The Dirichlet problem for the minimal surface equation in non-regular domains

Summary In this paper we study the Dirichlet problem for the minimal surface equation in a open set Ω without any assumption about the regularity of ϖΩ. We prove an existence theorem using only the pseudoconvexity of Ω.

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Riassunto In questo lavoro studiamo il problema di Dirichlet per l'equazione delle superfici minime in un aperto Ω diR ⁿ sulla cui frontiera non si fa nessuna ipotesi di regolarità. Si ottiene un teorema di esistenza usando la sola pseudoconvessità di Ω.

     

Invariants of the group of a third order differential element

Summary In this note we discuss the invariant properties of the group of homographies which leave a third order differential element E₃ invariant.     

Photoabsorption of Atomic Sodium in the VUV

The absorption spectrum of atomic sodium in the photon energy region from 30 to 150 eV has been investigated. A great number of sharp absorption lines which can be attributed to the excitation of a 2p- or a 2s-electron has been detected. Simultaneous excitation of one 2p- and one 3s-electron gives rise to considerably strong broad and asymmetric absorption structures above the highest series limit (¹ P ₁) for the excitations of a single 2p-electron. Some of the assignments have been confirmed by Hartree-Fock calculations. The relative spectral dependence of the absorption cross-section in this energy range has been determined for the first time. The spectrum of free Na atoms has been compared with theL _{II, III} spectrum of solid sodium.     

Optimization of Gold Nanoparticle-Based DNA Detection for Microarrays

DNA microarrays are promising tools for fast and highly parallel DNA detection by means of fluorescence or gold nanoparticle labeling. However, substrate modification with silanes (as a prerequisite for capture DNA binding) often leads to inhomogeneous surfaces and/or nonspecific binding of the labeled DNA. We examined both different substrate cleaning and activating protocols and also different blocking strategies for optimizing the procedures, especially those for nanoparticle labeling. Contact angle measurements as well as fluorescence microscopy, atomic force microscopy (AFM), and a flatbed scanner were used to analyze the multiple-step process. Although the examined different cleaning and activating protocols resulted in considerably different contact angles, meaning different substrate wettability, silanization led to similar hydrophobic surfaces which could be revealed as smooth surfaces of about 2–4 nm roughness. The two examined silanes (3-glycidoxypropyltrimethoxysilane (GOPS) and 3-aminopropyltriethoxysilane (APTES)) differed in their DNA binding homogeneity, maximum signal intensities, and sensitivity. Nonspecific gold binding on APTES/PDC surfaces could be blocked by treatment in 3% bovine serum albumin (BSA).     

Reflection absorption infrared spectroscopy and temperature-programmed desorption studies of the adsorption and desorption of amorphous and crystalline water on a graphite surface

Reflection absorption infrared spectroscopy (RAIRS) and temperature-programmed desorption (TPD) have been used to perform a detailed investigation of the adsorption of water on highly oriented pyrolytic graphite (HOPG) at 90 K. RAIRS shows that water is physisorbed on HOPG at all coverages, as expected. Experiments at higher surface temperatures show marked changes in the O-H stretching region of the spectrum which can be assigned to the observation of the amorphous to crystalline ice phase transition. The infrared signature of both phases of solid water has been determined on HOPG and can be used to identify the phase of the ice. TPD spectra show the desorption of multilayers of crystalline ice. At high exposures a small bump appears in the TPD spectrum, on the low temperature side of the main peak, which is attributed to the amorphous to crystalline phase transition. At very low exposures of water, it is possible to distinguish the desorption of water from two- and three-dimensional islands and hence to determine the growth mode of water on the HOPG surface. Isothermal TPD studies have also been performed and show that the desorption of water does not obey perfect zero-order kinetics. Desorption orders, derived directly from the TPD spectra, confirm this observation. Desorption energies and preexponential factors have also been determined for this adsorption system.     

Real-time evolution of the distribution of nanoparticles in an ultrathin-polymer-film-based waveguide

We report a novel application of an ultrathin-polymer-film-based, resonance-enhanced x-ray waveguide as a real-time nanoprobe for elucidating dilute, yet disordered, gold nanoparticles embedded in the polymer matrix. This nanoprobe promises a sensitivity enhancement of several orders of magnitude, hence revealing in real time the lateral nanoparticle distribution with subnanometer spatial resolution. We observed that the motion of the nanoparticles is strongly anisotropic, with in-plane coalescence taking place more rapidly than out-of-plane diffusion, which can ultimately facilitate the formation of two-dimensional structures.     

Toward a theory of wave energy transport in large irregular structures

An ansatz is proposed by which the energy transport behavior observed at early times in a direct numerical simulation (DNS) of a large irregular structure may be extrapolated to arbitrary times. In the slow-transport limit, this ansatz leads to a diffusion-like equation, similar to that of time-domain statistical energy analysis (SEA), but it does not require substructuring. The model is successfully used to extract diffusion parameters from simulated data of unambiguously diffusive character. The model is then successfully used to extract diffusion parameters from data obtained in a DNS of a simple undamped two-room structure of a kind typically analyzed by SEA or room acoustics.     

Ideals in a perfect closure, linear growth of primary decompositions, and tight closure

This paper is concerned with tight closure in a commutative Noetherian ring of prime characteristic , and is motivated by an argument of K. E. Smith and I. Swanson that shows that, if the sequence of Frobenius powers of a proper ideal of has linear growth of primary decompositions, then tight closure (of ) `commutes with localization at the powers of a single element'. It is shown in this paper that, provided has a weak test element, linear growth of primary decompositions for other sequences of ideals of that approximate, in a certain sense, the sequence of Frobenius powers of would not only be just as good in this context, but, in the presence of a certain additional finiteness property, would actually imply that tight closure (of ) commutes with localization at an arbitrary multiplicatively closed subset of .

Work of M. Katzman on the localization problem for tight closure raised the question as to whether the union of the associated primes of the tight closures of the Frobenius powers of has only finitely many maximal members. This paper develops, through a careful analysis of the ideal theory of the perfect closure of , strategies for showing that tight closure (of a specified ideal of ) commutes with localization at an arbitrary multiplicatively closed subset of and for showing that the union of the associated primes of the tight closures of the Frobenius powers of is actually a finite set. Several applications of the strategies are presented; in most of them it was already known that tight closure commutes with localization, but the resulting affirmative answers to Katzman's question in the various situations considered are believed to be new.

     

Als Reaction auf Weinsteins?ure in freiem Zustande und in ihren Verbindungen

Ohne Zusammenfassung     

Quantitative Spectralanalyse

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