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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

Immersed Boundary Approach to Biofilm Spread on Surfaces

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Communications in Computational Physics 2022年第1期31卷 257-292页

作者： Ana Carpio Rafael Gonzalez-Albaladejo departamento de matematica aplicada Universidad Complutense28040 MadridSpain

We propose a computational model to study the growth and spread of bacterial biofilms on interfaces,as well as the action of antibiotics on them.Bacterial membranes are represented by boundaries immersed in a fluid matrix and subject to interaction forces.Growth,division and death of bacterial cells follow dynamic energy budget rules,in response to variations in environmental concentrations of nutrients,toxicants and substances released by the cells.In this way,we create,destroy and enlarge boundaries,either spherical or rod-like.Appropriate forces represent details of the interaction between cells,and the interaction with the environment.We can investigate geometrical arrangements and the formation of porous structures.Numerical simulations illustrate the evolution of top views and diametral slices of small biofilm seeds,as well as the action of antibiotics.We show that cocktails of antibiotics targeting active and dormant cells can entirely eradicate a biofilm.

关键词： Hybrid multiscale models immersed boundary methods dynamic energy budget models bacterial biofilm antibiotic resistance

A nonlinear relapse model with disaggregated contact rates:Analysis of a forward-backward bifurcation

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Infectious Disease Modelling 2023年第3期8卷 769-782页

作者： Jimmy Calvo-Monge Fabio Sanchez Juan Gabriel Calvo Dario Mena Escuela de matematica Universidad de Costa RicaCiudad Universitaria Rodrigo FacioSan Jose11501Costa Rica Centro de Investigacion en matematica Pura y aplicada Universidad de Costa RicaCiudad Universitaria Rodrigo FacioSan Jose11501Costa Rica

Throughout the progress of epidemic scenarios,individuals in different health classes are expected to have different average daily contact behavior.This contact heterogeneity has been studied in recent adaptive models and allows us to capture the inherent differences across health statuses better.Diseases with reinfection bring out more complex scenarios and offer an important application to consider contact disaggregation.Therefore,we developed a nonlinear differential equation model to explore the dynamics of relapse phenomena and contact differences across health statuses.Our incidence rate function is formulated,taking inspiration from recent adaptive algorithms.It incorporates contact behavior for individuals in each health class.We use constant contact rates at each health status for our analytical results and prove conditions for different forward-backward bifurcation scenarios.The relationship between the different contact rates heavily in-fluences these conditions.Numerical examples highlight the effect of temporarily recov-ered individuals and initial conditions on infected population persistence.

关键词： Nonlinear relapse Nonlinear incidence MaMthematical model Backward bifurcation Adaptive behavior 2000 MSC 37N25 92B05

Triply Factorised Groups and the Structure of Skew Left Braces

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Communications in Mathematics and Statistics 2022年第2期10卷 353-370页

作者： A.Ballester-Bolinches R.Esteban-Romero departament de Matematiques Universitat de ValenciaDr.Moliner5046100 BurjassotValenciaSpain Institut Universitari de matematica Pura i aplicada Universitat Politecnica de ValenciaCami de Veras/n46022 ValenciaSpain

The algebraic structure of skew left brace has proved to be useful as a source of settheoretic solutions of theYang-Baxter equation.We study in this paper the connections between left and right π-nilpotency and the structure of finite skew left braces.We also study factorisations of skew left braces and their impact on the skew left brace structure.As a consequence of our study,we define a Fitting-like ideal of a left brace.Our approach depends strongly on a description of a skew left brace in terms of a triply factorised group obtained from the action of the multiplicative group of the skew left brace on its additive group.

关键词： Skew left brace Trifactorised group Triply factorised group Left nilpotent skew left brace Right nilpotent skew left brace Ideal Left Fitting ideal Factorised skew left brace

NUMERICAL ANALYSIS OF A PROBLEM INVOLVING A VISCOELASTIC BODY WITH DOUBLE POROSITY

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Journal of Computational Mathematics 2022年第3期40卷 415-436页

作者： Noelia Bazarra Jose R.Fernandez MariCarme Leseduarte Antonio Magana Ramon Quintanilla departamento de matematica aplicada I Universidade de VigoETSI TelecomunicacionCampus As Lagoas Marcosende s/n36310 VigoSpain departamento de matematicas E.S.E.I.A.A.T.-U.P.C.Colom 1108222 TerrassaBarcelonaSpain

We study from a numerical point of view a multidimensional problem involving a viscoelastic body with two porous structures.The mechanical problem leads to a linear system of three coupled hyperbolic partial differential equations.Its corresponding variational formulation gives rise to three coupled parabolic linear equations.An existence and uniqueness result,and an energy decay property,are recalled.Then,fully discrete approximations are introduced using the finite element method and the implicit Euler scheme.A discrete stability property and a priori error estimates are proved,from which the linear convergence of the algorithm is derived under suitable additional regularity conditions.Finally,some numerical simulations are performed in one and two dimensions to show the accuracy of the approximation and the behaviour of the solution.

关键词： Viscoelasticity with double porosity Finite elements A priori estimates Numerical simulations

Open Frobenius Cluster-Tilted Algebras

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Algebra Colloquium 2022年第1期29卷 1-22页

作者： Viviana Gubitosi Instituto de matematica y Estadistica Rafael Laguaxdia Facultad de Ingeniena-UdelaR Montevideo 11200Uruguay

In this paper,we compute the Frobenius dimension of any cluster-tilted algebra of finite type.Moreover,we give conditions on the bound quiver of a cluster-tilted algebra A such that八has non-trivial open Frobenius str... 详细信息

关键词： cluster-tilted algebras gentle algebras open Frobenius algebras nearly Probe-nius algebras 1

Global multiplicity of solutions to a defocusing quasilinear Schrodinger equation with the singular term

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Science China Mathematics 2023年第8期66卷 1789-1812页

作者： Siyu Chen Carlos Alberto Santos Minbo Yang Jiazheng Zhou department of Mathematics Zhejiang Normal UniversityJinhua 321004China departamento de matematica Universidade de BrasiliaBraslia 70910-900Brazil

We consider a class of modified quasilinear Schrodinger equations-△u+k/2u△u^(2)=λα(x)u^(-α)+b(x)u^(β) in Ω with u(x)=0 on■Ω,where Ω■R^(N)is a bounded domain with a regular boundary,N≥3,a and b are bounded mensurable functions,0<α<1<β<2*-1 and k,λ≥0 are two parameters.We establish the global existence and multiplicity results of positive solutions in H^(1)_(0)(Ω)∩L^(∞)(Ω)for appropriate classes of parameters k andλand coefficients a(x)and b(x).

关键词： quasilinear Schrodinger equation singular term square diffusion term

COMPLEXITY OF LARGE TIME BEHAVIOUR OF EVOLUTION EQUATIONS WITH BOUNdeD DATA

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Chinese Annals of Mathematics,Series B 2002年第2期23卷 293-310页

作者： J.L.VZQUEZ E.ZUAZUA departamento de matematicas Universidad AutonomaDepartamento de Matematica AplicadaUniversidadComplutense 28049MadridSpain28040 M

The authors study the asymptotic behaviour of solutions of the heat equation and a number of evolution equations using scaling techniques. It is proved that in the framework of bounded data stabilization need not occur and the general asymptotic behaviour is complex. This behaviour reflects for large times, even on compact sets, the complexity of the initial data at infinity.

关键词：复杂性大时间行为发展方程有界数据热方程 Omega极限双曲守恒定律半群收敛性

PHASE PORTRAITS OF THE LESLIE-GOWER SYSTEM

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Acta Mathematica Scientia 2022年第5期42卷 1734-1742页

作者： Jaume LLIBRE Claudia VALLS departament de Matematiques Universitat Autonoma de Barcelona08193BellaterraBarcelonaCataloniaSpain departamento de matematica Instituto Superior TecnicoUniversidade de LisboaAu.Rovisco Pais 1049-001LisboaPortugal

In this paper we characterize the phase portraits of the Leslie-Gower model for competition among species.We give the complete description of their phase portraits in the Poincarédisc(i.e.,in the compactification of R^(2) adding the circle S1 of the infinity)modulo topological equivalence.It is well-known that the equilibrium point of the Leslie-Gower model in the interior of the positive quadrant is a global attractor in this open quadrant,and in this paper we characterize where the orbits attracted by this equilibrium born.

关键词： predator-prey models Leslie-Gower system Poincare compactification global phaseportraits