A Faint Star-Forming System Viewed Through the Lensing Cluster Abell 2218: First Light at z~5.6?

We discuss the physical nature of a remarkably faint pair of Lyman alpha-emitting images discovered close to the giant cD galaxy in the lensing cluster Abell 2218 (z=0.18) during a systematic survey for highly-magnified star-forming galaxies beyond z=5. A well-constrained mass model suggests the pair arises via a gravitationally-lensed source viewed at high magnification. Keck spectroscopy confirms the lensing hypothesis and implies the unlensed source is a very faint (I~30) compact (<150 pc) and isolated object at z=5.576 whose optical emission is substantially contained within the Lyman alpha emission line; no stellar continuum is detectable. The available data suggest the source is a promising candidate for an isolated ~10^6 solar mass system seen producing its first generation of stars close to the epoch of reionization.Comment: 11 pages, 3 figures, to appear in Ap J Lett, minor revision following referee's repor

On analytic properties of Meixner-Sobolev orthogonal polynomials of higher order difference operators

In this contribution we consider sequences of monic polynomials orthogonal with respect to Sobolev-type inner product $$\left\langle f,g\right\rangle= \langle {\bf u}^{\tt M},fg\rangle+\lambda \mathscr T^j f (\alpha)\mathscr T^{j}g(\alpha),$$ where ${\bf u}^{\tt M}$ is the Meixner linear operator, $\lambda\in\mathbb{R}_{+}$, $j\in\mathbb{N}$, $\alpha \leq 0$, and $\mathscr T$ is the forward difference operator $\Delta$, or the backward difference operator $\nabla$. We derive an explicit representation for these polynomials. The ladder operators associated with these polynomials are obtained, and the linear difference equation of second order is also given. In addition, for these polynomials we derive a $(2j+3)$-term recurrence relation. Finally, we find the Mehler-Heine type formula for the $\alpha\le 0$ case

Organising metabolic networks: cycles in flux distributions

Metabolic networks are among the most widely studied biological systems. The topology and interconnections of metabolic reactions have been well described for many species, but are not sufficient to understand how their activity is regulated in living organisms. The principles directing the dynamic organisation of reaction fluxes remain poorly understood. Cyclic structures are thought to play a central role in the homeostasis of biological systems and in their resilience to a changing environment. In this work, we investigate the role of fluxes of matter cycling in metabolic networks. First, we introduce a methodology for the computation of cyclic and acyclic fluxes in metabolic networks, adapted from an algorithm initially developed to study cyclic fluxes in trophic networks. Subsequently, we apply this methodology to the analysis of three metabolic systems, including the central metabolism of wild type and a deletion mutant of Escherichia coli, erythrocyte metabolism and the central metabolism of the bacterium Methylobacterium extorquens. The role of cycles in driving and maintaining the performance of metabolic functions upon perturbations is unveiled through these examples. This methodology may be used to further investigate the role of cycles in living organisms, their pro-activity and organisational invariance, leading to a better understanding of biological entailment and information processing

Orbitally stable standing waves of a mixed dispersion nonlinear Schr\"odinger equation

We study the mixed dispersion fourth order nonlinear Schr\"odinger equation \begin{equation*} %\tag{\protect{4NLS}}\label{4nls} i \partial_t \psi -\gamma \Delta^2 \psi +\beta \Delta \psi +|\psi|^{2\sigma} \psi =0\ \text{in}\ \R \times\R^N, \end{equation*} where $\gamma,\sigma>0$ and $\beta \in \R$. We focus on standing wave solutions, namely solutions of the form $\psi (x,t)=e^{i\alpha t}u(x)$, for some $\alpha \in \R$. This ansatz yields the fourth-order elliptic equation \begin{equation*} %\tag{\protect{*}}\label{4nlsstar} \gamma \Delta^2 u -\beta \Delta u +\alpha u =|u|^{2\sigma} u. \end{equation*} We consider two associated constrained minimization problems: one with a constraint on the $L^2$-norm and the other on the $L^{2\sigma +2}$-norm. Under suitable conditions, we establish existence of minimizers and we investigate their qualitative properties, namely their sign, symmetry and decay at infinity as well as their uniqueness, nondegeneracy and orbital stability.Comment: 37 pages. To appear in SIAM J. Math. Ana

The influence of residual oxidizing impurities on the synthesis of graphene by atmospheric pressure chemical vapor deposition

The growth of graphene on copper by atmospheric pressure chemical vapor deposition in a system free of pumping equipment is investigated. The emphasis is put on the necessity of hydrogen presence during graphene synthesis and cooling. In the absence of hydrogen during the growth step or cooling at slow rate, weak carbon coverage, consisting mostly of oxidized and amorphous carbon, is obtained on the copper catalyst. The oxidation originates from the inevitable occurrence of residual oxidizing impurities in the reactor's atmosphere. Graphene with appreciable coverage can be grown within the vacuum-free furnace only upon admitting hydrogen during the growth step. After formation, it is preserved from the destructive effect of residual oxidizing contaminants once exposure at high temperature is minimized by fast cooling or hydrogen flow. Under these conditions, micrometer-sized hexagon-shaped graphene domains of high structural quality are achieved.Comment: Accepted in Carbo