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Stochastic Maximum Principle for 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 Federica 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 effects of the advertisement and with memory effects 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 efforts. We treat the problem by means of the stochastic Pontryagin maximum principle, that here is considered for 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 formulated using a first-order adjoint Backward Stochastic differential Equations (BSDEs), which can be explicitly computed due to the specific characteristics of the model, and a second-order adjoint relation.

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

On the Regularity of Shear Thickening Viscous Fluids

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Chinese Annals of Mathematics,Series B 2009年第3期30卷 273-280页

作者： Francesca CRISPO dipartimento di matematica applicata "u.dini" Università di PisaVia Buonarroti 1/c56127 PisaItaly.

The aim of this note is to improve the regularity results obtained by H. Beirao da Veiga in 2008 for a class of p-fluid flows in a cubic domain. The key idea is exploiting the better regularity of solutions in the tan... 详细信息

关键词： Non-Newtonian fluids Shear dependent viscosity Boundary regularity

On singular Lüroth quartics

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Science China Mathematics 2011年第8期54卷 1757-1766页

作者： OTTAVIANI Giorgio SERNESI Edoardo dipartimento di matematica "u.dini" Università di Firenzeviale Morgagni 67/A50134 FirenzeItaly dipartimento di matematica Università Roma TreLargo S.L.Murialdo 100146 RomaItaly

Plane quartics containing the ten vertices of a complete pentalateral and limits of them are called Lüroth *** locus of singular Lüroth quartics has two irreducible components,both of codimension two in *** compute the degree of them and discuss the consequences of this computation on the explicit form of the Lüroth *** important tool is the Cremona hexahedral equations of the cubic *** also compute the class in M 3 of the closure of the locus of nonsingular Lüroth quartics.

关键词： plane quartics Lueroth quartics invariant moduli space of curves

Global-in-time uniform Convergence for Linear Hyperbolic-Parabolic Singular Perturbations

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Acta Mathematica Sinica,English Series 2006年第4期22卷 1161-1170页

作者： Marina GHISI Massimo GOBBINO universitàdegli Studi di Pisa Dipartimento di Matematicavia M.Buonarroti 256127 PISAItaly universitàdegli Studi di Pisa Dipartimento di Matematica Applicata "Ulisse Dini"via Bonanno 25/B56126 PISAItaly

We consider the Cauchy problem εu^″ε ＋ δu′ε ＋ Auε = 0, uε（0） = uo, u′ε（0） = ul, where ε 〉 0, δ 〉 0, H is a Hilbert space, and A is a self-adjoint linear non-negative operator on H with dense domain D（A）. We study the convergence of （uε） to the solution of the limit problem ,δu＇＋ Au = 0, u（0） = u0. For initial data （u0, u1） ∈ D（A1/2）× H, we prove global-in-time convergence with respect to strong topologies. Moreover, we estimate the convergence rate in the case where （u0, u1）∈ D（A3/2） ∈ D（A1/2）, and we show that this regularity requirement is sharp for our estimates. We give also an upper bound for ｜u′ε（t）｜ which does not depend on ε.

关键词： Parabolic equations Damped hyperbolic equations Singular perturbations

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 formulated via the Lagrangian equations of motion, the specific 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 final result performs selection among the peculiar parameters of the physical process （the length, the ratio of masses, the friction and damping coefficients, and the stiffness of the spring）, providing a tendency to synchronization.

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

A mathematical model for the evolution of solute concentrations in a hemodialysis filter

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International Journal of Biomathematics 2018年第1期11卷 337-348页

作者： A. Fasano G. Guarnieri A. Farina dipartimento di matematica e Informatica "u. dini" universita degli Studi di Firenze Firenze Italy

We consider the process of hemodialysis performed by means of a hollow fiber dialyzer with a special focus on the dynamics of the light solutes （including metabolic waste products） through the porous fibers membrane. The model we illustrate here completes the one formulated in a previous paper in which solutes concentrations in the dialyzate were neglected. Exploiting the large difference between the characteristic time of the processes in the machine and the relaxation time to equilibrium in the body, we confine our study to the case of constant input data in order to emphasize the role of the solute transport mechanisms. Numerical solutions show that diffusion is dominant at the early stage of filtration.

关键词： Hemodialysis solute concentration upscaling.

LOW MACH NuMBER LIMIT ON EXTERIOR DOMAINS

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Acta Mathematica Scientia 2012年第1期32卷 164-176页

作者： Donatella Donatelli Pierangelo Marcati dipartimento di matematica Pura ed applicata Universita degli Studi dell'Aquila

This paper is concerned with the low Mach number limit for the compressible Navier-Stokes equations in an exterior domain. We present here an approach based on Strichartz estimate defined on a non trapping exterior do... 详细信息

关键词： exterior domain compressible and incompressible Navier-Stokes equation low Mach number limit hyperbolic equations wave equations rescaling dispersive estimates Strichartz estimates

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 Gianfranco Palumbo Donato Sorgente Luigi Tricarico dipartimento di Meccanica Matematica e Management Politecnico di Bari

The present work demonstrates the effectiveness of combining the hydromechanical deep-drawing process with the Tailored Heat Treated Blank（THTB） technique. In the hydromechanical deep-drawing process, the fluid pressure is used for postponing the fracture occurrence in the blank, while the THTB technique allows to create a material property gradient through a suitable artificial aging treatment carried out prior to the forming process. Since the number of process variables is large, in the present work the authors propose an optimization loop for 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 finite element model（Abaqus） with a multiobjective optimization platform（mode FRONTIER）. A preliminary experimental campaign was carried out for determining the effect of the aging treatment on the mechanical（through tensile tests） and deformative（through formability tests）behavior of the AC170 PX aluminum alloy. Optimization results prove the effectiveness 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 simplify the process since it is conducted at room temperature.

关键词： Aluminum alloy Aging Hydromechanical deep drawing Finite element analysis Mechanical characterization Formability

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 Ferretti dipartimento di matematica Università di Roma Tre

We compare in this paper two major implementations of large time-step schemes for advection equations, i.e., Semi-Lagrangian and Lagrange-Galerkin techniques. We show that SL schemes are equivalent to exact LG schemes via a suitable definition of the basis functions. In this paper, this equivalence will be proved assuming some simplifying hypoteses, mainly constant advection speed, uniform space grid, symmetry and translation invariance of the cardinal basis functions for interpolation. As a byproduct of this equivalence, we obtain a simpler proof of stability for SL schemes in the constant-coefficient case.

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