L 2-Harmonic 1-Forms on Submanifolds with Finite Total Curvature

Let $x:M^{m}\to\bar{M}$ , m≥3, be an isometric immersion of a complete noncompact manifold M in a complete simply connected manifold $\bar{M}$ with sectional curvature satisfying $-k^{2}\leq K_{\bar{M}}\leq0$ , for some constant k. Assume that the immersion has finite total curvature in the sense that the traceless second fundamental form has finite L ^m -norm. If $K_{\bar{M}}\not\equiv0$ , assume further that the first eigenvalue of the Laplacian of M is bounded from below by a suitable constant. We prove that the space of the L ² harmonic 1-forms on M has finite dimension. Moreover, there exists a constant Λ>0, explicitly computed, such that if the total curvature is bounded from above by Λ then there are no nontrivial L ²-harmonic 1-forms on M.     

Realization of 2D convolutional codes of rate \frac{1}{n} by separable Roesser models

In this paper, two-dimensional convolutional codes constituted by sequences in $(\mathbb F ^n)^{\mathbb{Z }^{2}}$ where $\mathbb F $ is a finite field, are considered. In particular, we restrict to codes with rate $\frac{1}{n}$ and we investigate the problem of minimal dimension for realizations of such codes by separable Roesser models. The encoders which allow to obtain such minimal realizations, called R-minimal encoders, are characterized.     

Local Estimates for Minimizers of Some Convex Integral Functional of the Gradient and the Strong Maximum Principle

We consider a class of convex integral functionals with lagrangeans depending only on the gradient and satisfying a generalized symmetry assumption, which includes as a particular case the rotational symmetry. Adapting the method by A. Cellina we obtain a kind of local estimates for minimizers in the respective variational problems, which is applied then to deduce some versions of the Strong Maximum Principle in the variational setting.     

Velocity renormalization and carrier lifetime in graphene from the electron-phonon interaction

We present a first-principles investigation of the phonon-induced electron self-energy in graphene. The energy dependence of the self-energy reflects the peculiar linear band structure of graphene and deviates substantially from the usual metallic behavior. The effective band velocity of the Dirac fermions is found to be reduced by 4%-8%, depending on doping, by the interaction with lattice vibrations. Our results are consistent with the observed linear dependence of the electronic linewidth on the binding energy in photoemission spectra.     

The Synthesis of Some Fused Pyrazolo‐1,4‐Naphthoquinones

New fused pyrazolo‐1,4‐naphthoquinones were prepared from the reaction of hydrazines with 6‐(4‐methyl‐3‐pentenyl)‐1,4‐naphthoquinone. The reaction was extended to hydroxylamine to afford the corresponding isoxazolo‐1,4‐napthoquinone compound.     

ClcR-based biosensing system in the detection of cis-dihydroxylated (chloro-)biphenyls

Polychlorinated biphenyls (PCBs) are a group of organic pollutants that are persistent when released into the environment. Among the metabolites of PCBs, dihydroxylated PCBs are also considered as toxic compounds. Various studies have shown that dihydroxylated PCBs affect the reproductive, immune, nervous, and endocrine systems. Detection of these chemicals in environmental and biological samples could provide first-hand information about their levels and lead to a better understanding of their role in toxicity. To that end, we developed a sensing system for the detection of dihydroxylated PCBs based on the clc operon. The Pseudomonas putida clc operon encodes a catabolic pathway for degradation of chlorocatechols, which are major metabolites of a large number of chlorinated compounds. In P. putida, the expression of these genes is regulated by a protein encoded by the gene clcR located upstream from the clcABD genes. We demonstrate here for the first time that dihydroxy PCBs can also induce the clc operon. Our sensing system employs P. putida bacteria harboring a plasmid in which the reporter gene, lacZ, is under the control of the regulatory protein ClcR. Consequently, when exposed to dihydroxy PCBs, the bacteria express β-galactosidase in an amount related to the concentration of the corresponding dihydroxy PCB. Various dihydroxylated PCBs, differing in the number and position of chlorines and in the position of hydroxyls, were tested for their ability to induce expression of β-galactosidase. Detection limits as low as 1×10⁻⁶ mol L⁻¹ were obtained for various dihydroxylated PCBs. Electronic Supplementary Material Supplementary material is available for this article at and is accessible for authorized users.     

Electron-phonon renormalization of the direct band gap of diamond

We calculate from first principles the temperature-dependent renormalization of the direct band gap of diamond arising from electron-phonon interactions. The calculated temperature dependence is in good agreement with spectroscopic ellipsometry measurements, and the zero-point renormalization of the band gap is found to be as large as 0.6 eV. We also calculate the temperature-dependent broadening of the direct absorption edge and find good agreement with experiment. Our work calls for a critical revision of the band structures of other carbon-based materials calculated by neglecting electron-phonon interactions.     

On-line preparation of microsamples prior to CE

An experimental setup is presented here for the automated analysis of microsamples, based on the on-line coupling of a capillary SPE module and a CE unit using a two-position six-port valve, an open-closed valve to isolate electrically the sample preparation from the CE unit and a "T" interface. A C18 trapping microcolumn (dimensions 2.5 cm x 100 microm id x 360 microm od) was used for the SPE step. The utility of the proposed experimental setup was demonstrated by applying it to the determination of quinolone antibiotics in serum microsamples, which was efficiently carried out in less than 20 min (4 min for protein denaturation and 15 min for analytes preconcentration and CE-UV separation-determination). A complete optimization study was performed for preconcentration and cleanup of quinolones, the coupling of sample preparation module to the CE unit and electrophoretic separation of quinolones. A preconcentration factor of 10.4 was achieved. The volume injected with the proposed method was 125 nL versus 160 nL introduced by hydrodynamic injection. The volume required for the analysis was 2 microL, which makes the proposed experimental setup very useful for the analysis of microsamples in fields of current interest such as metabolomics or proteomics.