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Stochastic Maximum Principle f.r Optimal Advertising Models with Delay and Non-Convex Control Spaces

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Advances in Pure Mathematics 2024年第6期14卷 442-450页

作者： Giuseppina Guatteri f.derica Masiero dipartimento di matematica Politecnico di Milano via Bonardi Milano Italia dipartimento di matematica e Applicazioni Universit di Milano-Bicocca via Cozzi Milano Italia

In this paper we study optimal advertising problems that model the introduction of.a new product into the market in the presence of.carryover ef.ects of.the advertisement and with memory ef.ects in the level of.goodwill. In particular, we let the dynamics of.the product goodwill to depend on the past, and also on past advertising ef.orts. We treat the problem by means of.the stochastic Pontryagin maximum principle, that here is considered f.r a class of.problems where in the state equation either the state or the control depend on the past. Moreover the control acts on the martingale term and the space of.controls U can be chosen to be non-convex but now the space of.controls U can be chosen to be non-convex. The maximum principle is thus f.rmulated using a f.rst-order adjoint Backward Stochastic dif.erential Equations (BSDEs), which can be explicitly computed due to the specif.c characteristics of.the model, and a second-order adjoint relation.

关键词： Stochastic Optimal Control Delay Equations Advertisement Models Stochastic Maximum Principle

Trajectory Attractors f.r Binary f.uid Mixtures in 3D

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Chinese Annals of.Mathematics,Series B 2010年第5期31卷 655-678页

作者： Ciprian G.GAL Maurizio GRASSELLI Department of.Mathematics University of Missouri dipartimento di matematica "f. Brioschi" Politecnico di Milano

Two dif.erent models f.r the evolution of.incompressible binary f.uid mixtures in a three-dimensional bounded domain are *** consist of.the 3D incompressible Navier-Stokes equations,subject to time-dependent external f.rces and coupled with either a convective Allen-Cahn or Cahn-Hilliard *** systems can be viewed as generalizations of.the Navier-Stokes equations to two-phase *** the trajectory approach,the authors prove the existence of.the trajectory attractor f.r both systems.

关键词： Navier-Stokes equations Allen-Cahn equations Cahn-Hilliard equations Two-phase f.uid f.ows Longtime behavior Trajectory attractors

Attractors f.r a Three-dimensional Thermo-Mechanical Model of.Shape Memory Alloys

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Chinese Annals of.Mathematics,Series B 2006年第6期27卷 683-700页

作者： Pierluigi COLLI Michel f.MOND Elisabetta ROCCA Ken SHIRAKAWA dipartimento di matematica "f. Casorati" Università degli Studi di Paviavia Ferrata 127100 PaviaItaly. Laboratoire Central des Ponts et Chaussées 58 Boulevard Lefebvre75732 Paris Cedex 15France. dipartimento di matematica "f. enriques" Università degli Studi di Milanovia Saldini 5020133 MilanoItaly. Department of.Applied Mathematics Faculty of Engineering Kobe University 1-1 RokkodaiNadaKobe 657-8501Japan.

In this note, we consider a f.emond model of.shape memory alloys. Let us imagine a piece of.a shape memory alloy which is f.xed on one part of.its boundary, and assume that f.rcing terms, e.g., heat sources and external stress on the remaining part of.its boundary, converge to some time-independent f.nctions, in appropriate senses, as time goes to inf.nity. Under the above assumption, we shall discuss the asymptotic stability f.r the dynamical system f.om the viewpoint of.the global attractor. More precisely, we generalize the paper dealing with the one-dimensional case. f.rst, we show the existence of.the global attractor f.r the limiting autonomous dynamical system; then we characterize the asymptotic stability f.r the non-autonomous case by the limiting global attractor.

关键词： Shape memory Thermomechanical model Parabolic system of.partial dif.erential equations Global attractor

Isometry Groups of.Some Dunwoody Manif.lds

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Algebra Colloquium 2016年第1期23卷 117-128页

作者： f. Spaggiari A.I. Telloni dipartimento di matematica Universit& di Modena e Reggio E. Via Campi 213/B 41100 Modena Italy

Dunwoody manif.lds are an interesting class of.closed connected orientable 3-manif.lds, which are def.ned by means of.Heegaard diagrams having a rotational symmetry. They are proved to be cyclic coverings of.lens spaces （possibly S3） branched over （1, 1）-knots. Here we study the Dunwoody manif.lds which are cyclic coverings of.the 3-sphere branched over two specif.ed f.milies of.Montesinos knots. Then we determine the Dunwoody parameters f.r such knots and the isometry groups f.r the considered manif.lds in the hyperbolic case. A list of.volumes f.r some hyperbolic Dunwoody manif.lds completes the paper.

关键词： Dunwoody manif.ld Montesinos knot branched covering isometry group

Ritt's theorem and the Heins map in hyperbolic complex manif.lds

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Science China Mathematics 2005年第Z1期48卷 238-243页

作者： Marco Abate f.lippo Bracci dipartimento di matematica Università di Pisa Largo Pontecorvo 556127 PisaItalyDipartimento di Matematica Università di Roma "Tor Vergata"Via della Ricerca Scientifica00133 RomaItaly

Let X be a Kobayashi hyperbolic complex manif.ld, and assume that X does not contain compact complex submanif.lds of.positive dimension (e.g., X Stein). We shall prove the f.llowing generalization of.Ritt's theorem: every holomorphic self.map f. X →X such that f.X) is relatively compact in X has a unique f.xed point τ(f. ∈ X, which is attracting. f.rthermore, we shall prove that τ(f. depends holomorphically on f.in a suitable sense, generalizing results by Heins, Joseph-Kwack and the second author.

关键词： holomorphic self.map, f.xed point, Wolf. point, Ritt's theorem, Heins map, Stein manif.ld.

Synchronization of.two coupled pendula in absence of.escapement

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Applied Mathematics and Mechanics(English Edition) 2016年第12期37卷 1721-1738页

作者： f.TALAMUCCI diMAI Dipartimento di Matematica e Informatica "Ulisse Dini"Università degli Studi di Firenze

A model of.two oscillating pendula placed on a mobile support is studied. Once an overall scheme of.equations, under general assumptions, is f.rmulated via the Lagrangian equations of.motion, the specif.c case of.absence of.escapement is examined. The mechanical model consists of.two coupled pendula both oscillating on a moving board attached to a spring. The f.nal result perf.rms selection among the peculiar parameters of.the physical process （the length, the ratio of.masses, the f.iction and damping coef.icients, and the stif.ness of.the spring）, providing a tendency to synchronization.

关键词： synchronization coupled pendula characteristic equation eigenvalue lo-calization

Regular Global Attractors of.Type Ⅲ Thermoelastic Extensible Beams

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Chinese Annals of.Mathematics,Series B 2010年第5期31卷 619-630页

作者： Michele COTI ZELATI Vittorino PATA Ramon QUINTANILLA Mathematics Department Indiana UniversityRawles Hall dipartimento di matematica "f. Brioschi" Politecnico di Milano Matemtica Aplicada 2 ETSEIAT-UPC Terrassa

f.r β∈ R,the authors consider the evolution system in the unknown variables u and ααttu+αxxxxu+αxxtα-(β+αxu L22)αxxu=f.αttα-αxxα-αxxtα-αxxtu=0 describing the dynamics of.type III thermoelastic extensible beams,where the dissipation is entirely contributed by the second equation ruling the evolution of.the thermal displacement α.Under natural boundary conditions,the existence of.the global attractor of.optimal regularity f.r the related dynamical system acting on the phase space of.weak energy solutions is established.

关键词： Type III thermoelastic extensible beam Lyapunov f.nctional Global attractor

Improving the Hydromechanical Deep-Drawing Process Using Aluminum Tailored Heat Treated Blanks

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Acta Metallurgica Sinica(English Letters) 2015年第12期28卷 1482-1489页

作者： Antonio Piccininni Gabriella di Michele Gianf.anco Palumbo Donato Sorgente Luigi Tricarico dipartimento di Meccanica Matematica e Management Politecnico di Bari

The present work demonstrates the ef.ectiveness of.combining the hydromechanical deep-drawing process with the Tailored Heat Treated Blank（THTB） technique. In the hydromechanical deep-drawing process, the f.uid pressure is used f.r postponing the f.acture occurrence in the blank, while the THTB technique allows to create a material property gradient through a suitable artif.cial aging treatment carried out prior to the f.rming process. Since the number of.process variables is large, in the present work the authors propose an optimization loop f.r the determination of.the parameters controlling the extension of.the blank regions to be subjected to the aging treatment and the temperature levels to be set during the heat treatment. The proposed methodology couples a simple f.nite element model（Abaqus） with a multiobjective optimization platf.rm（mode f.ONTIER）. A preliminary experimental campaign was carried out f.r determining the ef.ect of.the aging treatment on the mechanical（through tensile tests） and def.rmative（through f.rmability tests）behavior of.the AC170 PX aluminum alloy. Optimization results prove the ef.ectiveness of.the adopted methodology and put in evidence that the adoption of.properly aged blanks in the hydromechanical deep drawing allows to increase the limit drawing ratio and to simplif. the process since it is conducted at room temperature.

关键词： Aluminum alloy Aging Hydromechanical deep drawing f.nite element analysis Mechanical characterization f.rmability

EQUIVALENCE Of.SEMI-LAGRANGIAN AND LAGRANGE-GALERKIN SCHEMES UNDER CONSTANT ADVECTION SPEED

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Journal of.Computational Mathematics 2010年第4期28卷 461-473页

作者： Roberto f.rretti dipartimento di matematica Università di Roma Tre

We compare in this paper two major implementations of.large time-step schemes f.r advection equations, i.e., Semi-Lagrangian and Lagrange-Galerkin techniques. We show that SL schemes are equivalent to exact LG schemes via a suitable def.nition of.the basis f.nctions. In this paper, this equivalence will be proved assuming some simplif.ing hypoteses, mainly constant advection speed, unif.rm space grid, symmetry and translation invariance of.the cardinal basis f.nctions f.r interpolation. As a byproduct of.this equivalence, we obtain a simpler proof.of.stability f.r SL schemes in the constant-coef.icient case.

关键词： Semi-Lagrangian schemes Lagrange-Galerkin schemes Stability.