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On Nonlinearly Elastic Membranes under Compression

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Chinese Annals of Mathematics,Series B 2006年第4期27卷 379-392页

作者： Karim TRABELSI Centre de Mathématiques Appliquées (cmap) Ecole Polytechnique91128 Palaiseau cedexFrance

The classical equations of a nonlinearly elastic plane membrane made of Saint Venant-Kirchhoff material have been justified by Fox, Raoult and Simo （1993） and Pantz （2000）. We show that, under compression, the associated minimization problem admits no solution. The proof is based on a result of non-existence of minimizers of non-convex functionals due to Dacorogna and Marcellini （1995）. We generalize the application of their result from Diane elasticity to three-dimensional Diane membranes.

关键词： Nonlinear elasticity Minimization Quasiconvexity Quasiconvex envelope Rank- 1-convexity

A FAST FREE MEMORY METHOD FOR AN EFFICIENT COMPUTATION OF CONVOLUTION KERNELS

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Journal of Computational Mathematics 2023年第6期41卷 1093-1116页

作者： Matthieu Aussal Marc Bakry Ecole Polytechnique(cmap) INRIAInstitut Polytechnique ParisRoute de Saclay 91128PalaiseauFrance

We introduce the Fast Free Memory method(FFM),a new implementation of the Fast Multipole Method(FMM)for the evaluation of convolution *** FFM aims at being easier to implement while maintaining a high level of performance,capable of handling industrially-sized *** FFM avoids the implementation of a recursive tree and is a kernel independent *** give the algorithm and the relevant complexity *** quasi-linear complexity enables the evaluation of convolution products with up to one billion *** illustrate numerically the capacities of the FFM by solving Boundary Integral Equations problems featuring dozen of millions of *** implementation is made freely available under the GPL 3.0 license within the Gypsilab framework.

关键词： Convolution product Fast multipole method Boundary integral equations Open-source

NUMERICAL LOCALIZATION OF ELECTROMAGNETIC IMPERFECTIONS FROM A PERTURBATION FORMULA IN THREE DIMENSIONS

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Journal of Computational Mathematics 2008年第2期26卷 149-195页

作者： M.Asch S.M.Mefire LAMFA Université de PicardieCNRs33rue Saint-Leu80039 AmiensFrance cmap Ecole PolytechniqueCNRSRoute de Saclay91128 PalaiseauFrance

This work deals with the numerical localization of small electromagnetic inhomogeneities. The underlying inverse problem considers, in a three-dimensional bounded domain, the time-harmonic Maxwell equations formulated in electric field. Typically, the domain contains a finite number of unknown inhomogeneities of small volume and the inverse problem attempts to localize these inhomogeneities from a finite number of boundary measurements. Our localization approach is based on a recent framework that uses an asymptotic expansion for the perturbations in the tangential boundary trace of the curl of the electric field. We present three numerical localization procedures resulting from the combination of this asymptotic expansion with each of the following inversion algorithms： the Current Projection method, the MUltiple Signal Classification （MUSIC） algorithm, and an Inverse Fourier method. We perform a numerical study of the asymptotic expansion and compare the numerical results obtained from the three localization procedures in different settings.

关键词： Inverse problems Maxwell equations Electric fields Three-dimensional inho-mogeneities Electrical impedance tomography Current projection method MUSIC algo-rithm FFT Edge elements Numerical boundary measurements

A SIMPLE PRECONDITIONED DOMAIN DECOMPOSITION METHOD FOR ELECTROMAGNETIC SCATTERING PROBLEMS

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Journal of Computational Mathematics 2013年第1期31卷 1-21页

作者： F. Alouges J. Bo-urguignon-Mirebeau - I D.P. Levadoux cmap Ecole Polytechnique Palaiseau France Laboratoire de Mathdmatiques Universitd Paris-Sud XI Orsay France DEMR-SFM ONERA Palaiseau France

We present a domain decomposition method （DDM） devoted to the iterative solution of time-harmonic electromagnetic scattering problems, involving large and resonant cavities. This DDM uses the electric field integral equation （EFIE） for the solution of Maxwell problems in both interior and exterior subdomains, and we propose a simple preconditioner for the global method, based on the single layer operator restricted to the fictitious interface between the two subdomains.

关键词： Electromagnetism integral equations methods Domain decomposition meth-ods Preconditioning Cavities.

Guillaume Broux-Quemerais,Sarah Kaakai, Anis Matoussi,Wissal Sabbagh

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Probability, Uncertainty and Quantitative Risk 2024年第2期9卷 149-180页

作者： Guillaume Broux-Quemerais Sarah Kaakarl Anis Matoussi Wissal Sabbagh Laboratoire Manceau de Mathematiques&FR CNRS No 2962 Institut du Risque et de I'AssuranceLeMansUniversityFrance Centre de Mathématiques Appliquees(cmap) CNRSEcole polytechniqueInstitut Polytechnique de Paris91120 PalaiseauFrance

In this paper,we present a probabilistic numerical method for a class of forward utilities in a stochastic factor *** this purpose,we use the representation of forward utilities using the ergodic Backward Stochastic Differential Equations(eBSDEs)introduced by Liang and Zariphopoulou in[27].We establish a connection between the solution of the ergodic BSDE and the solution of an associated BSDE with random terminal time T,defined as the hitting time of the positive recurrent stochastic *** viewpoint based on BSDEs with random horizon yields a new characterization of the ergodic cost^which is a part of the solution of the *** particular,for a certain class of eBSDEs with quadratic generator,the Cole-Hopf transformation leads to a semi-explicit representation of the solution as well as a new expression of the ergodic cost>.The latter can be estimated with Monte Carlo *** also propose two new deep learning numerical schemes for ***,we present numerical results for different examples of eBSDEs and forward utilities together with the associated investment strategies.

关键词： Deep leaming scheme Forward utilities Ergodic BSDEs Markovian solution Deep learning algorithm

Floristic diversity and carbon stocks in the periphery of Deng–Deng National Park,Eastern Cameroon

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Journal of Forestry Research 2020年第3期31卷 989-1003页

作者： Louis Paul Roger Kabelong Banoho Louis Zapfack Robert Bertrand Weladji Cedric Chimi Djomo Melanie Chichi Nyako Yannick Enock Bocko Damien Marie Essono Julliete Mancho Nasang Nade`ge Madountsap Tagnang Charles Innocent Memvi Abessolo Kenneth Roger Mvondo Sakouma Farikou Mamadou Souahibou Florence Jeanne Sarah Palla Tonga Ketchatang Peguy Remi Jiagho Thierry Loic Kenmou Ulrich Arnaud Choumele Kana Jumo Boris Armel Anyam Yi Andjik Roger Bruno Tabue Mbobda Department of Plant Biology Faculty of ScienceUniversity of Yaounde IBP 812 YaoundeCameroon IUCN World Commission On Protected Areas Co-Vice Chair Commission Mondiale des Aires Protegees-Afrique Centrale(CMAP-UICN)GlandSwitzerland Organisation pour la Conservation et le Developpement(OCD) BP 33323 YaoundeCameroun Department of Biology Concordia University7141 Sherbrooke St.W.MontrealMontrealQC H4B 1R6Canada Institute of Agricultural Research for Development(IRAD) PO.BOX 2123YaoundeCameroon Laboratoire de Botanique et Ecologie Facultedes Sciences et TechniquesUniversiteMarien NgouabiBrazzavilleCongo Ministry of Forestry and Wildlife BP 34430 YaoundeCameroon Programme National de Developpement Participatif(PNDP) YaoundeCameroun Observatoire des Forets du Bassin du Congo(OFAC) BP 20818 YaoundeCameroun Fokabs International PO BOX 14097YaoundeCameroon International Union for Conservation of Nature Programme CamerounBP:5506 YaoundeCameroun Secretariat Technique REDD BP 320 YaoundeCameroun

Carbon is continuously being removed from the atmosphere by photosynthesis and stored in carbon pools(live,dead,and soil carbon)of forest ***,carbon stock in dead wood and of trees with diameters at breast height(dbh)between 5 and 10 cm is often not considered in many studies carried out in the Congo Basin *** relationship between tree diversity,life-forms and carbon stocks has received little *** study was carried out on the outskirts of Deng Deng National Park(DDNP)to determine tree diversity(dominant families,species richness and Shannon index),assess carbon stocks in the five carbon compartments(living tree,understory,fine roots,dead wood and litter)as well as to analyze the relationship between(1)carbon stocks and tree diversity;and,(2)between carbon stock and *** Shannon index of trees≥10 cm dbh ranged from 2.6 in riparian forest to 4.3 in secondary forest;and for the tree between 5 and 10 cm,it ranged to 1.56 in riparian forest to 3.68 in the secondary *** study site housed 16 species,7 genera and 3 families which are only found in trees of dbh between 5 and 10 *** average total carbon stock of the five compartments varied from 200.1 t ha-1 in forest residues to 439.1 t ha-1 in secondary *** wood carbon stock varied from 1.2 t ha-1 in riparian forests to 12.51t ha-1 in *** above ground carbon stocks for trees with diameter between 5 and 10 cm varied from 0.7 t ha-1 in young fallow fields to 5.02 t ha-1 in old secondary *** study reveals a low but positive correlation between species richness and total carbon stocks,as well as a significant positive relationship between life-forms and total carbon *** findings highlight the need for more data concerning carbon content of dead wood,carbon of trees≥5 cm<10 cm dbh and the relationship between carbon stocks and tree diversity from other areas of the Congo Basin for a good understanding of the contribution of tropical forests

关键词： Deng Deng national park Carbon stocks Land cover types Species diversity Dead wood