z}{}_{\mathrm{n}}\text{?S}{}^1\text{?}\text{Z}$. We compute the primary obstruction $\text{cεH}{}^{\mathrm{2m}}\text{(X;}\text{Z}\text{)}$ to embedding π equivariantly into p. If dim X?2m, then c=0 if and only if π admits an equivariant embedding into p. If dim X>2m and π embeds equivariantly into p, then c=0. Other embedding criteria exist in case p is the trivial m-plane bundle ε^m. We use these criteria for a discussion of the classification of the equivalence classes of principal $\text{Z}$-bundles that admit equivariant embeddings into ε^m. Finally, we offer an example of a principal $\text{Z}$-bundle that admit an ordinary but not an equivariant embedding into ε¹.     

Microwave spectra of isotopic pyrazoles and molecular structure of pyrazole

Microwave spectra of the complete set of monosubstituted isotopic pyrazoles have been investigated and the complete r_s structure of pyrazole determined. The deuterated and ¹⁵N species of pyrazole were prepared, while the ¹³C species were examined in natural abundance. The spectrum of the parent compound was remeasured yielding rotational and centrifugal distortion constants.The mutual position of the hydrogen atoms and the direction of the dipole moment in the pyrazole principal axis system has been unambiguously established.The ¹⁴N quadrupole hyperfine structure was resolved and the quadrupole coupling constants derived by Blackman et al. [8] were confirmed.An estimated r_z structure is compared to crystal structures derived by X-ray and neutron diffraction showing the N-H bond in the crystal to be prolonged. But, otherwise no significant differences seem to develop when bringing the molecule from its isolated state into the crystal with its strong hydrogen bonds.     

A strong uniform boundedness principle in Banach spaces

We discuss the term ``thick" set. With the help of this term we deduce a strong Uniform Boundedness Principle valid for all Banach spaces. As an application we give a new proof of Seever's theorem.