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Global Phase Portraits of Quadratic Systems with a Complex Ellipse as Invariant Algebraic Curve

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Acta Mathematica Sinica,English Series 2018年第5期34卷 801-811页

作者： Jaume LLIBRE claudia valls Departament de Mateatiques Universitat Autonoma de Barcelona 08193 Bellaterra Barcelona Catalonia Spain Departamento de Matemdtica Instituto Superior Tecnico Universidade de Lisboa 1049-001 Lisboa Portugal

In this paper, we study a new class of quadratic systems and classify all its phase portraits. More precisely, we characterize the class of all quadratic polynomial differential systems in the plane having a complex ellipse x^2 ＋ y^2 ＋ 1 = 0 as invariant algebraic curve. We provide all the different topological phase portraits that this class exhibits in the Poincare disc.

关键词： Quadratic system complex ellipse invariant algebraic curves phase portrait Poincare disc

Liouvillian and Analytic Integrability of the Quadratic Vector Fields Having an Invariant Ellipse

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Acta Mathematica Sinica,English Series 2014年第3期30卷 453-466页

作者： Jaume LLIBRE claudia valls Departament de Matemàtiques Universitat Autònoma de Barcelona Departamento de Matemtica Instituto Superior TcnicoUniversidade Tcnica de Lisboa

We characterize the Liouvillian and analytic integrability of the quadratic polynomial vector fields in R2 having an invariant *** precisely,a quadratic system having an invariant ellipse can be written into the form x=x2＋y2-1＋y（ax＋by＋c）,y=x（ax＋by＋c）,and the ellipse becomes x2＋y2=*** prove that（i） this quadratic system is analytic integrable if and only if a=0;（ii） if x2＋y2=1 is a periodic orbit,then this quadratic system is Liouvillian integrable if and only if x2＋y2=1 is not a limit cycle;and（iii） if x2＋y2=1 is not a periodic orbit,then this quadratic system is Liouvilian integrable if and only if a=0.

关键词： Liouvillian integrability quadratic planar polynomial vector fields invariant ellipse

On the Darboux Integrability of the Hindmarsh–Rose Burster

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Acta Mathematica Sinica,English Series 2018年第6期34卷 947-958页

作者： Jaume LLIBRE claudia valls Departament de Matematiques Universitat Autonoma de Barcelona 08193 BeUaterra Barcelona Catalonia Spain Departamento de Matematica Instituto Superior TecnicoUniversidade Tecnica de Lisboa Av. Rovisco Pals 1049-001 Lisboa Portugal

We study the Hindmarsh-Rose burster which can be described by the differential system x^·=y-x^3＋bx^2＋I-z,y^·=1-5x^2-y,z^·=μ（s（x-x0）-z）where b, I, μ, s, x0 are parameters. We characterize all its invariant algebraic surfaces and all its exponential factors for all values of the parameters. We also characterize its Darboux integrability in function of the parameters. These characterizations allow to study the global dynamics of the system when such invariant algebraic surfaces exist.

关键词： Polynomial integrability rational integrability Darboux polynomials Darboux first integrals invariant algebraic surfaces exponential factors Hindmarsh Rose burster

Weierstrass Integrability of Complex Differential Equations

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Acta Mathematica Sinica,English Series 2021年第10期37卷 1497-1506页

作者： Jaume LLIBRE claudia valls Departament de Matematiques Universitat Autonoma de Barcelona08193 BellaterraBarcelonaCataloniaSpain Departamento de Matematica Instituto Superior TecnicoUniversidade de LisboaAv.Rovisco Pais 1049–001LisboaPortugal

We characterize the complex differential equations of the form dy/dx=a_(n)(x)y^)n_+a_(n-1)(x)y^(n-1)+…+a_(1)(x)y+a_(0)(x) where a_(j)(x) are meromorphic functions in the variable x for j = 0,..., n that admit either ... 详细信息

关键词： Weierstrass first integrals Weierstrass inverse integrating factor complex differential equations

Integrability of Hamiltonian Systems with Two Degrees of Freedom and Homogenous Potential of Degree Zero

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Journal of Applied Mathematics and Physics 2018年第11期6卷 2192-2201页

作者： Jaume Llibre claudia valls Departament de Matemàtiques Universitat Autònoma de Barcelona Barcelona Spain Departamento de Matemática Instituto Superior Técnico Universidade de Lisboa Lisboa Portugal

We provide necessary conditions in order that the Hamiltonian systems with Hamiltonian ,?and one of the following potentials ?are integrable in the Liouville sense.

关键词： Hamiltonian System Liouville Integrability Darboux Points Homogeneous Potentials of Degree Zero

Olfactory receptors in neural regeneration in the central nervous system

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Neural Regeneration Research 2025年第9期20卷 2480-2494页

作者： Rafael Franco claudia Garrigós Toni Capó Joan Serrano-Marín Rafael Rivas-Santisteban Jaume Lillo Molecular Neurobiology Laboratory Department of Biochemistry and Molecular BiomedicineFacultat de BiologiaUniversitat de BarcelonaBarcelonaSpain CiberNed Network Center for Biomedical Research in Neurodegenerative Diseases Spanish National Health Institute Carlos ⅢMadridSpain School of Chemistry Universitat de BarcelonaBarcelonaSpain Department of Biochemistry and Physiology School of Pharmacy and Food SciencesUniversitat de BarcelonaBarcelonaSpain Laboratory of Computational Medicine Biostatistics UnitFaculty of MedicineAutonomous University of BarcelonaCampus BellaterraBarcelonaSpain

Olfactory receptors are crucial for detecting odors and play a vital role in our sense of smell,influencing behaviors from food choices to emotional *** receptors also contribute to our perception of flavor and have potential applications in medical diagnostics and environmental *** ability of the olfactory system to regenerate its sensory neurons provides a unique model to study neural regeneration,a phenomenon largely absent in the central nervous *** gained from how olfactory neurons continuously replace themselves and reestablish functional connections can provide strategies to promote similar regenerative processes in the central nervous system,where damage often results in permanent *** the molecular and cellular mechanisms underpinning olfactory neuron regeneration could pave the way for developing therapeutic approaches to treat spinal co rd injuries and neurodegenerative diseases like Alzheimer's *** ctory receptors are found in almost any cell of eve ry orga n/tissue of the mammalian *** ectopic expression provides insights into the chemical structures that can activate olfactory *** addition to odors,olfactory receptors in ectopic expression may respond to endogenous compounds and molecules produced by mucosal colonizing *** analysis of the function of olfactory receptors in ectopic expression provides valuable information on the signaling pathway engaged upon receptor activation and the receptor's role in proliferation and cell differentiation *** review explo res the ectopic expression of olfa ctory receptors and the role they may play in neural regeneration within the central nervous system,with particular attention to compounds that can activate these receptors to initiate regenerative *** suggests that olfactory receptors could serve as potential therapeutic targets for enhancing neural repair and recovery following central nervous syste

关键词： adenosine receptors adrenergic receptors ectopic expression G proteincoupled receptors glia neurons

Crystal structure evolution of complex metal aluminum hydrides upon hydrogen release

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Journal of Energy Chemistry 2020年第3期29卷 133-143页

作者： claudia Weidenthaler Max-Planck-Institut für Kohlenforschung 45470 Mülheim an der RuhrGermany

Complex aluminum hydrides have been widely studied as potential hydrogen storage materials but also,for some time now, for electrochemical applications. This review summarizes the crystal structures of alkali and alkaline earth aluminum hydrides and correlates structure properties with physical and chemical properties of the hydride compounds. The crystal structures of the alkali metal aluminum hydrides change significantly during the stepwise dehydrogenation. The general pathway follows a transformation of structures built of isolated [AlH4]- tetrahedra to structures built of isolated [Al H6]3- *** crystal structure relations in the group of alkaline earth metal aluminum hydrides are much more complicated than those of the alkali metal aluminum hydrides. The structures of the alkaline earth metal aluminum hydrides consist of isolated tetrahedra but the intermediate structures exhibit chains of cornershared octahedra. The coordination numbers within the alkali metal group increase with cation sizes which goes along with an increase of the decomposition temperatures of the primary hydrides. Alkaline earth metal hydrides have higher coordination numbers but decompose at slightly lower temperatures than their alkali metal counterparts. The decomposition pathways of alkaline metal aluminum hydrides have not been studied in all cases and require future research.

关键词： Complex aluminum hydrides Hydrogen storage Crystal structure

HOMOGENIZATION RESULTS FOR ENZYME CATALYZED REACTIONS THROUGH POROUS MEDIA

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Acta Mathematica Scientia 2009年第1期29卷 74-82页

作者： claudia Timofte Department of Mathematics Faculty of Physics University of BucharestP.O. Box MG-11

The aim of this article is to study the effective behavior of the solution of a nonlinear problem arising in the modelling of enzyme catalyzed reactions through the exterior of a domain containing periodically distributed reactive solid obstacles,with period ε.The asymptotic behavior of the solution of such a problem is governed by a new elliptic boundary-value problem,with an extra zero-order term that captures the effect of the enzymatic reactions.

关键词： Homogenization enzyme reactive flows Michaelis-Menten mechanism

Adult mammalian neurogenesis and motivated behaviors

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Integrative Zoology 2018年第6期13卷 655-672页

作者： claudia JORGENSEN Behavioral Science Department Utah Valley UniversityOremUtahUSA

Adult neurogenesis continues to captivate the curiosity of the scientific community;and researchers seem to have a particular interest in identifying the functional implications of such *** the majority of research focuses on the association between adult neurogenesis and learning and memory(including spatial learning associated with hippocampal neurogenesis and olfactory discrimination associated with neurogenesis in the olfactory system),the following review will explore the link to motivated *** particular,goal-directed behaviors such as sociosexual,parental,aggressive,as well as depression-and anxiety-like behaviors and their reciprocal association to adult neurogenesis will be *** review will detail research in humans and other mammalian ***,the potential mechanisms underlying these neurogenic alterations will be ***,the review will conclude with a discussion on the functional significance of these newly generated cells in mediating goal-directed behaviors.

关键词： adult neurogenesis aggression anxiety depression reproduction