Quantum-chaotic scattering effects in semiconductor microstructures

We show that classical chaotic scattering has experimentally measurable consequences for the quantum conductance of semiconductor microstructures. These include the existence of conductance fluctuations-a sensitivity of the conductance to either Fermi energy or magnetic field-and weak-localization-a change in the average conductance upon applying a magnetic field. We develop a semiclassical theory and present numerical results for these two effects in which we model the microstructures by billiards attached to leads. We find that the difference between chaotic and regular classical scattering produces a qualitative difference in the fluctuation spectrum and weak-localization lineshape of chaotic and nonchaotic structures. While the semiclassical theory within the diagonal approximation accounts well for the weak-localization lineshape and for the spectrum of the fluctuations, we uncover a surprising failure of the semiclassical diagonal-approximation theory in describing the magnitude of these quantum transport effects.     

Synthesis,magnetic and spectral studies of iron(III) and cobalt(II,III) complexes of 4-formylantipyrine N(4)-substituted thiosemicarbazones

The synthesis and characterization of complexes of iron(III), cobalt(II) and cobalt(III) with 4-formylantipyrine N(4)-methyl-, N(4)-dimethyl-, and 3-piperidylthiosemicarbazones are reported. Elemental analyses, molar conductivities, magnetic measurements and spectral (i.r., electronic and e.s.r.) studies have been used to elucidate the nature of the metal complexes. The i.r. spectra show that the thiosemicarbazones behave as bidentate or tridentate ligands, either in the thione or thiolato form. Different stereochemistries are proposed for the various cobalt(II) complexes on the basis of spectral and magnetic studies. This revised version was published online in June 2006 with corrections to the Cover Date.     

Formation of nitrogen‐containing heterocycles using di(imidazole‐1‐yl)methanimine

A mild and efficient synthesis of five‐ and six‐membered nitrogen containing heterocyclic compounds, in which di(imidazole‐1‐yl)methanimine serves as a one‐carbon source, is reported.     

LAMMA mass spectra of β-diketone,bis(benzoylacetone)ethylenediimine and bis(salicylidene)ethylenediimine complexes of some transition metals

Complexes of 2,4-pentanedione (acetylacetone, acac), [Cu(acac)₂], [VO(acac)₂] and [CO(acac)₃], and the chromium(III) derivative of 3-methyl-2,4-pentanedione (methylacetylacetone, meac), [Cr(meac)₃], the ligands bis(benzoylacetone)ethylenediimine and bis(salicylidene)ethylenediimine, and their cobalt(II), nickel(II) and copper(II) chelates were analysed by laser desorption mass spectrometry (LAMMA) and compared to electron impact (EI) results. The positive ion LAMMA spectra generally reveal mostly small fragments, although metal cationization peaks are seen for most complexes. Negative ion LAMMA produce carbon clusters and some structurally important fragments.     

Synthesis and photolysis of doxyl derivatives of 5β-androstan-3-ones

In an unsuccessful attempt to effect remote functionalization at C9, 4,4-dimethyloxazolidine-N-oxyl (doxyl) derivatives at C3 of 5β-androstan-3,17-dione and 5β-androstan-17β-ol-3-one were prepared and photolyzed. The former doxyl yielded its C13 stereoisomer; the latter was converted very slowly to intractable material.     

A copper-catalyzed C-N bond formation involving sp-hybridized carbons. A direct entry to chiral ynamides via N-alkynylation of amides

A copper-catalyzed new C-N bond formation involving a sp-hybridized carbon is described here leading to a facile entry for syntheses of chiral ynamides. This direct N-alkynylation of amides should have a significant impact on the future development of synthetic methodologies employing ynamides.     

Two families of mixed finite elements for second order elliptic problems

Summary Two families of mixed finite elements, one based on triangles and the other on rectangles, are introduced as alternatives to the usual Raviart-Thomas-Nedelec spaces. Error estimates inL ² () andH ^–5 () are derived for these elements. A hybrid version of the mixed method is also considered, and some superconvergence phenomena are discussed.     

The convergence of spline collocation for strongly elliptic equations on curves

Summary Most boundary element methods for two-dimensional boundary value problems are based on point collocation on the boundary and the use of splines as trial functions. Here we present a unified asymptotic error analysis for even as well as for odd degree splines subordinate to uniform or smoothly graded meshes and prove asymptotic convergence of optimal order. The equations are collocated at the breakpoints for odd degree and the internodal midpoints for even degree splines. The crucial assumption for the generalized boundary integral and integro-differential operators is strong ellipticity. Our analysis is based on simple Fourier expansions. In particular, we extend results by J. Saranen and W.L. Wendland from constant to variable coefficient equations. Our results include the first convergence proof of midpoint collocation with piecewise constant functions, i.e., the panel method for solving systems of Cauchy singular integral equations.Dedicated to Prof. Dr. Dr. h.c. mult. Lothar Collatz on the occasion of his 75th birthdayThis work was begun at the Technische Hochschule Darmstadt where Professor Arnold was supported by a North Atlantic Treaty Organization Postdoctoral Fellowship. The work of Professor Arnold is supported by NSF grant BMS-8313247. The work of Professor Wendland was supported by the Stiftung Volkswagenwerk     

Synthesis of fluorinated 1,8-naphthyridinone derivatives

Processes for the synthesis of fluorinated 1,8-naphthyridinone derivatives including 6,7-difluoro-1,8-naphthyridin-2-one are described.