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From Control Theory to Gravitational Waves

Advances in Pure Mathematics 2024年第2期14卷 49-100页

作者： jean-francois pommaret CERMICS Ecole des Ponts Paris Tech Paris France

When D:ξ→η is a linear ordinary differential (OD) or partial differential (PD) operator, a “direct problem” is to find the generating compatibility conditions (CC) in the form of an operator D1:η→ξ such that Dξ = η implies D1η = 0. When D is involutive, the procedure provides successive first-order involutive operators D1,...,Dn when the ground manifold has dimension n. Conversely, when D1 is given, a much more difficult “inverse problem” is to look for an operator D:ξ→η having the generating CC D1η = 0. If this is possible, that is when the differential module defined by D1 is “torsion-free”, that is when there does not exist any observable quantity which is a sum of derivatives of η that could be a solution of an autonomous OD or PD equation for itself, one shall say that the operator D1 is parametrized by D. The parametrization is said to be “minimum” if the differential module defined by D does not contain a free differential submodule. The systematic use of the adjoint of a differential operator provides a constructive test with five steps using double differential duality. We prove and illustrate through many explicit examples the fact that a control system is controllable if and only if it can be parametrized. Accordingly, the controllability of any OD or PD control system is a “built in” property not depending on the choice of the input and output variables among the system variables. In the OD case and when D1 is formally surjective, controllability just amounts to the formal injectivity of ad(D1), even in the variable coefficients case, a result still not acknowledged by the control community. Among other applications, the parametrization of the Cauchy stress operator in arbitrary dimension n has attracted many famous scientists (G. B. Airy in 1863 for n = 2, J. C. Maxwell in 1870, E. Beltrami in 1892 for n = 3, and A. Einstein in 1915 for n = 4).

关键词： Differential Operator Differential Sequence Killing Operator Riemann Operator Bianchi Operator Cauchy Operator Control Theory Controllability Elasticity General Relativity

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Homological Solution of the Lanczos Problems in Arbitrary Dimension

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Journal of Modern Physics 2021年第6期12卷 829-858页

作者： jean-francois pommaret CERMICS Ecole des Ponts ParisTech France

When D is a linear partial differential operator of any order, a direct problem is to look for an operator D1 generating the compatibility conditions (CC) D1η = 0 of Dξ = η. Conversely, when D1 is given, an inverse problem is to look for an operator D such that its CC are generated by D1 and we shall say that D1 is parametrized by D = D0. We may thus construct a differential sequence with successive operators D, D1, D2, ..., each operator parametrizing the next one. Introducing the formal adjoint ad() of an operator, we have but ad (Di-1) may not generate all the CC of ad (Di). When D = K [d1, ..., dn] = K [d] is the (non-c

关键词： Differential Sequence Variational Calculus Lanczos Potential Lanczos Operator Vessiot Structure Equations

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Differential Homological Algebra and General Relativity

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Journal of Modern Physics 2019年第12期10卷 1454-1486页

作者： jean-francois pommaret CERMICS Ecole des Ponts Paris Tech Paris France

In 1916, F.S. Macaulay developed specific localization techniques for dealing with “unmixed polynomial ideals” in commutative algebra, transforming them into what he called “inverse systems” of partial differential equations. In 1970, D.C. Spencer and coworkers studied the formal theory of such systems, using methods of homological algebra that were giving rise to “differential homological algebra”, replacing unmixed polynomial ideals by “pure differential modules”. The use of “differential extension modules” and “differential double duality” is essential for such a purpose. In particular, 0-pure differential modules are torsion-free and admit an “absolute parametrization” by means of arbitrary potential like functions. In 2012, we have been able to extend this result to arbitrary pure differential modules, introducing a “relative parametrization” where the potentials should satisfy compatible “differential constraints”. We recently noticed that General Relativity is just a way to parametrize the Cauchy stress equations by means of the formal adjoint of the Ricci operator in order to obtain a “minimum parametrization” by adding sufficiently many compatible differential constraints, exactly like the Lorenz condition in electromagnetism. In order to make this difficult paper rather self-contained, these unusual purely mathematical results are illustrated by many explicit examples, two of them dealing with contact transformations, and even strengthening the comments we recently provided on the mathematical foundations of General Relativity and Gauge Theory. They also bring additional doubts on the origin and existence of gravitational waves.

关键词： Homological Algebra Extension Module Torsion-Free Module Pure Module Purity Filtration Involution Electromagnetism General Relativity

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The Mathematical Foundations of Gauge Theory Revisited

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Journal of Modern Physics 2014年第5期5卷 157-170页

作者： jean-francois pommaret CERMICS Ecole des Ponts ParisTech 77455 Marne-la-Vallée Cedex 02 France

We start recalling with critical eyes the mathematical methods used in gauge theory and prove that they are not coherent with continuum mechanics, in particular the analytical mechanics of rigid bodies (despite using the same group theoretical methods) and the well known couplings existing between elasticity and electromagnetism (piezzo electricity, photo elasticity, streaming birefringence). The purpose of this paper is to avoid such contradictions by using new mathematical methods coming from the formal theory of systems of partial differential equations and Lie pseudo groups. These results finally allow unifying the previous independent tentatives done by the brothers E. and F. Cosserat in 1909 for elasticity or H. Weyl in 1918 for electromagnetism by using respectively the group of rigid motions of space or the conformal group of space-time. Meanwhile we explain why the Poincaré duality scheme existing between geometry and physics has to do with homological algebra and algebraic analysis. We insist on the fact that these results could not have been obtained before 1975 as the corresponding tools were not known before.

关键词： Gauge Theory Curvature Torsion Maurer-Cartan Forms Maurer-Cartan Equations Lie Groups Lie Pseudo Groups Differential Sequence Janet Sequence Spencer Sequence Differential Module Homological Algebra Extension Modules

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The Mathematical Foundations of General Relativity Revisited

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Journal of Modern Physics 2013年第8期4卷 223-239页

作者： jean-francois pommaret CERMICS Ecole des Ponts ParisTech Marne-la-Vall_ee Cedex 02 France

The purpose of this paper is to present for the first time an elementary summary of a few recent results obtained through the application of the formal theory of partial differential equations and Lie pseudogroups in order to revisit the mathematical foundations of general relativity. Other engineering examples (control theory, elasticity theory, electromagnetism) will also be considered in order to illustrate the three fundamental results that we shall provide successively. 1) VESSIOT VERSUS CARTAN: The quadratic terms appearing in the “Riemann tensor” according to the “Vessiot structure equations” must not be identified with the quadratic terms appearing in the well known “Cartan structure equations” for Lie groups. In particular, “curvature + torsion” (Cartan) must not be considered as a generalization of “curvature alone” (Vessiot). 2) JANET VERSUS SPENCER: The “Ricci tensor” only depends on the nonlinear transformations (called “elations” by Cartan in 1922) that describe the “difference” existing between the Weyl group (10 parameters of the Poincaré subgroup + 1 dilatation) and the conformal group of space-time (15 parameters). It can be defined without using the indices leading to the standard contraction or trace of the Riemann tensor. Meanwhile, we shall obtain the number of components of the Riemann and Weyl tensors without any combinatoric argument on the exchange of indices. Accordingly and contrary to the “Janet sequence”, the “Spencer sequence” for the conformal Killing system and its formal adjoint fully describe the Cosserat equations, Maxwell equations and Weyl equations but General Relativity is not coherent with this result. 3) ALGEBRA VERSUS GEOMETRY: Using the powerful methods of “Algebraic Analysis”, that is a mixture of homological agebra and differential geometry, we shall prove that, contrary to other equations of physics (Cauchy equations, Cosserat equations, Maxwell equations), the Einstein equations cannot be “parametrized”, that is the ge

关键词： General Relativity Riemann Tensor Weyl Tensor Ricci Tensor Einstein Equations Lie Groups Lie Pseudogroups Differential Sequence Spencer Operator Janet Sequence Spencer Sequence Differential Module Homological Algebra Extension Modules Split Exact Sequence

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Design and Experimental Testing of a Moving Coil Actuator with Compensation Coil

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CSEE Journal of Power and Energy Systems 2024年第2期10卷 707-716页

作者： Boyuan Yin Xianwu Zeng John Frederick Eastham Emelie Nilsson jean-francois Rouquette jean Rivenc Ludovic Ybanez Xiaoze Pei Department of Electronics&Electrical Engineering University of BathBathBA27AYUnited Kingdom Airbus UpNext BlangnacFrance Airbus CRT BlangnacFrance Department of Mechanical Engineering University of BathBathBA27AYUnited Kingdom

Hydrogen-powered electric aircraft have attracted significant interests aiming to achieve decarbonization *** DC electric networks are facing great challenges in DC fault protection *** interrupters are widely used in low voltage and medium voltage power systems due to being environmentally friendly with low *** this paper a moving coil actuator with compensation coils for a vacuum interrupter,as part of a hybrid direct current circuit breaker,is designed and experimentally *** coils are used to improve operating speed compared with original moving coil *** between four possible connections of compensation coils and original moving coil actuator are carried *** results show comparisons between different connections of actuator coils in terms of opening time and coil current with a range of pre-charged capacitor *** performance of each actuator connection is also *** actuator with compensation coils is shown to have a higher current rising rate and achieve faster opening speed,which is a critical requirement for electric aircraft network *** parallel connection actuator achieves the highest opening speed within 3.5 ms with capacitor voltage of 50 V.

关键词： Circuit breaker compensation coil moving coil actuator vacuum interrupter

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构建安全连接,筑牢通信行业高质量发展底座

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数字经济 2024年第4期 93-95页

作者： jean-francois Ouillet 泰雷兹集团

身处数字化时代,以新一代信息通信技术为核心的物联网(IoT)正在重塑各行各业,为数字经济发展注入强劲动力;同时,也在改变着每个人与周围世界互动的方式,为日常生活带来更多便捷选择。物联网不断为行业数字化转型提供新支撑、为数字经济... 详细信息

身处数字化时代,以新一代信息通信技术为核心的物联网(IoT)正在重塑各行各业,为数字经济发展注入强劲动力;同时,也在改变着每个人与周围世界互动的方式,为日常生活带来更多便捷选择。物联网不断为行业数字化转型提供新支撑、为数字经济发展拓展新空间,整个市场也在持续探索更灵活便捷、安全可靠的连接方式,以应对新挑战。

关键词：信息通信技术通信行业数字化转型数字化时代安全连接强劲动力灵活便捷连接方式

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21世纪全球新建水库编目:丰度、热点区及总蓄水量

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Science Bulletin 2024年第14期69卷 2179-2182页

作者：范晨雨宋春桥 Jida Wang Yongwei Sheng 蔺亚玲苑春雨 Md Safat Sikder jean-francois Crétaux 刘凯陈探曾繁轩柯灵红 Key Laboratory of Watershed Geographic Sciences Nanjing Institute of Geography and LimnologyChinese Academy of SciencesNanjing 210008China University of Chinese Academy of Sciences Beijing 100049China University of Chinese Academy of Sciences Nanjing(UCASNJ)Nanjing 211135China Department of Geography and Geographic Information Science University of Illinois Urbana-ChampaignUrbana IL 61801USA Department of Geography and Geospatial Sciences Kansas State UniversityManhattan KS 66506USA Department of Geography University of CaliforniaLos Angeles CA 90095USA Laboratoire d’Études en Géophysique et Océanographie Spatiales(LEGOS) CNES-IRD-CNRS-UT3Universitéde ToulouseToulouse 31401France College of Hydrology and Water Resources Hohai UniversityNanjing 210098China State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering Hohai UniversityNanjing 210098China

Dams and reservoirs play an essential role in regulating and managing water *** the middle of the 20th century,the growing demand for water and hydropower has led to an unprecedented boom in reservoir construction worldwide[1,2].Meanwhile,reservoir construction has also resulted in a variety of ecological and socioeconomic impacts[3–5].Reservoirs transform natural flow regimes into conditions favored by human *** associated flow regulations,especially in reservoirs constructed in recent decades(e.g.,after 2000)with greater seasonal variability[6,7],represent a strong human-induced alteration of the hydrologic *** reservoir construction continues to boom in many parts of the world,an up-to-date and openaccess inventory of reservoirs worldwide remains critically desired.

关键词： reservoir reservoirs alteration

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Application of near-infrared spectroscopy for fast germplasm analysis and classification in multi-environment using intact-seed peanut(Arachis hypogaea L.)

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Oil Crop Science 2024年第2期9卷 132-141页

作者： Fentanesh Chekole Kassie Gilles Chaix Hermine Bille Ngalle Maguette Seye Coura Fall Hodo-Abalo Tossim Aissatou Sambou Olivier Gibert Fabrice Davrieux Joseph Martin Bell jean-francois Rami Daniel Fonceka Joel Romaric Nguepjop Department of Plant Biology and Physiology Faculty of SciencesUniversity of Yaounde IYaoundeP.O.Box 337Cameroon Department of Plant Science College of AgricultureWolaita Sodo UniversitySodoP.O.Box 138Ethiopia CIRAD UMR AGAP InstitutMontpellierFrance AGAP Institut Univ MontpellierCIRADINRAEInstitut AgroMontpellierFrance ChemHouse Research Group MontpellierFrance Centre D’Etudes Regional Pour L’Amelioration de L’Adaptation a La Secheresse(CERAAS/ISRA) Route de KhomboleThiesBP 3320Senegal Dispositif de Recherche et de Formation en Partenariat Innovation et Amelioration Varietale en Afrique de L’Ouest(IAVAO)CERAASRoute de KhomboleThiesBP 3320Senegal CIRAD UMR QUALISUDSaint PierreFrance

Peanut is a worldwide oilseed crop and the need to assess germplasm in a non-destructive manner is important for seed nutritional *** this study,Near Infrared Spectroscopy(NIRS)was applied to rapidly assess germplasm variability from whole seed of 699 samples,field-collected and assembled in four genetic and environmentbased sets:one set of 300 varieties of a core-collection and three sets of 133 genotypes of an interspecific population,evaluated in three environments in a large spatial scale of two countries,Mbalmayo and Bafia in Cameroon and Nioro in Senegal,under rainfed *** elemental spectra were gathered on six subsets of seeds of each sample,after three rotation scans,with a spectral resolution of 16 cm-1over the spectral range of867 nm to 2530 *** were then processed by principal component analysis(PCA)coupled with Partial least squares-discriminant analysis(PLS-DA).As results,a huge variability was found between varieties and genotypes for all NIR wavelength within and between *** magnitude of genetic variation was particularly observed at 11 relevant wavelengths such as 1723 nm,usually related to oil content and fatty acid *** yielded the most chemical attributes in three significant PCs(i.e.,eigenvalues>10),which together captured 93%of the total variation,revealing genetic and environment structure of varieties and genotypes into four clusters,corresponding to the four samples *** pattern of genetic variability of the interspecific population covers,remarkably half of spectrum of the core-collection,turning out to be the ***,a PLS-DA model was developed and a strong accuracy of 99.6%was achieved for the four sets,aiming to classify each seed sample according to environment *** confusion matrix achieved for the two sets of Bafia and Nioro showed 100%of instances classified correctly with 100%at both sensitivity and specificity,confirming that their seed quality was different f

关键词： Groundnut Oilseed Near infrared spectroscopy Germplasm analysis Environment Nutritional Breeding

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Computation of Shock Profiles in Radiative Hydrodynamics

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Communications in Computational Physics 2009年第10期6卷 1118-1136页

作者： jean-francois Coulombel Pauline Lafitte CNRS Laboratoire Paul Painleve and Project Team SIMPAF INRIA FutursUniversite Lille 1Cite Scientifique59655 VILLENEUVE D’ASCQ CedexFrance Laboratoire Paul Painleve and Project Team SIMPAF INRIA Futurs Universite Lille 1Cite Scientifique59655 VILLENEUVE D’ASCQ CedexFrance

This article is devoted to the construction of a numerical scheme to solve the equations of radiative *** use this numerical procedure to compute shock profiles and illustrate some earlier theoretical results about their smoothness and monotonicity *** first consider a scalar toy model,then we extend our analysis to a more realistic system for the radiative hydrodynamics that couples the Euler equations and an elliptic equation.

关键词： Radiative transfer shock profiles Euler equations numerical profiles

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