The construction of a seventh-order Jupiter-Saturn analytical theory

We extend the construction of the Jupiter-Saturn theory to include all the terms up to the seventh order in the masses. The Hori-Lie transformation technique is employed. The Jacobian coordinates are adopted and the theory is expressed in terms of the canonical non-singular variables of H. Poincaré.     

The construction of a third order secular

In this part we find out the 24 equations of secular perturbation equations for the subsystem J-S-U-N. The solution of these equations by the Lagrange-Laplace procedure and the Eigen value Eigen vector is analysed. Also we refer to Hurwitz theorem to test stability.     

Expansion of the planetary mutual distance raised to any negative power by the method of symbolic differential operators

We present a literal approach to evaluate ^–s necessary for the construction of high order planetary theories. This approach is valid to be applied on very large scale digital computers with standard Poisson series programs, for high order and high degree planetary theories. We apply the method of symbolic differential operators for single variable functions, and the binomial theorem expansions, for the evaluation of ^–s . We utilize Laplace coefficients and its derivatives to carry out the development, without dealing with Newcomb operators or Hansen's coefficients.     

On the elimination of the critical term in a general first-order Uranus-Neptune theory

A solution of the Uranus-Neptune planetary canonical equations of motion through the Von Zeipel technique is presented. A unique determinging function which depends upon mixed canonical variables, reduces the 12 critical terms of the Hamiltonian to the set of its secular terms. The Poincaré canonical variables are used. We refer to a common fixed plane, and apply the Jacobi-Radau set of origins. In our expansion we neglected terms of power higher than the fourth with respect to the eccentricities and sines of the inclinations.     

The expansion of negative powers of mutual distance between two planets

In this part we obtain the expression for ^–s by the application of Smart's method, which involves Taylor's theorem for functions of several variables. We neglected terms of power higher than the fourth with respect to eccentricities and tangents of inclinations.     

A pan-sharpening method based on NSCT and formulated as compressive sensing problem

In this paper, a pan-sharpening method, using non-subsampled contourlet transform (NSCT) and the theory of compressive sensing (CS), is proposed. The NSCT is used for sparse image representation to perform a multiscale and directional decomposition of source images in order to express their detail and express the sparsity of their high frequency. The CS is used to merge the multispectral (MS) and panchromatic (pan) images from partial random measurements. Two different fusion rules are then applied. The final pan-sharpened image is obtained by inverse NSCT. Experimental results show the efficiency of the proposed method, compared with pan sharpening based on standard NSCT, in terms of visual quality and objective assessment. Moreover, the proposed technique is very effective when the storage and transmission bandwidth are limited.     

Assessing seasonal variations and aquifer vulnerability in coastal aquifers of semi-arid regions using a multi-tracer isotopic approach: the case of Grombalia (Tunisia)

The Grombalia aquifer (NE Tunisia) is an example of an important source of water supply for regional and national development, where the weak controls over abstraction, fertilizer application and waste disposal, coupled with limited knowledge of aquifer dynamics, is causing aquifer over-exploitation and water quality degradation. Assessing the key role of groundwater in water-resources security is therefore of paramount importance to support new actions to preserve water quality and quantity in the long-run. This study presents one of the first investigations targeted at a complete assessment of aquifer dynamics in the Grombalia aquifer. A multi-tracer hydrogeochemical and isotopic (δ²H, δ¹⁸O and ³H) approach was used to study the influence of seasonal variation on piezometric levels, chemical and isotopic compositions, and groundwater recharge. A total of 116 samples were collected from private wells and boreholes during three periods in a 1 year monitoring campaign (February–March 2014, September 2014 and February 2015). Results revealed the overall unsuitability of groundwater for drinking and irrigation purposes (NO₃?>?50 mg/L in 51% of the wells; EC >1,000 μS/cm in 99% of the wells). Isotopic balance coupled to piezometric investigation indicated the contribution of the shallow aquifer to deep groundwater recharge. The study also revealed the weakness of ‘business as usual’ management practices, highlighting possible solutions to tackle water-related challenges in the Grombalia region, where climate change, population growth and intensive agricultural activities have generated a large gap between demand and available water reserves, hence becoming a possible driver for social insecurity.     

Salinisation origin and hydrogeochemical behaviour of the Djerid oasis water table aquifer (southern Tunisia)

The shallow Plio-Quaternary (PQ) water table, present over almost the whole Djerid and Chott El Gharsa basins (southern Tunisia), is used as a complement of oases irrigation, especially in summer season. The simplicity of the Plio-Quaternary lithology is confronted to the complexity of the mineralisation mechanisms and the water origin in this aquifer. An approach combining the use of water-dissolved chemical species and isotopic contents has been used to better understand the PQ behaviour under severe increasing exploitation and to determinate the origin of its different water bodies. In southern Tunisia, the aquifer system is composed of the upper unconfined PQ aquifer, the intermediate semi-confined/confined Complexe Terminal (CT) and the deeper confined Continental Intercalaire (CI). Chemical analyses highlighted an origin of mineralisation in close relationship to the dissolution of both sulphated salts (MgSO₄ and Na₂SO₄) and chlorinated salts (NaCl and MgCl) abundant in the surface and subsurface gypsum crust. Positive correlations between gypsum anhydrite, mirabilite, thenardite and halite saturation indexes with respective mineral species, confirm evaporites dissolutions. Isotopic data showed that in addition of sporadic rainfall events, there is a contribution from the CI and the CT Saharan groundwaters, recharging the PQ aquifer in the study area. Return flow irrigation is partly affected by evaporation, before recharging the shallow aquifer, in oases limits.     

The elimination of the critical terms of a first order Uranus-Neptune theory through Hori's method

An outline for the elimination of the critical terms of a first order Uranus-Neptune theory is presented with a stress on the application of Hori's procedure to the problem.     

First-order secular planetary theory up to fourth power in eccentricities and inclinations

We construct a first-order secular general planetary theory, using the Jacobi-Radau set of origins, referring to common fixed plane and in terms of Poincaré canonical variables. We neglect powers higher than the fourth with respect to the eccentricities and sines of inclinations.