Sampling and interpolation in the Paley-Wiener spaces Lp π, 0 < p ≤ 1

Following Beurling's ideas concerning sampling and interpolation in the Paley-Wiener space L∞τ , we find necessary and sufficient density conditions for sets of sampling and interpolation in the Paley-Wiener spaces Lp τ for 0 < p ≤ 1

Wavelets on Discrete Fields

International audienceAn arithmetic version of continuous wavelet analysis is described. Starting from a square-integrable representation of the affine group of Z Z p (or Z Z) it is shown how wavelet decom-positions of ℓ 2 (Z Z p) can be obtained. Moreover, a redefinition of the dilation operator on ℓ 2 (Z Z p) directly yields an algorithmic structure similar to that appearing with multiresolution analyses

Implementation of the EU CCS Directive in Europe: results and development in 2013

Directive 2009/31/EC of the European Parliament on the geological storage of carbon dioxide, entered into force on June 25th 2009. By the end 2013 the CCS Directive has been fully transposed into national law to the satisfaction of the EC in 20 out of 28 EU Member States, while six EU countries (Austria, Cyprus, Hungary, Ireland, Sweden and Slovenia) had to complete transposing measures. In July 2014 the European Commission closed infringement procedures against Cyprus, Hungary and Ireland, which have notified the EC that they have taken measures to incorporate the CCS Directive into national law. Among other three countries Sweden has updated its legislation and published a new law in their country in March 2014, permitting CO2 storage offshore. The evaluation of the national laws in Poland, which were accepted at national level in November 2013, and Croatia, which entered the EU on 7 July 2013 and simultaneously transposed the CCS directive, is still ongoing in 2014. The first storage permit under the Directive (for the ROAD Project in the offshore Netherlands) has been approved by the EC. While CO2 storage is permitted in a number of European countries, temporary restrictions were applied in Czech Republic, Denmark and Poland. CO2 storage is prohibited except for research and development in Estonia, Finland, Luxembourg, two regions in Belgium and Slovenia due to their geological conditions, but also forbidden in Austraia, Ireland and Latvia. The size of exploration areas for CO2 storage sites is limited in Bulgaria and Hungary. In Germany, only limited CO2 storage will be permitted until 2018 (up to 4 Mt CO2 annually)

Sampling and interpolation in the Paley-Wiener spaces Lp π, 0 < p ≤ 1

Following Beurling's ideas concerning sampling and interpolation in the Paley-Wiener space L∞τ , we find necessary and sufficient density conditions for sets of sampling and interpolation in the Paley-Wiener spaces Lp τ for 0 < p ≤ 1

Running Head: Filter Banks over Commutative Rings Contact Address:

The relation between ladder and lattice implementations of twochannel lter banks is discussed and it is shown that these two concepts di er in general. An elementary proof is given for the fact that over any integral domain which is not a eld there exist causal realizable perfect reconstructing lter banks that can not be implemented with causal lifting lters. A complete parametrization of lter banks with coe cients in local rings and semiperfect rings is given. 2 Q rational numbers Z integers Z=NZ integers modulo N List of Symbols A a commutative ring with identit

Two-Channel Perfect Reconstruction FIR Filter Banks over Commutative Rings

The relation between ladder and lattice implementations of two-channel filter banks is discussed and it is shown that these two concepts differ in general. An elementary proof is given for the fact that over any integral domain which is not a field there exist causal realizable perfect reconstructing filter banks that can not be implemented with causal lifting filters. A complete parametrization of filter banks with coefficients in local rings and semiperfect rings is given. 1 Filter Banks Let A be a commutative ring. We assume that all signals and filters are elements of the Laurent polynomial ring B = A[z; z \Gamma1 ]. Note that B is isomorphic to the group algebra A[Z]. Therefore, we refer to the multiplication in B as a convolution or filter operation. We define a downsampling operation [ # 2] on B by [ # 2] a(z) = a e (z), where a(z) = a e (z 2 ) + za o (z 2 ). An upsampling operation [ &quot; 2] on B is defined by [ &quot; 2] a(z) = a(z 2 ). A two-channel filter bank con..

Methodologies and technologies for mitigation of undesired CO 2 migration in the subsurface

International audienceThe development and implementation of the CO2 Capture and Storage (CCS) technology is highly dependent on the assurance of the storage process safety with regards to a potential CO2 leakage from the target zone. Low permeability caprocks are viewed as critical element for a safe containment of CO2 in the target storage formation. As a result, the presence of any potential pathway is of a major concern since it may allow buoyant CO2 to migrate along and reach an overlying formation or be emitted at the surface, potentially impacting drinking water resources or sensitive stakes at the surface. Undesired CO2 migration may occur through man-made (abandoned and operational wells) and/or natural (caprock sealing defects including faults, fractures and high permeability areas) pathways. Managing a potential CO2 leakage risk scenario is of first importance and a dedicated, site-specific strategy has to be set up. The storage safety could be guaranteed through an adequate site selection and characterization leading to the choice of a site where the evolution of the CO2 plume and potential impacts of the storage are judged acceptable. Specifically to this given storage site, a proper risk-management process should be set up to anticipate the potential deviations from this acceptable behavior, including assessing the risks, monitoring the site to detect any potential loss of confinement, mitigating any potential leakage and remediating possible impacts.This study is focused on the risk treatment stage, more specifically on the methodologies and technologies for mitigation and remediation of unpredicted CO2 migration in the subsurface. To date this subject has not been addressed effectively although it is currently receiving more attention from the industrial and scientific communities. This evolution may be linked with the new regulations on CO2 geological storage, notably in Australia, Europe and in the USA, which specify requirements on mitigation and remediation methods.A comprehensive knowledge of mitigation techniques is needed to meet these requirements, which can be summarized with the three following categories:- Technical issue – the first challenge is to determine which ones of the existing technologies applied on the source, the transfer pathway or directly on the impacts may be adapted to avoid, reduce or correct any potential impacts induced by a CO2 migration. In other words, these are the scientifically conceivable measures;- Operational issue – from an operational perspective, the maturity of a technology is essential to ensure its feasibility. The achievability of one measure is dependent on additional criteria especially on the balance between the benefits (impact avoided) and the costs (economiccosts and potential environmental negative impacts of the measure). The second challenge is therefore to specify properly those criteria for the measures and to develop tools to assess the relevance of each conceivable measures;- Implementation issue – the third challenge is, based on the knowledge available at a given time, to produce an intervention plan as required by the above-cited regulations. This plan should answer to the identified risk events, and also prepare the operator and the competent authority to make an informed decision for choosing the best mitigation and/or remediation option at the time of the detection of an abnormal behavior in the CO2 storage complex.The technical issue has already been tackled and with several technical papers devoted to specific techniques aiming at reducing the potential risks and impacts of CO2 based on either existing work conducted in other fields (e.g. oil and gas industry, soil or water remediation) or specifically developed for CO2 storage. However, new categories of remediation techniques have recently appeared based on newly emerging technologies. In addition there is a need of comparative data to help operators to select the most adapted measure. Decision-making tools are also required to balance the benefits gained by the implementation of a mitigation measure and its economic costs and potential environmental impacts. Finally, there is a lack of integrated studies on the mitigation plan setting-up process. For instance, no comparison between the different intervention strategies of existing and future CO2 storage projects has been published. There is thus a need of gathering the best practices for mitigation of undesired CO2 migration based on the scientific literature and experience gained from various CO2 geological projects.In line with these statements, BRGM and IRIS conducted a literature and experience review on the methodologies and technologies for mitigation of undesired CO2 migration in the subsurface on behalf of the IEA Greenhouse Gas R&D Program.The state of knowledge of CO2 leakage mitigation and remediation technologies has been first presented from a technical point of view. Thus, for different scenarios, the potential actions for avoiding, reducing or correcting impacts caused by an unwanted CO2 migration have been reviewed. The choice of the appropriate measure strongly depends on the nature of the leak. The intervention on leakage through man-made pathways (well remediation) stems from the oil and gas industry experience, and for some of them are considered as standard operations. However, in some cases of man-made leakage pathways, and more importantly in most cases of natural ones, the operator may not be able to rely on the well engineering experience, and may rather rely on either fluid management techniques or new breakthrough technologies for modifying the leaking paths or fluid properties. In case of an impacting CO2 migration, measures may be applied to remediate environmental impacts.The state of knowledge presented in this study integrates both measures that are standard and technically feasible at the present time as well as innovative and under development ones. For each measure and when possible, a technical description of the intervention technique, generic cost and time elements (intervention delay, efficiency time duration) as well as a discussion on the maturity of the technique are provided. Decision-making tools (cost-benefit, cost-effectiveness and multi-criteria analyses) integrating those criteria to help choosing the optimal series of remediation actions are presented in this study. The third part of the work is a review of the existing plans and guidelines for designing such intervention plans. A qualitative survey has been performed among a list of CO2 and natural gas storage sites. Recommendations – research and development directions or best practices - are proposed according to the outcomes of the entire study