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On the Stability of Racing Sailing Boats with Foils

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Chinese Annals of mathematics,Series B 2018年第3期39卷 427-450页

作者： Philippe deSTUYNdeR Caroline FABRE département d'ingénierie mathématique Laboratoire M2N Conservatoire National des Arts et Métiers 292rue saint Martin75003 ParisFrance Laboratoire de mathématiques d'Orsay Univ.Paris-SudCNRSUniversitéParis-Saclay 91405 OrsayFrance

The development of foils for racing boats has changed the strategy of ***,the America's cup held in San Francisco,has been the theatre of a tragicomic history due to the foils. during the last round,the New-Zealand boat was winning by 8 to1 against the defender USA. The winner is the first with 9 victories. USA team understood suddenly(may be) how to use the control of the pitching of the main foils by adjusting the rake in order to stabilize the ship. And USA won by 9 victories against 8 to the challenger NZ. The goal in this paper is to point out few aspects which could be taken into account in order to improve this mysterious control law which is known as the key of the victory of the USA team. There are certainly many reasons and in particular the cleverness of the sailors and of all the engineering team behind this project. But it appears interesting to have a mathematical discussion,even if it is a partial one,on the mechanical behaviour of these extraordinary sailing boats. The numerical examples given here are not the true *** have just been invented in order to explain the theoretical developments concerning three points: The possibility of tacking on the foils for sailing upwind,the nature of foiling instabilities,if there are,when the boat is flying and the control laws.

关键词：不稳定性航行控制轮船旧金山美国法律水手

Fast Computation of Pareto Set for Bicriteria Linear Programs with Application to a diet Formulation Problem

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American Journal of Operations Research 2018年第5期8卷 323-342页

作者： F. dubeau M. E. Ntigura Habingabwa département de mathématiques Université de Sherbrooke Sherbrooke Canada

In case of mathematical programming problems with conflicting criteria, the Pareto set is a useful tool for a decision maker. Based on the geometric properties of the Pareto set for a bicriteria linear programming problem, we present a simple and fast method to compute this set in the criterion space using only an elementary linear program solver. We illustrate the method by solving the pig diet formulation problem which takes into account not only the cost of the diet but also nitrogen or phosphorus excretions.

关键词： Bicriteria Linear Program Pareto Set Criterion Space Weighted-Sum diet Formulation Taxation System

COMMON FIXEd POINT THEOREMS FOR MULTI-VALUEd MAPS

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Acta mathematica Scientia 2012年第2期32卷 818-824页

作者： Boško damjanovic Bessem Samet Calogero Vetro department of mathematics Faculty of AgricultureNemanjina 6BelgradeSerbia Universitéde Tunis Département de MathématiquesEcole Supérieure des Sciences et Techniques de Tunis department of mathematics and Informatics University of PalermoVia Archirafi3490123 PalermoItaly

We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and sev... 详细信息

关键词： Coincidence point common fixed point multi-valued maps

Natural frequencies of composite beams with a variable fiber volume fraction including rotary inertia and shear deformation

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Applied mathematics and Mechanics(English Edition) 2009年第6期30卷 717-726页

作者： Y. Bedjilili A. Tounsi H. M. Berrabah I. Mechab E. A. Adda Bedia S. Benaissa Université de Tlemcen Faculté des Sciences de l'ingénieurDépartement de Génie MécaniqueAlgérie Laboratoire des Matériaux et Hydrologie Université de Sidi Bel AbbesAlgérie Laboratoire de mathématiques Université de Sidi Bel AbbesAlgérie

The present study is concerned with the vibration analysis of symmetric composite beams with a variable fiber volume fraction through thickness. First-order shear deformation and rotary inertia have been included in the analysis. The solution procedure is applicable to arbitrary boundary conditions. Continuous gradation of the fiber volume fraction is modeled in the form of an m-th power polynomial of the coordinate axis in the thickness direction of the beam. By varying the fiber volume fraction within the symmetric composite beam to create a functionally graded material （FGM）, certain vibration characteristics are affected. Results are presented to demonstrate the effects of shear deformation, fiber volume fraction, and boundary conditions on the natural frequencies and mode shapes of composite beams.

关键词： free vibration functionally graded materials first-order shear deformationtheory

Global-in-Time L^(p)-L^(q) Estimates for Solutions of the Kramers-Fokker-Planck Equation

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Communications in mathematical Research 2022年第4期38卷 560-578页

作者： Xue Ping Wang Lu Zhu Laboratoire de mathématiques Jean Leray UMR CNRS 6629Universitéde Nantes44322 Nantes Cedex 3France College of Science Hohai University210024 NanjingChina

In this work,we prove an optimal global-in-time L^(p)-L^(q) estimate for solutions to the Kramers-Fokker-Planck equation with short range potential in dimension *** result shows that the decay rate as t-→+∞ is the same as the heat equation in x-variables and the divergence rate as t→O_(+) is related to the sub-ellipticity with loss of one third derivatives of the Kramers-Fokker-Planck operator.

关键词： Global-in-time estimates nonselfadjoint operators kinetic equation Kramers-Fokker-Planck operator

A survey of the Szeg? equation dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

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Science China mathematics 2019年第6期62卷 1087-1100页

作者： Patrick Gérard Sandrine Grellier Laboratoire de mathématiques d'Orsay Université Paris-Sud CNRSUniversité Paris-Saclay Institut denis Poisson-Université d'Orléans/Université de Tours CNRS UMR

We survey the main properties of the cubic Szeg? equation from the Pde viewpoint, emphasising global existence of smooth solutions, analytic regularity, growth of high Sobolev norms and the effects of weak damping.

关键词： cubic Szego equation integrable system Hankel operator spectral analysis analytic regularity wave turbulence

Combinatorial rigidity of unicritical maps

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Science China mathematics 2010年第3期53卷 831-848页

作者： PENG WenJuan 1, & TAN Lei 2 1 School of mathematical Sciences, Peking University, Beijing 100871, China 2 departement de mathematiques, Universited’Angers, Angers 49045, France School of mathematical Sciences Peking University Beijing China departement de mathématiques Université d’Angers Angers France

In this paper, we combine the KSS nest constructed by Kozlovski, Shen and van Strien, and the analytic method proposed by Avila, Kahn, Lyubich and Shen to prove the combinatorial rigidity of unicritical maps.

关键词： combinatorial rigidity unicritical maps KSS nest

Very Regular Solutions for the Landau-Lifschitz Equation with Electric Current

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Chinese Annals of mathematics,Series B 2018年第5期39卷 889-916页

作者： Gilles CARBOU Rida JIZZINI Laboratoire de mathématiques Appliquées de Pau UMR CNRS 5142 Université de Pau et des Pays de l'Adour Institut de mathématiques de Bordeaux UMR CNRS 5251 Université de Bordeaux 351 cours de la Libération

The authors consider a model of ferromagnetic material subject to an electric current, and prove the local in time existence of very regular solutions for this model in the scale of H^k spaces. In particular, they des... 详细信息

关键词：电流 La 方程相容性条件铁磁性模型

Semi-classical analysis on H-type groups dedicated to Professor Jean-Yves Chemin on the Occasion of His 60th Birthday

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Science China mathematics 2019年第6期62卷 1057-1086页

作者： Clotilde Fermanian Kammerer Véronique Fischer Université Paris-Est Laboratoire d’Analyse et de Mathématiques Appliquées (UMR 8050) department of mathematical Sciences University of Bath

In this paper, we develop semi-classical analysis on H-type groups. We define semi-classical pseudodifferential operators, prove the boundedness of their action on square integrable functions and develop a symbolic calculus. Then, we define the semi-classical measures of bounded families of square integrable functions which consist of a pair formed by a measure defined on the product of the group and its unitary dual, and by a field of trace class positive operators acting on the Hilbert spaces of the representations. We illustrate the theory by analyzing examples, which show in particular that this semi-classical analysis takes into account the finite-dimensional representations of the group, even though they are negligible with respect to the Plancherel measure.

关键词： H-type groups semi-classical pseudodifferential operators semi-classical measures Wigner transform asymptotic analysis microlocal analysis