Whitney's extension problem for multivariate -functions

We prove that the trace of the space to an arbitrary closed subset is characterized by the following ``finiteness' property. A function belongs to the trace space if and only if the restriction to an arbitrary subset consisting of at most can be extended to a function such that

The constant is sharp.

The proof is based on a Lipschitz selection result which is interesting in its own right.

     

Scalar Domination and Normal Fluctuations in N-Vector Quantum Anharmonic Crystals

A lattice model of N-dimensional quantum anharmonic oscillators with a polynomial anharmonicity and a ferroelectric pair interaction is considered. For arbitrary N , correlation inequalities, showing that the temperature Green functions of this model are dominated by the corresponding Green functions of the scalar (N=1) model, are proven. These inequalities are then used to prove that the fluctuations of displacements of particles remain normal at all temperatures provided the model parameters obey a certain condition. In particular this means that the smallest distance between the energy levels of the corresponding one-dimensional isolated oscillator should be large enough or its mass should be small enough.     

Power losses in the international linear collider 20 mrad extraction line at 1 TeV

We have performed a detailed study of the power losses in the post-collision extraction line of a TeV e ⁺ e ⁻ collider with a crossing angle of 20 mrad at the interaction point. Five cases were considered: four luminosity configurations for ILC and one for CLIC. For all of them, the strong beam-beam effects at the interaction point lead to an emittance growth for the outgoing beam, as well as to the production of beamstrahlung photons and e ⁺ e ⁻ coherent pairs. The power losses along the extraction line, which are due to energy deposition by a fraction of the disrupted beam, of the beamstrahlung photons and of the coherent pairs, were estimated in the case of ideal collisions, as well as with a vertical position or angular offset at the interaction point.      

Growth of Fe on Ge(1 1 1) at room temperature studied by X-ray photoelectron diffraction

The growth of ultrathin Fe films of various coverages on Ge(1 1 1) at room temperature using molecular beam epitaxy (MBE) was studied via X-ray photoelectron diffraction (XPD or XPED) together with low energy electron diffraction (LEED) and X-ray photoelectron spectroscopy (XPS). All experimentally observed XPD patterns suggested local order structures of the Fe layers for all thicknesses studied. The short-range order of the resulting structures was found to be enhanced for thinner layers whereas the long-range order was gradually lost with increasing Fe thicknesses. At a very low coverage of 0.8 Å Fe and Ge tend to react to the partly ordered structure in which Fe atoms were located in local environments similar to those for higher Fe coverages. Comparison of theoretical and experimental XPD patterns, along with XPS results, showed that intermixing between Fe and Ge occurred during the pseudomorphic growth with a stacking fault near the interface for all Fe coverages under study. Nevertheless, small percentage of domains without the stacking fault was also found to coexist with those with the stacking fault by performing a quantitative analysis of a reliability factor R of the Fe2p pattern for 5.4 Å. The orientation changes of the Ge2p and Ge3d XPD patterns with Fe thickness were unambiguously explained in terms of their different dependencies on the overlayer thickness due to the different inelastic mean free path lengths used in the simulations. Also, Fe got increasingly enriched in the grown layers with increased Fe coverage. The resulting structures and intermixing are discussed in detail.     

Quantitative real-time measurements of DNA hybridization with alkylated nonoxidized silicon nanowires in electrolyte solution

The quantitative, real-time detection of single-stranded oligonucleotides with silicon nanowires (SiNWs) in physiologically relevant electrolyte solution is demonstrated. Debye screening of the hybridization event is circumvented by utilizing electrostatically adsorbed primary DNA on an amine-terminated NW surface. Two surface functionalization chemistries are compared: an amine-terminated siloxane monolayer on the native SiO2 surface of the SiNW, and an amine-terminated alkyl monolayer grown directly on a hydrogen-terminated SiNW surface. The SiNWs without the native oxide exhibit improved solution-gated field-effect transistor characteristics and a significantly enhanced sensitivity to single-stranded DNA detection, with an accompanying 2 orders of magnitude improvement in the dynamic range of sensing. A model for the detection of analyte by SiNW sensors is developed and utilized to extract DNA-binding kinetic parameters. Those values are directly compared with values obtained by the standard method of surface plasmon resonance (SPR) and demonstrated to be similar. The nanowires, however, are characterized by higher detection sensitivity. The implication is that SiNWs can be utilized to quantitate the solution-phase concentration of biomolecules at low concentrations. This work also demonstrates the importance of surface chemistry for optimizing biomolecular sensing with silicon nanowires.     

Estrogenic Activity of Mycoestrogen (3β,5α,22E)-Ergost-22-en-3-ol via Estrogen Receptor α-Dependent Signaling Pathways in MCF-7 Cells

Armillariella tabescens (Scop.) Sing., a mushroom of the family Tricholomataceae, has been used in traditional oriental medicine to treat cholecystitis, improve bile secretion, and regulate bile-duct pressure. The present study evaluated the estrogen-like effects of A. tabescens using a cell-proliferation assay in an estrogen-receptor-positive breast cancer cell line (MCF-7). We found that the methanol extract of A. tabescens fruiting bodies promoted cell proliferation in MCF-7 cells. Using bioassay-guided fractionation of the methanol extract and chemical investigation, we isolated and identified four steroids and four fatty acids from the active fraction. All eight compounds were evaluated by E-screen assay for their estrogen-like effects in MCF-7 cells. Among the tested isolates, only (3β,5α,22E)-ergost-22-en-3-ol promoted cell proliferation in MCF-7 cells; this effect was mitigated by the ER antagonist, ICI 182,780. The mechanism underlying the estrogen-like effect of (3β,5α,22E)-ergost-22-en-3-ol was evaluated using Western blot analysis to detect the expression of extracellular signal-regulated kinase (ERK), phosphatidylinositol 3-kinase (PI3K), Akt, and estrogen receptor α (ERα). We found that (3β,5α,22E)-ergost-22-en-3-ol induced an increase in phosphorylation of ERK, PI3K, Akt, and ERα. Together, these experimental results suggest that (3β,5α,22E)-ergost-22-en-3-ol is responsible for the estrogen-like effects of A. tabescens and may potentially aid control of estrogenic activity in menopause.     

Three-dimensional elastic wave scattering by a layer containing vertical periodic fractures

Elastic wave scattering off a layer containing a single set of vertical periodic fractures is examined using a numerical technique based on the work of Hennion et al. [J. Acoust. Soc. Am. 87, 1861-1870 (1990)]. This technique combines the finite element method and plane wave method to simulate three-dimensional scattering off a two-dimensional fractured layer structure. Each fracture is modeled explicitly, so that the model can simulate both discrete arrivals of scattered waves from individual fractures and multiply scattered waves between the fractures. Using this technique, we examine changes in scattering characteristics of plane elastic waves as a function of wave frequency, angle of incidence, and fracture properties such as fracture stiffness, height, and regular and irregular spacing.     

Comparison of a Rapid Light-Induced and Forced Test to Study the Oxidative Stability of White Wines

The oxidation processes of white wines can occur during storage and commercialization due to several factors, and these can negatively affect the color, aroma, and quality of the wine. Wineries should have faster and simpler methods that provide valuable information on oxidation stability of wines and allow fast decision-making procedures, able to trigger suitable technological interventions. Using a portable prototype instrument for light irradiations at different wavelengths and times was considered and evaluated on sensorial, spectrophotometric, and colorimetric parameters of white wines. The sensorial analysis revealed that white and light blue were the most significant, after only 1 h of irradiation. The experimental results showed that hydrogen peroxide could enhance the effect of light treatment, allowing a contemporary evaluation of the oxidation stability of wine against light and chemical stresses. As expected, a good correlation (R² > 0.89) between optical density at 420 nm and b* parameter was highlighted. The synergic effect of light and H₂O₂ was also studied on the hydrolyzable and condensed tannins’ additions to white wine. The proposed methodology could be used to evaluate the oxidative stability of white wines, but also to evaluate the effect of some oenological adjuvants on wine stability.