Electronic transport in a controllably grown carbon nanotube-silicon heterojunction array

A uniform array of a new type of heterojunction formed between carbon nanotubes and silicon is studied. The heterojunction array was controllably grown with parallel and uniform nanotubes vertically aligned to the silicon substrate using a self-organized nanopore array template. The pronounced rectifying characteristics of the heterojunction were measured with an on/off ratio as high as 10(5) at 4 V. The analysis shows a large and type-I band offset at the heterojunction. The charge transport in the nanotubes is found to be strongly coupled to and limited by the dielectric charging and polarization in the hosting alumina matrix surrounding the nanotubes.     

Two comments on Dvoretzky’s sphericity theorem

For any two positive integersk, l and anyɛ>0 there exists anN(k, l, ɛ) so that given anyl convex bodiesC ₁, …,C _l symmetric about the origin inE ⁿ withn≧N there exists a subspaceE ^k so that eachC _i intersectsE ^k, or has a projection intoE ^k, in a set which is nearly spherical (asphericity <ɛ). The measure of the totality ofE ^k which intersect a given body inE ⁿ in a nearly ellipsoidal set is considered and an affine invariant measure is introduced for that purpose.     

Norm properties of C-numerical radii

Given n×n complex matrices A, C, the C-numerical radius of A is the nonnegative quantity

$\text{r}{}_{\mathrm{c}}\text{(A)≡ma{|tr(CU}{}^1\text{AU)|:U unitary}}$

. For C=diag(1,0,…,0) it reduces to the classical numerical radius $\text{r(A)= max{|x}{}^1\text{Ax|:x}{}^1\text{x=1}}$. We show that r_c is a generalized matrix norm if and only if C is nonscalar and trC≠0. Next, we consider an arbitrary generalized matrix norm and characterize all constants v?0 for which vN is multiplicative. A technique to obtain such v is then applied to C-numerical radii with Hermitian C. In particular we find that vr is a matrix norm if and only if v?4.     

Multiplicativity factors for C-numerical radii

For matrices $\text{A, C?}\text{C}{}_{\mathrm{n}}\text{x}{}_{\mathrm{n}}$ , the C-numerical radius of A is the nonnegative quantity

$\text{r}{}_{\mathrm{c}}\text{(A)=max{|tr(CU}{}^1\text{AU)|:Uunitary}}$

. This generalizes the classical numerical radius r(A). It is known that r_c constitutes a norm on $\text{C}{}_{\mathrm{n}}\text{x}{}_{\mathrm{n}}$ if and only if C is nonscalar and trC≠0. For all such C we obtain multiplicativity factors for r_c, i.e., constant μ>0 for which μr_c is submultiplicative on $\text{C}{}_{\mathrm{n}}\text{x}{}_{\mathrm{n}}$.     

Probing the Gaseous Structure of a β-Hairpin Peptide with H/D Exchange and Electron Capture Dissociation

An improved understanding of the extent to which native protein structure is retained upon transfer to the gas phase promises to enhance biological mass spectrometry, potentially streamlining workflows and providing fundamental insights into hydration effects. Here, we investigate the gaseous conformation of a model β-hairpin peptide using gas-phase hydrogen–deuterium (H/D) exchange with subsequent electron capture dissociation (ECD). Global gas-phase H/D exchange levels, and residue-specific exchange levels derived from ECD data, are compared among the wild type 16-residue peptide GB1p and several variants. High protection from H/D exchange observed for GB1p, but not for a truncated version, is consistent with the retention of secondary structure of GB1p in the gas phase or its refolding into some other compact structure. Four alanine mutants that destabilize the hairpin in solution show levels of protection similar to that of GB1p, suggesting collapse or (re)folding of these peptides upon transfer to the gas phase. These results offer a starting point from which to understand how a key secondary structural element, the β-hairpin, is affected by transfer to the gas phase. This work also demonstrates the utility of a much-needed addition to the tool set that is currently available for the investigation of the gaseous conformation of biomolecules, which can be employed in the future to better characterize gaseous proteins and protein complexes.

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Graphical Abstract ?

     

Lifetime measurements of the excited states of N2 AND N2 by laser-induced fluorescence

Absorption and fluorescent scattering of nitrogen laser radiation by a low-pressure RF laboratory plasma (n_e = 10¹² cm⁻³) has been observed for the first negative system of N₂⁺. A 67±1 ns lifetime of N₂⁺ (B ²Σ_u⁺) was experimentally measured from the laser-induced fluorescence. In addition, enough collisionally excited N₂ (B ³Π_g) was produced to observe laser-induced fluorescence for the second positive system of N₂. The lifetime of N₂ (C ³Π_u) was found to be 41±2 ns. The measured lifetimes are in good agreement with published values calculated from theory.     

Inclusion relations involving k-numerical ranges

Let W_k(A) denote the k-numerical range of an n × n matrix A. It is known that W_i(A) ? W_j(A) for 1 ? j? i? n. It this paper we derive more general inclusion relations of the form Σⁿ_iλ_iW_i(A) ? Σⁿ_iμ_iW_i(A), where λ_i, μ_i are real coefficients.     

Proper orthogonal decomposition of solar photospheric motions

The spatiotemporal dynamics of the solar photosphere is studied by performing a proper orthogonal decomposition (POD) of line of sight velocity fields computed from high resolution data coming from the MDI/SOHO instrument. Using this technique, we are able to identify and characterize the different dynamical regimes acting in the system. Low-frequency oscillations, with frequencies in the range 20-130 microHz, dominate the most energetic POD modes (excluding solar rotation), and are characterized by spatial patterns with typical scales of about 3 Mm. Patterns with larger typical scales of approximately 10 Mm, are associated to p-modes oscillations at frequencies of about 3000 microHz.