Integral representations for a generalized Hermite linear functional

In this paper we find new integral representations for the {\it generalized Hermite linear functional} in the real line and the complex plane. As application, new integral representations for the Euler Gamma function are given.Comment: 4 figure

Lagoon water-level oscillations driven by rainfall and wave climate

Barrier breaching and subsequent inlet formation represent critical processes that ensure the temporary or permanent connection and transference of water, nutrients, or living organisms between a lagoon and the open sea. Here, we investigate the conditions inducing natural barrier breaching through a 34 months monitoring program of water-level oscillations within a shallow lagoon and the adjacent nearshore, at the Northern coast of the Iberian Peninsula, Louro lagoon. Seven natural openings were identified to have occurred during the three monitored wet seasons, from the 2009 to 2012, (Wet1, Wet2 and Wet3); four in the Wetl, two in the Wet2 and one in. the Wet3. The openings were grouped in three types depending on the observed relation between the lagoon water-level (L-wl), the estimated berm height (B-h) and the water-level at the beach (B-wl): (i) openings by lagoon outflow, which include those characterized by L-wl higher than B-h and lower B-wl; (ii) openings by wave inundation, including those induced by B-wl higher than B-h, and (iii) mixed openings, which result from a combination of the two previous conditions. We observed that L-wl is modulated by the rainfall regime (R-f) and can be explained by the accumulated precipitation. We estimated applying runup equations to obtain B-h and B-wl which depend on the wave climate and tidal level. The inlet lifespan was found to be regulated by the wave climate and rainfall regime; in particular barrier sealing was associated with a sudden increase in wave period and a reduction in precipitation. This work proves that the natural openings could be predicted successfully with support to medium term water-level monitoring programs, which in turn may significantly contribute to strategic decision making for management and conservation purposes.Xunta de Galicia [08MDS036000PR, PlanI2C-ED481B 2014/132-0]MICINN [CTM2012-39599-C03-01]Portuguese Science Foundation [IF/01047/2014]info:eu-repo/semantics/publishedVersio

Content enrichment through dynamic annotation

This paper describes a technique for interceding between users and the information that they browse. This facility, that we term 'dynamic annotation', affords a means of editing Web page content 'on-the-fly' between the source Web server and the requesting client. Thereby, we have a generic way of modifying the content displayed to local users by addition, removal or reorganising any information sourced from the World-Wide Web, whether this derives from local or remote pages. For some time, we have been exploring the scope for this device and we believe that it affords many potential worthwhile applications. Here, we describe two varieties of use. The first variety focuses on support for individual users in two contexts (second-language support and second language learning). The second variety of use focuses on support for groups of users. These differing applications have a common goal which is content enrichment of the materials placed before the user. Dynamic annotation provides a potent and flexible means to this end

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