PUBLICACIÓN

Uniqueness of limit cycles for quadratic vector fields

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ACCEDER A LA PUBLICACIÓN: Scopus Orcid

Bravo J.L., Fernandez M., Ojeda I., Sanchez F.

2019 DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS

Analysis (Q1), Applied Mathematics (Q1), Discrete Mathematics and Combinatorics (Q1)

JCR: 1.338

SJR: 1.362

CITAS

2

DOI

10.3934/dcds.2019020

EID

2-s2.0-85056121985

ISSN

1078-0947

EISSN

1553-5231

BIBTEX

@article{Bravo2019,title = {Uniqueness of limit cycles for quadratic vector fields},journal = {Discrete and Continuous Dynamical Systems- Series A},year = {2019},volume = {39},number = {1},pages = {483-502},author = {Bravo, J.L. and Fern{\'a}ndez, M. and Ojeda, I. and S{\'a}nchez, F.}}

AUTORES DE LA UEX

José Luis Bravo Trinidad
Manuel Fernández García-Hierro
Ignacio Ojeda Martínez De Castilla

OTRAS PUBLICACIONES DE INTERÉS

Norms In Product Spaces Which Preserve Approximation Porperties
Minimal Free Resolution Of Generalized Repunit Algebras
On The Depth Of Simplicial Affine Semigroup Rings
Minimal Free Resolution Of Generalized Repunit Algebras
On The Depth Of Simplicial Affine Semigroup Rings
Infinitesimal And Tangential 16-Th Hilbert Problem On Zero-Cycles
On The Depth Of Simplicial Affine Semigroup Rings
Infinitesimal And Tangential 16-Th Hilbert Problem On Zero-Cycles
The Multiples Of A Numerical Semigroup
Infinitesimal And Tangential 16-Th Hilbert Problem On Zero-Cycles
The Multiples Of A Numerical Semigroup
Arithmetic Varieties Of Numerical Semigroups
The Multiples Of A Numerical Semigroup
Arithmetic Varieties Of Numerical Semigroups
Stability Of Singular Limit Cycles For Abel Equations Revisited
Arithmetic Varieties Of Numerical Semigroups
Stability Of Singular Limit Cycles For Abel Equations Revisited
Quartic Rigid Systems In The Plane And In The Poincaré Sphere
Stability Of Singular Limit Cycles For Abel Equations Revisited
Quartic Rigid Systems In The Plane And In The Poincaré Sphere
Universally Free Numerical Semigroups
Quartic Rigid Systems In The Plane And In The Poincaré Sphere
Universally Free Numerical Semigroups
Hilbert Number For A Family Of Piecewise Nonautonomous Equations
Universally Free Numerical Semigroups
Hilbert Number For A Family Of Piecewise Nonautonomous Equations
The Frobenius Problem For Generalized Repunit Numerical Semigroups
Hilbert Number For A Family Of Piecewise Nonautonomous Equations
The Frobenius Problem For Generalized Repunit Numerical Semigroups
Hilbert Number For A Family Of Piecewise Nonautonomous Equations
The Frobenius Problem For Generalized Repunit Numerical Semigroups
Hilbert Number For A Family Of Piecewise Nonautonomous Equations
Rational Limit Cycles Of Abel Differential Equations
Hilbert Number For A Family Of Piecewise Nonautonomous Equations
Rational Limit Cycles Of Abel Differential Equations
Stability Of Singular Limit Cycles For Abel Equations Revisited
Rational Limit Cycles Of Abel Differential Equations
Stability Of Singular Limit Cycles For Abel Equations Revisited
Quartic Rigid Systems In The Plane And In The Poincaré Sphere
Stability Of Singular Limit Cycles For Abel Equations Revisited
Quartic Rigid Systems In The Plane And In The Poincaré Sphere
Infinitesimal And Tangential 16-Th Hilbert Problem On Zero-Cycles
Quartic Rigid Systems In The Plane And In The Poincaré Sphere
Infinitesimal And Tangential 16-Th Hilbert Problem On Zero-Cycles
Rational Solutions Of Abel Differential Equations
Infinitesimal And Tangential 16-Th Hilbert Problem On Zero-Cycles
Rational Solutions Of Abel Differential Equations
Planar Systems And Abel Equations
Rational Solutions Of Abel Differential Equations
Planar Systems And Abel Equations
Minimal Systems Of Binomial Generators For The Ideals Of Certain Monomial Curves
Planar Systems And Abel Equations
Minimal Systems Of Binomial Generators For The Ideals Of Certain Monomial Curves
A Note On Decomposable And Reducible Integer Matrices
Minimal Systems Of Binomial Generators For The Ideals Of Certain Monomial Curves
A Note On Decomposable And Reducible Integer Matrices
Critical Binomial Ideals Of Northcott Type
A Note On Decomposable And Reducible Integer Matrices
Critical Binomial Ideals Of Northcott Type
The Set Of Numerical Semigroups Of A Given Multiplicity And Frobenius Number
Critical Binomial Ideals Of Northcott Type
The Set Of Numerical Semigroups Of A Given Multiplicity And Frobenius Number
Rational Solutions Of Abel Differential Equations
The Set Of Numerical Semigroups Of A Given Multiplicity And Frobenius Number
Rational Solutions Of Abel Differential Equations
Infinitesimal Center Problem On Zero Cycles And The Composition Conjecture
Rational Solutions Of Abel Differential Equations
Infinitesimal Center Problem On Zero Cycles And The Composition Conjecture
Characterization Of The Existence Of Non-Trivial Limit Cycles For Generalized Abel Equations
Infinitesimal Center Problem On Zero Cycles And The Composition Conjecture
Characterization Of The Existence Of Non-Trivial Limit Cycles For Generalized Abel Equations
Upper Bounds Of Limit Cycles In Abel Differential Equations With Invariant Curves
Characterization Of The Existence Of Non-Trivial Limit Cycles For Generalized Abel Equations
Upper Bounds Of Limit Cycles In Abel Differential Equations With Invariant Curves
Commutative Monoids And Their Corresponding Affine K -Schemes
Upper Bounds Of Limit Cycles In Abel Differential Equations With Invariant Curves
Commutative Monoids And Their Corresponding Affine K -Schemes
The Arithmetic Extensions Of A Numerical Semigroup
Commutative Monoids And Their Corresponding Affine K -Schemes
The Arithmetic Extensions Of A Numerical Semigroup
On Pseudo-Frobenius Elements Of Submonoids Of Nd
The Arithmetic Extensions Of A Numerical Semigroup
On Pseudo-Frobenius Elements Of Submonoids Of Nd
Poincare Compactification For Non-Polynomial Vector Fields
On Pseudo-Frobenius Elements Of Submonoids Of Nd
Poincare Compactification For Non-Polynomial Vector Fields
Infinitesimal Center Problem On Zero Cycles And The Composition Conjecture
Poincare Compactification For Non-Polynomial Vector Fields
Infinitesimal Center Problem On Zero Cycles And The Composition Conjecture
Upper Bounds Of Limit Cycles In Abel Differential Equations With Invariant Curves
Infinitesimal Center Problem On Zero Cycles And The Composition Conjecture
Upper Bounds Of Limit Cycles In Abel Differential Equations With Invariant Curves
Experimental Validation Of Track Inspection Trolley Using A Rigorous Self-Checking Procedure
Upper Bounds Of Limit Cycles In Abel Differential Equations With Invariant Curves
Experimental Validation Of Track Inspection Trolley Using A Rigorous Self-Checking Procedure
Poincaré Compactification For Non-Polynomial Vector Fields
Experimental Validation Of Track Inspection Trolley Using A Rigorous Self-Checking Procedure
Poincaré Compactification For Non-Polynomial Vector Fields
Alien Limit Cycles In Abel Equations
Poincaré Compactification For Non-Polynomial Vector Fields
Alien Limit Cycles In Abel Equations
Uniqueness Of Limit Cycles For Quadratic Vector Fields
Alien Limit Cycles In Abel Equations
Uniqueness Of Limit Cycles For Quadratic Vector Fields
Almost Symmetric Numerical Semigroups With Given Frobenius Number And Type
Uniqueness Of Limit Cycles For Quadratic Vector Fields
Almost Symmetric Numerical Semigroups With Given Frobenius Number And Type
Almost Symmetric Numerical Semigroups With High Type
Almost Symmetric Numerical Semigroups With Given Frobenius Number And Type
Almost Symmetric Numerical Semigroups With High Type
Binomial Ideals And Congruences On ℕ N
Almost Symmetric Numerical Semigroups With High Type
Binomial Ideals And Congruences On ℕ N
Uniqueness Of Limit Cycles For Quadratic Vector Fields
Binomial Ideals And Congruences On ℕ N
Uniqueness Of Limit Cycles For Quadratic Vector Fields
Centers And Limit Cycles For A Family Of Abel Equations
Uniqueness Of Limit Cycles For Quadratic Vector Fields
Centers And Limit Cycles For A Family Of Abel Equations
Equilibria In Some Families Of Kolmogorov Systems
Centers And Limit Cycles For A Family Of Abel Equations
Equilibria In Some Families Of Kolmogorov Systems
Estimating The Accuracy Of Track-Surveying Trolley Measurements For Railway Maintenance Planning
Equilibria In Some Families Of Kolmogorov Systems
Estimating The Accuracy Of Track-Surveying Trolley Measurements For Railway Maintenance Planning
The Short Resolution Of A Semigroup Algebra
Estimating The Accuracy Of Track-Surveying Trolley Measurements For Railway Maintenance Planning
The Short Resolution Of A Semigroup Algebra
Limit Cycles Of Abel Equations Of The First Kind
The Short Resolution Of A Semigroup Algebra
Limit Cycles Of Abel Equations Of The First Kind
Stability Of Singular Limit Cycles For Abel Equations
Limit Cycles Of Abel Equations Of The First Kind
Stability Of Singular Limit Cycles For Abel Equations
Limit Cycles Of Abel Equations Of The First Kind
Stability Of Singular Limit Cycles For Abel Equations
Limit Cycles Of Abel Equations Of The First Kind
On The Computation Of The Apéry Set Of Numerical Monoids And Affine Semigroups
Limit Cycles Of Abel Equations Of The First Kind
On The Computation Of The Apéry Set Of Numerical Monoids And Affine Semigroups
Kronecker Square Roots And The Block Vec Matrix
On The Computation Of The Apéry Set Of Numerical Monoids And Affine Semigroups
Kronecker Square Roots And The Block Vec Matrix
Frobenius Vectors, Hilbert Series And Gluings Of Affine Semigroups
Kronecker Square Roots And The Block Vec Matrix
Frobenius Vectors, Hilbert Series And Gluings Of Affine Semigroups
On The Trigonometric Moment Problem
Frobenius Vectors, Hilbert Series And Gluings Of Affine Semigroups
On The Trigonometric Moment Problem
An Indispensable Classification Of Monomial Curves In A{Double-Struck}4(K{Double-Struck})
On The Trigonometric Moment Problem
An Indispensable Classification Of Monomial Curves In A{Double-Struck}4(K{Double-Struck})
Vanishing Abelian Integrals On Zero-Dimensional Cycles
An Indispensable Classification Of Monomial Curves In A{Double-Struck}4(K{Double-Struck})
Vanishing Abelian Integrals On Zero-Dimensional Cycles
Existence Of Non-Trivial Limit Cycles In Abel Equations With Symmetries
Vanishing Abelian Integrals On Zero-Dimensional Cycles
Existence Of Non-Trivial Limit Cycles In Abel Equations With Symmetries
Limit Cycles Of Non-Autonomous Scalar Odes With Two Summands
Existence Of Non-Trivial Limit Cycles In Abel Equations With Symmetries
Limit Cycles Of Non-Autonomous Scalar Odes With Two Summands
Inductive Solution Of The Tangential Center Problem On Zero-Cycles
Limit Cycles Of Non-Autonomous Scalar Odes With Two Summands
Inductive Solution Of The Tangential Center Problem On Zero-Cycles
Affine Semigroups Having A Unique Betti Element
Inductive Solution Of The Tangential Center Problem On Zero-Cycles
Affine Semigroups Having A Unique Betti Element
Factorization Invariants In Half-Factorial Affine Semigroups
Affine Semigroups Having A Unique Betti Element
Factorization Invariants In Half-Factorial Affine Semigroups
Abel-Like Differential Equations With A Unique Limit Cycle
Factorization Invariants In Half-Factorial Affine Semigroups
Abel-Like Differential Equations With A Unique Limit Cycle
Existence Of A Polycycle In Non-Lipschitz Gause-Type Predator-Prey Models
Abel-Like Differential Equations With A Unique Limit Cycle
Existence Of A Polycycle In Non-Lipschitz Gause-Type Predator-Prey Models
Binomial Canonical Decompositions Of Binomial Ideals
Existence Of A Polycycle In Non-Lipschitz Gause-Type Predator-Prey Models
Binomial Canonical Decompositions Of Binomial Ideals
Doubling Rational Normal Curves
Binomial Canonical Decompositions Of Binomial Ideals
Doubling Rational Normal Curves
Binomial Canonical Decomposition Of Binomial Ideals
Doubling Rational Normal Curves
Binomial Canonical Decomposition Of Binomial Ideals
Periodic Solutions Of A Singular Equation With Indefinite Weight
Binomial Canonical Decomposition Of Binomial Ideals
Periodic Solutions Of A Singular Equation With Indefinite Weight
Indispensable Binomials In Semigroup Ideals
Periodic Solutions Of A Singular Equation With Indefinite Weight
Indispensable Binomials In Semigroup Ideals
Uniquely Presented Finitely Generated Commutative Monoids
Indispensable Binomials In Semigroup Ideals
Uniquely Presented Finitely Generated Commutative Monoids
Simplicial Complexes And Minimal Free Resolution Of Monomial Algebras
Uniquely Presented Finitely Generated Commutative Monoids
Simplicial Complexes And Minimal Free Resolution Of Monomial Algebras
Doubling Rational Normal Curves
Simplicial Complexes And Minimal Free Resolution Of Monomial Algebras
Doubling Rational Normal Curves
Uniqueness Of Limit Cycles For Polynomial First-Order Differential Equations
Doubling Rational Normal Curves
Uniqueness Of Limit Cycles For Polynomial First-Order Differential Equations
The Number Of Limit Cycles For Generalized Abel Equations With Periodic Coefficients Of Definite Sign
Uniqueness Of Limit Cycles For Polynomial First-Order Differential Equations
The Number Of Limit Cycles For Generalized Abel Equations With Periodic Coefficients Of Definite Sign
The Hydrogen Abstraction Reaction H+ Ch4. I. New Analytical Potential Energy Surface Based On Fitting To Ab Initio Calculations
The Number Of Limit Cycles For Generalized Abel Equations With Periodic Coefficients Of Definite Sign
The Hydrogen Abstraction Reaction H+ Ch4. I. New Analytical Potential Energy Surface Based On Fitting To Ab Initio Calculations
Limit Cycles For Some Abel Equations Having Coefficients Without Fixed Signs
The Hydrogen Abstraction Reaction H+ Ch4. I. New Analytical Potential Energy Surface Based On Fitting To Ab Initio Calculations
Limit Cycles For Some Abel Equations Having Coefficients Without Fixed Signs
Implementación European Credit Transfer System En Un Curso De Programación En Ingeniería
Limit Cycles For Some Abel Equations Having Coefficients Without Fixed Signs
Implementación European Credit Transfer System En Un Curso De Programación En Ingeniería
Matemáticas Para Primero De Ciencias
Implementación European Credit Transfer System En Un Curso De Programación En Ingeniería
Matemáticas Para Primero De Ciencias
Métodos Matemáticos Para Estadística
Matemáticas Para Primero De Ciencias
Métodos Matemáticos Para Estadística
State-To-State Dynamics Analysis Of The F + Chd3 Reaction: A Quasiclassical Trajectory Study
Métodos Matemáticos Para Estadística
State-To-State Dynamics Analysis Of The F + Chd3 Reaction: A Quasiclassical Trajectory Study
Abel-Like Differential Equations With No Periodic Solutions
State-To-State Dynamics Analysis Of The F + Chd3 Reaction: A Quasiclassical Trajectory Study
Abel-Like Differential Equations With No Periodic Solutions
Local And Global Bifurcation In Periodic Scalar Odes
Abel-Like Differential Equations With No Periodic Solutions
Local And Global Bifurcation In Periodic Scalar Odes
Examples Of Generic Lattice Ideals Of Codimension 3
Local And Global Bifurcation In Periodic Scalar Odes
Examples Of Generic Lattice Ideals Of Codimension 3
Weakly Lefschetz Symplectic Manifolds
Examples Of Generic Lattice Ideals Of Codimension 3
Weakly Lefschetz Symplectic Manifolds
In Memoriam: Pilar Pisón Casares, In Memoriam
Weakly Lefschetz Symplectic Manifolds
In Memoriam: Pilar Pisón Casares, In Memoriam
Experiencia Piloto De Adaptación Del Primer Curso De La Titulación De Química Al Eees En La Uex
In Memoriam: Pilar Pisón Casares, In Memoriam
Experiencia Piloto De Adaptación Del Primer Curso De La Titulación De Química Al Eees En La Uex
Experiencia Piloto De Adaptación Del Segundo Curso De Ingeniería Técnica En Informática De Sistemas Del Centro Universitario De Mérida De La Universidad De Extremadura Al Espacio Europeo De Educación Superior
Experiencia Piloto De Adaptación Del Primer Curso De La Titulación De Química Al Eees En La Uex
Experiencia Piloto De Adaptación Del Segundo Curso De Ingeniería Técnica En Informática De Sistemas Del Centro Universitario De Mérida De La Universidad De Extremadura Al Espacio Europeo De Educación Superior
The Set Of Periodic Scalar Differential Equations With Cubic Nonlinearities
Experiencia Piloto De Adaptación Del Segundo Curso De Ingeniería Técnica En Informática De Sistemas Del Centro Universitario De Mérida De La Universidad De Extremadura Al Espacio Europeo De Educación Superior
The Set Of Periodic Scalar Differential Equations With Cubic Nonlinearities
New Analytical Potential Energy Surface For The F(2p) + Ch 4 Hydrogen Abstraction Reaction: Kinetics And Dynamics
The Set Of Periodic Scalar Differential Equations With Cubic Nonlinearities
New Analytical Potential Energy Surface For The F(2p) + Ch 4 Hydrogen Abstraction Reaction: Kinetics And Dynamics
Periodic Solutions Of A Periodic Scalar Piecewise Ode
New Analytical Potential Energy Surface For The F(2p) + Ch 4 Hydrogen Abstraction Reaction: Kinetics And Dynamics
Periodic Solutions Of A Periodic Scalar Piecewise Ode
Orthogonality Of Matrices
Periodic Solutions Of A Periodic Scalar Piecewise Ode
Orthogonality Of Matrices
La Geometría Algebraica De Los Campos Aleatorios De Markov
Orthogonality Of Matrices
La Geometría Algebraica De Los Campos Aleatorios De Markov
Even G-Liaison Classes Of Some Unions Of Curves
La Geometría Algebraica De Los Campos Aleatorios De Markov
Even G-Liaison Classes Of Some Unions Of Curves
Non Degenerate Projective Curves With Very Degenerate Hyperplane Section
Even G-Liaison Classes Of Some Unions Of Curves
Non Degenerate Projective Curves With Very Degenerate Hyperplane Section
The Number Of Bifurcation Points Of A Periodic One-Parameter Ode With At Most Two Periodic Solutions
Non Degenerate Projective Curves With Very Degenerate Hyperplane Section
The Number Of Bifurcation Points Of A Periodic One-Parameter Ode With At Most Two Periodic Solutions
On The Hull Resolution Of An Affine Monomial Curve
The Number Of Bifurcation Points Of A Periodic One-Parameter Ode With At Most Two Periodic Solutions
On The Hull Resolution Of An Affine Monomial Curve
Location Of The Fermat-Torricelli Medians Of Three Points
On The Hull Resolution Of An Affine Monomial Curve
Location Of The Fermat-Torricelli Medians Of Three Points
Weighted P-Centers And The Convex Hull Property
Location Of The Fermat-Torricelli Medians Of Three Points
Weighted P-Centers And The Convex Hull Property
Index Of Nilpotency Of Binomial Ideals
Weighted P-Centers And The Convex Hull Property
Index Of Nilpotency Of Binomial Ideals
Nilpotent Complex Structures
Index Of Nilpotency Of Binomial Ideals
Nilpotent Complex Structures
The Set Of First-Order Differential Equations With Periodic Or Bounded Solutions
Nilpotent Complex Structures
The Set Of First-Order Differential Equations With Periodic Or Bounded Solutions
Resolución Envolvente De Curvas Monomiales En A3 (K)
The Set Of First-Order Differential Equations With Periodic Or Bounded Solutions
Resolución Envolvente De Curvas Monomiales En A3 (K)
Sobre La Efectividad En El Nullstellensatz De Sistemas Tóricos
Resolución Envolvente De Curvas Monomiales En A3 (K)
Sobre La Efectividad En El Nullstellensatz De Sistemas Tóricos
Smooth Points Of Essentially Bounded Vector Function Spaces
Sobre La Efectividad En El Nullstellensatz De Sistemas Tóricos
Smooth Points Of Essentially Bounded Vector Function Spaces
Cellular Binomial Ideals. Primary Decomposition Of Binomial Ideals
Smooth Points Of Essentially Bounded Vector Function Spaces
Cellular Binomial Ideals. Primary Decomposition Of Binomial Ideals
Smith's Counterexample About Uniform Rotundity In Every Direction
Cellular Binomial Ideals. Primary Decomposition Of Binomial Ideals
Smith's Counterexample About Uniform Rotundity In Every Direction
On The Norm Of The Product Of Linear Functionals
Smith's Counterexample About Uniform Rotundity In Every Direction
On The Norm Of The Product Of Linear Functionals
Directions Of Uniform Rotundity In Direct Sums Of Normed Spaces
On The Norm Of The Product Of Linear Functionals
Directions Of Uniform Rotundity In Direct Sums Of Normed Spaces
Suitable Norms For Simultaneous Approximation
Directions Of Uniform Rotundity In Direct Sums Of Normed Spaces
Suitable Norms For Simultaneous Approximation
Directional Uniform Rotundity In Spaces Of Essentially Bounded Vector Functions
Suitable Norms For Simultaneous Approximation
Directional Uniform Rotundity In Spaces Of Essentially Bounded Vector Functions
Continuity Of The Uniform Rotundity Modulus Relative To Linear Subspaces
Directional Uniform Rotundity In Spaces Of Essentially Bounded Vector Functions
Continuity Of The Uniform Rotundity Modulus Relative To Linear Subspaces
A Brunn-Blaschke-Kakutani Type Theorem On The Shadow Boundary Of A Convex Set
Continuity Of The Uniform Rotundity Modulus Relative To Linear Subspaces
A Brunn-Blaschke-Kakutani Type Theorem On The Shadow Boundary Of A Convex Set
Location Of Best Simultaneous Approximations
A Brunn-Blaschke-Kakutani Type Theorem On The Shadow Boundary Of A Convex Set
Location Of Best Simultaneous Approximations
Suitable Norms For Simultaneous Approximation
Location Of Best Simultaneous Approximations
Suitable Norms For Simultaneous Approximation
Relative Rotundity In Lp(X)
Suitable Norms For Simultaneous Approximation
Relative Rotundity In Lp(X)
On The Chebyshev Alternation Theorem
Relative Rotundity In Lp(X)
On The Chebyshev Alternation Theorem
Relative Rotundity In Lp(X)
On The Chebyshev Alternation Theorem
Relative Rotundity In Lp(X)
Directional Uniform Rotundity In Spaces Of Essentially Bounded Functions
Relative Rotundity In Lp(X)
Directional Uniform Rotundity In Spaces Of Essentially Bounded Functions
Sobre Los Diversos Lenguajes Matemáticos Y Del Paso De Unos A Otros
Directional Uniform Rotundity In Spaces Of Essentially Bounded Functions
Sobre Los Diversos Lenguajes Matemáticos Y Del Paso De Unos A Otros
Functional Characterization Of Best And Good Approximation In Normed Product Spaces
Sobre Los Diversos Lenguajes Matemáticos Y Del Paso De Unos A Otros
Functional Characterization Of Best And Good Approximation In Normed Product Spaces
Aproximación Simultánea En Espacios Normandos
Functional Characterization Of Best And Good Approximation In Normed Product Spaces
Aproximación Simultánea En Espacios Normandos
Norms In Product Spaces Which Preserve Approximation Properties
Aproximación Simultánea En Espacios Normandos
Norms In Product Spaces Which Preserve Approximation Properties
Norms In Product Spaces Which Preserve Approximation Porperties
Norms In Product Spaces Which Preserve Approximation Properties
Norms In Product Spaces Which Preserve Approximation Porperties
Minimal Free Resolution Of Generalized Repunit Algebras
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