Characterization of q-Dunkl Appell symmetric orthogonal q-polynomials

AbstractWe introduce a q-Dunkl operator T(θ,q)≔Hq+θH−1 where Hq is the q-derivative one and we determine all symmetric T(θ,q)-Appell classical orthogonal q-polynomials. Up to a dilatation, the solution is a q2-analogue of generalized Hermite polynomials orthogonal with respect to the form H(μ,q2). Integral representation and discrete measure of H(μ,q2) are given for some values of parameters

Le comportement d'un système hydrologique en climat méditerranéen par l'analyse corrélatoire et spectrale des débits et des pluies. Cas de trois sous bassins sud-méditerranéens : (oued Sebdou, Moulah et Isser - Tafna - NW Algérie)

Les analyses corrélatoire et spectrale des chroniques de la pluie (entrée) et de débits (sortie) journaliers enregistrés au niveau des trois bassins sud méditerranéens Sebdou, Mouilah et Isser durant un seul cycle hydrologique nous ont permis d’obtenir des informations sur le fonctionnement de ces systèmes hydrologiques. Bien que la structure du signal « pluie » semble présenter les mêmes caractéristiques pour les trois bassins, le signal de sortie « débit » indique que l’oued Sebdou réagit différemment par rapport aux oueds Mouilah et Isser.The aim of this work was to show that correlation and spectral analyses can be used to understand the functioning of hydrological systems. Accordingly, a study was carried out on three southern Mediterranean basins: Sebdou; Mouilah and Isser; located in the north western of Algeria. (Figure 1). Correlation and spectral analyses of daily rainfall and discharge rates for one hydrological cycle were carried out.Simple analysisSimple analysis of rainfall showed that the correlograms (Figure 2) decreased rapidly for the three basins, reaching a value of 0.2 within 1-2 days. This result indicated that rainfall was a quasi-random phenomenon. The variance density spectrum (Figure 3) showed that the rainfall distribution was not monotonous and presented a “Leigh” signal structure.The simple analysis of discharge rates indicated that the Sebdou system was different. The correlogram (Figure 4a) decreased quickly, characterising independent events without memory and with non-significant amounts of water. However, the Mouilah and Isser correlograms (Figure 4 b,c) decreased slowly. They represent important memory effects with regulation of significant amounts of water. The spectral band (Figure 5) confirmed that the Sebdou system did not modify the input information. The regulation time was about 5 d for Sebdou, 21 and 43 d respectively for Mouilah and Isser.Cross analysisThe correlograms (Figure 6) show that the Mouilah and Isser rivers have a great buffering ability. The Sebdou River was characterised by a composite response of the surface flow and an important groundwater flow. The amplitude function (Figure 7) indicated that the Sebdou system had good inertia. The lag time (Figure 8) was 9, 2 and 5 days respectively for the Sebdou, Mouilah and Isser rivers. The amplification and attenuation of the input signal (Figure 10) show that the Sebdou basin is the most karstified system. The non-linearity of the relationship between rainfall and discharge was expressed by the coherence coefficient (Figure 9), which was lower than 1

Can Artificial Noise Boost Further the Secrecy of Dual-hop RIS-aided Networks?

In this paper, we quantify the physical layer security of a dual-hop regenerative relaying-based wireless communication system assisted by reconfigurable intelligent surfaces (RISs). In particular, the setup consists of a source node communicating with a destination node via a regenerative relay. In this setup, a RIS is installed in each hop to increase the source-relay and relay-destination communications reliability, where the RISs' phase shifts are subject to quantization errors. The legitimate transmission is performed under the presence of a malicious eavesdropper attempting to compromise the legitimate transmissions by overhearing the broadcasted signal from the relay. To overcome this problem, we incorporate a jammer to increase the system's secrecy by disrupting the eavesdropper through a broadcasted jamming signal. Leveraging the well-adopted Gamma and Exponential distributions approximations, the system's secrecy level is quantified by deriving approximate and asymptotic expressions of the secrecy intercept probability (IP) metric in terms of the main network parameters. The results show that the secrecy is enhanced significantly by increasing the jamming power and/or the number of reflective elements (REs). In particular, an IP of approximately $10^{-4}$ can be reached with $40$ REs and $10$ dB of jamming power-to-noise ratio even when the legitimate links' average signal-to-noise ratios are $10$-dB less than the eavesdropper's one. We show that cooperative jamming is very helpful in strong eavesdropping scenarios with a fixed number of REs, and the number of quantization bits does not influence the secrecy when exceeding $3$ bits. All the analytical results are endorsed by Monte Carlo simulations

High sensitivity measurement of implanted As in the presence of Ge in GexSi1−x/Si layered alloys using trace element accelerator mass spectrometry

This article discusses high sensitivity measurement of implanted As in the presence of Ge in Ge(x)Si(1-x)/Si layered alloys using trace element accelerator mass spectrometry