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Ljusternik–Schnirelman theory in partially ordered Hilbert spaces
 Trans AMS
"... Abstract. We present several variants of LjusternikSchnirelman type theorems in partially ordered Hilbert spaces, which assert the locations of the critical points constructed by the minimax method in terms of the order structures. These results are applied to nonlinear Dirichlet boundary value p ..."
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Abstract. We present several variants of LjusternikSchnirelman type theorems in partially ordered Hilbert spaces, which assert the locations of the critical points constructed by the minimax method in terms of the order structures. These results are applied to nonlinear Dirichlet boundary value problems to obtain the multiplicity of signchanging solutions. 1.
What is the Role of Algebra in Applied Mathematics?
, 2005
"... When I first encountered abstract algebra in the late 1960s, I was drawn to its power and beauty. One of the liberating ideas of the subject is that in dealing with algebraic structures, you don’t need to worry about what the objects are; rather, it is how they behave that is important. Algebra is a ..."
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When I first encountered abstract algebra in the late 1960s, I was drawn to its power and beauty. One of the liberating ideas of the subject is that in dealing with algebraic structures, you don’t need to worry about what the objects are; rather, it is how they behave that is important. Algebra is a wonderful language for describing the behavior of mathematical objects. My fascination with algebra led me to algebraic geometry, which was then among the most abstract areas of pure mathematics. At the time, I would never have predicted that 25 years later I would be writing papers with computer scientists, where we use algebraic geometry and commutative algebra to solve problems in geometric modeling. The algebra that I learned as pure and abstract has come to have significant applications. What do these and other applications imply about the relation between algebra and applied mathematics? The purpose of this essay is explore some aspects of this relation in the hope of provoking useful discussions between pure and applied mathematics. Here, “applied mathematics ” includes not only what students learn in mathematics and applied mathematics departments, but also the mathematics learned in computer science, engineeering, and operations research departments. I begin with examples from geometric modeling, economics, and splines to illustrate the possible applications of algebra. I then discuss computer algebra and conclude with remarks on the role of algebra in the applied mathematics curriculum. Geometric Modeling, Cramer’s Rule, and Modules My first example concerns an unexpected application of Cramer’s Rule and the HilbertBurch Theorem on the structure of certain free resolutions. While Cramer’s Rule should be familiar, free resolutions (whatever they are) may sound rather abstract. As we will see, there are questions in geometric modeling where these topics arise naturally. My part of the story begins with the research of Tom Sederberg and Falai Chen on parametric curves in the plane. If we are given relatively prime polynomials a(t), b(t), c(t) of degree n, then the parametric equations (1) x = a(t) b(t), y = c(t) c(t)
Adaptive QoS for mobile multimedia services over wireless networks
 in Proc.IEEE ICME 2000
, 2000
"... AbsfrucfA wireless network that provides multimedia services should control the quality of the transmission link for users, allocating resources according to the service type of each user, be it voice, video, image or data. This paper proposes a scheme to allocate the desired signal to interference ..."
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AbsfrucfA wireless network that provides multimedia services should control the quality of the transmission link for users, allocating resources according to the service type of each user, be it voice, video, image or data. This paper proposes a scheme to allocate the desired signal to interference noise ratio (SINR) for those users with multimedia services by exploiting power control and smart antennas, while not affecting users with voice service. A method to quickly initialize new users into such a network is also proposed. I.
INTRASEASONAL VARIABILITY IN THE FAREAST PACIFIC: INVESTIGATION OF THE ROLE OF AIRSEA COUPLING IN A REGIONAL COUPLED MODEL
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Lithospheric Deformations in Central Asia derived from Gravity Data
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J. Phys. A: Math. Gen. 37 (2004) 11407–11429 PII: S03054470(04)843087 A geometric theory on the elasticity of biomembranes
, 2004
"... doi:10.1088/03054470/37/47/010 The purpose of this paper is to study the shapes and stabilities of biomembranes within the framework of exterior differential forms. After a brief review of the current status of theoretical and experimental studies on the shapes of biomembranes, a geometric scheme ..."
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doi:10.1088/03054470/37/47/010 The purpose of this paper is to study the shapes and stabilities of biomembranes within the framework of exterior differential forms. After a brief review of the current status of theoretical and experimental studies on the shapes of biomembranes, a geometric scheme is proposed to discuss the shape equation of closed lipid bilayers, the shape equation and boundary conditions of open lipid bilayers and twocomponent membranes, the shape equation and inplane strain equations of cell membranes with crosslinking structures, and the stabilities of closed lipid bilayers and cell membranes. The key point of this scheme is to deal with the variational problems on surfaces embedded in threedimensional Euclidean space by using exterior differential forms. PACS numbers: 87.16.Dg, 02.30.Xx, 02.40.Hw 1.
Habilitation à diriger des Recherches
"... JeanLuc Redelsperger Directeur de recherches (CNRS) Rapporteur ..."
Topology Evolution of Wireless Sensor Networks Based on Adaptive Freescale Networks ⋆
"... WSNs (Wireless Sensor Networks) have the characteristics of limited communication radius and easy invalidation. Aimed at these characteristics, based on complex networks theory, a topology evolution TEBAS (Topology Evolution of Wireless Sensor Networks Based on adaptive scalefree networks), which i ..."
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WSNs (Wireless Sensor Networks) have the characteristics of limited communication radius and easy invalidation. Aimed at these characteristics, based on complex networks theory, a topology evolution TEBAS (Topology Evolution of Wireless Sensor Networks Based on adaptive scalefree networks), which introduces tness and local world and more suitable for WSNs than ERW (Topology Evolution by Random Walker), is proposed. The dynamic analysis demonstrates that TEBAS can generate a topology of WSNs tting scalefree networks characteristics. Simulation shows that networks generated by TEBAS have good faulttolerance and perform better than ERW in energy balance.
NOTES AND CORRESPONDENCE Multiscale Organization of Convection in a Global Numerical Simulation of the December 2006 MJO Event Using Explicit Moist Processes
, 2008
"... Multiscale convective organization in a MaddenJulian Oscillation (MJO) event that occurred during December 2006 and January 2007 was studied by global numerical experiments using explicit moist physics. The simulations successfully reproduced the eastwardpropagating (@5 m s1) convective envelope ..."
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Multiscale convective organization in a MaddenJulian Oscillation (MJO) event that occurred during December 2006 and January 2007 was studied by global numerical experiments using explicit moist physics. The simulations successfully reproduced the eastwardpropagating (@5 m s1) convective envelope of the MJO with a zonal scale of 5000–10,000 km, which included eastwardpropagating (10–15 m s1) disturbances (EPDs) and westwardpropagating cloud clusters (CCs) with zonal scales of 1000–2000 km and O (100 km), respectively. The simulated EPDs were composed of CCs, with new clusters growing to the east of older ones. When the largescale circulation associated with the MJO intensified, the EPDs formed wellorganized squalltype clusters (rainbands). The dynamical structure of the simulated EPDs was reminiscent of moist Kelvin waves. Relevance of westwardpropagating wave disturbances including crossequatorial flow to convective organization in the EPDs was also suggested.
Chargé de Recherche à l’Institut de Recherches pour le Développement
"... BachLien Hua Directeur de recherches (Ifremer) Rapporteur JeanPhilippe Duvel Directeur de recherches (CNRS) Examinateur Thierry Delcroix Directeur de recherches (IRD) Examinateur Yves du Penhoat Directeur de recherches (IRD) Examinateur te l0 ..."
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BachLien Hua Directeur de recherches (Ifremer) Rapporteur JeanPhilippe Duvel Directeur de recherches (CNRS) Examinateur Thierry Delcroix Directeur de recherches (IRD) Examinateur Yves du Penhoat Directeur de recherches (IRD) Examinateur te l0