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Refinar búsquedaAdvances in Ring Theory / SpringerLink (Online service) ; Huynh, Dinh Van ; López-Permouth, Sergio R (2010)
Título : Advances in Ring Theory Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Huynh, Dinh Van ; López-Permouth, Sergio R Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2010 Colección: Trends in Mathematics Número de páginas: IX, 345 p Il.: online resource ISBN/ISSN/DL: 978-3-0346-0286-0 Idioma : Inglés (eng) Palabras clave: Mathematics Associative rings Rings (Algebra) Commutative algebra and Algebras Clasificación: 51 Matemáticas Resumen: This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra Nota de contenido: Applications of Cogalois Theory to Elementary Field Arithmetic -- On Big Lattices of Classes of R-modules Defined by Closure Properties -- Reversible and Duo Group Rings -- Principally Quasi-Baer Ring Hulls -- Strongly Prime Ideals of Near-rings of Continuous Functions -- Elements of Minimal Prime Ideals in General Rings -- On a Theorem of Camps and Dicks -- Applications of the Stone Duality in the Theory of Precompact Boolean Rings -- Over Rings and Functors -- On Some Classes of Repeated-root Constacyclic Codes of Length a Power of 2 over Galois Rings -- Couniformly Presented Modules and Dualities -- Semiclassical Limits of Quantized Coordinate Rings -- On Unit-Central Rings -- Symplectic Modules and von Neumann Regular Matrices over Commutative Rings -- Extensions of Simple Modules and the Converse of Schur’s Lemma -- Report on Exchange Rings -- Filtrations in Semisimple Lie Algebras, III -- On the Blowing-up Rings, Arf Rings and Type Sequences -- A Guide to Supertropical Algebra -- Projective Modules, Idempotent Ideals and Intersection Theorems -- On Ef-extending Modules and Rings with Chain Conditions -- On Clean Group Rings En línea: http://dx.doi.org/10.1007/978-3-0346-0286-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33672 Advances in Ring Theory [documento electrónico] / SpringerLink (Online service) ; Huynh, Dinh Van ; López-Permouth, Sergio R . - Basel : Birkhäuser Basel, 2010 . - IX, 345 p : online resource. - (Trends in Mathematics) .
ISBN : 978-3-0346-0286-0
Idioma : Inglés (eng)
Palabras clave: Mathematics Associative rings Rings (Algebra) Commutative algebra and Algebras Clasificación: 51 Matemáticas Resumen: This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra Nota de contenido: Applications of Cogalois Theory to Elementary Field Arithmetic -- On Big Lattices of Classes of R-modules Defined by Closure Properties -- Reversible and Duo Group Rings -- Principally Quasi-Baer Ring Hulls -- Strongly Prime Ideals of Near-rings of Continuous Functions -- Elements of Minimal Prime Ideals in General Rings -- On a Theorem of Camps and Dicks -- Applications of the Stone Duality in the Theory of Precompact Boolean Rings -- Over Rings and Functors -- On Some Classes of Repeated-root Constacyclic Codes of Length a Power of 2 over Galois Rings -- Couniformly Presented Modules and Dualities -- Semiclassical Limits of Quantized Coordinate Rings -- On Unit-Central Rings -- Symplectic Modules and von Neumann Regular Matrices over Commutative Rings -- Extensions of Simple Modules and the Converse of Schur’s Lemma -- Report on Exchange Rings -- Filtrations in Semisimple Lie Algebras, III -- On the Blowing-up Rings, Arf Rings and Type Sequences -- A Guide to Supertropical Algebra -- Projective Modules, Idempotent Ideals and Intersection Theorems -- On Ef-extending Modules and Rings with Chain Conditions -- On Clean Group Rings En línea: http://dx.doi.org/10.1007/978-3-0346-0286-0 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=33672 Ejemplares
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Título : Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Pragacz, Piotr Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2008 Colección: Trends in Mathematics Número de páginas: VIII, 236 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8537-8 Idioma : Inglés (eng) Palabras clave: Mathematics Algebra Algebraic geometry topology Geometry Topology Clasificación: 51 Matemáticas Resumen: The articles in this volume are devoted to: - moduli of coherent sheaves; - principal bundles and sheaves and their moduli; - new insights into Geometric Invariant Theory; - stacks of shtukas and their compactifications; - algebraic cycles vs. commutative algebra; - Thom polynomials of singularities; - zero schemes of sections of vector bundles. The main purpose is to give "friendly" introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before. Contributors: Jean-Marc Drézet, Tomás L. Gómez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber Nota de contenido: Notes on the Life and Work of Józef Maria Hoene-Wro?ski -- Exotic Fine Moduli Spaces of Coherent Sheaves -- Moduli Spaces of Coherent Sheaves on Multiples Curves -- Lectures on Principal Bundles over Projective Varieties -- Lectures on Torsion-free Sheaves and Their Moduli -- Miscellany on the Zero Schemes of Sections of Vector Bundles -- Thom Polynomials of Invariant Cones, Schur Functions and Positivity -- Geometric Invariant Theory Relative to a Base Curve -- Some Applications of Algebraic Cycles to Affine Algebraic Geometry -- to the Stacks of Shtukas En línea: http://dx.doi.org/10.1007/978-3-7643-8537-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34393 Algebraic Cycles, Sheaves, Shtukas, and Moduli : Impanga Lecture Notes [documento electrónico] / SpringerLink (Online service) ; Pragacz, Piotr . - Basel : Birkhäuser Basel, 2008 . - VIII, 236 p : online resource. - (Trends in Mathematics) .
ISBN : 978-3-7643-8537-8
Idioma : Inglés (eng)
Palabras clave: Mathematics Algebra Algebraic geometry topology Geometry Topology Clasificación: 51 Matemáticas Resumen: The articles in this volume are devoted to: - moduli of coherent sheaves; - principal bundles and sheaves and their moduli; - new insights into Geometric Invariant Theory; - stacks of shtukas and their compactifications; - algebraic cycles vs. commutative algebra; - Thom polynomials of singularities; - zero schemes of sections of vector bundles. The main purpose is to give "friendly" introductions to the above topics through a series of comprehensive texts starting from a very elementary level and ending with a discussion of current research. In these texts, the reader will find classical results and methods as well as new ones. The book is addressed to researchers and graduate students in algebraic geometry, algebraic topology and singularity theory. Most of the material presented in the volume has not appeared in books before. Contributors: Jean-Marc Drézet, Tomás L. Gómez, Adrian Langer, Piotr Pragacz, Alexander H. W. Schmitt, Vasudevan Srinivas, Ngo Dac Tuan, Andrzej Weber Nota de contenido: Notes on the Life and Work of Józef Maria Hoene-Wro?ski -- Exotic Fine Moduli Spaces of Coherent Sheaves -- Moduli Spaces of Coherent Sheaves on Multiples Curves -- Lectures on Principal Bundles over Projective Varieties -- Lectures on Torsion-free Sheaves and Their Moduli -- Miscellany on the Zero Schemes of Sections of Vector Bundles -- Thom Polynomials of Invariant Cones, Schur Functions and Positivity -- Geometric Invariant Theory Relative to a Base Curve -- Some Applications of Algebraic Cycles to Affine Algebraic Geometry -- to the Stacks of Shtukas En línea: http://dx.doi.org/10.1007/978-3-7643-8537-8 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34393 Ejemplares
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Título : Algebraic Multiplicity of Eigenvalues of Linear Operators Tipo de documento: documento electrónico Autores: López-Gómez, J ; SpringerLink (Online service) ; Mora-Corral, C Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Colección: Operator Theory: Advances and Applications num. 177 Número de páginas: XXII, 310 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8401-2 Idioma : Inglés (eng) Palabras clave: Mathematics Matrix theory Algebra Functional analysis Operator Physics Analysis Linear and Multilinear Algebras, Theory Mathematical Methods in Clasificación: 51 Matemáticas Resumen: This book brings together all the most important known results of research into the theory of algebraic multiplicities, from well-known classics like the Jordan Theorem to recent developments such as the uniqueness theorem and the construction of multiplicity for non-analytic families, which is presented in this monograph for the first time. Part I (the first three chapters) is a classic course on finite-dimensional spectral theory; Part II (the next eight chapters) contains the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families; and Part III (the last chapter) transfers these results from linear to nonlinear analysis. The text is as self-contained as possible. All the results are established in a finite-dimensional setting, if necessary. Furthermore, the structure and style of the book make it easy to access some of the most important and recent developments. Thus the material appeals to a broad audience, ranging from advanced undergraduates (in particular Part I) to graduates, postgraduates and reseachers who will enjoy the latest developments in the real non-analytic case (Part II) Nota de contenido: Finite-dimensional Classic Spectral Theory -- The Jordan Theorem -- Operator Calculus -- Spectral Projections -- Algebraic Multiplicities -- Algebraic Multiplicity Through Transversalization -- Algebraic Multiplicity Through Polynomial Factorization -- Uniqueness of the Algebraic Multiplicity -- Algebraic Multiplicity Through Jordan Chains. Smith Form -- Analytic and Classical Families. Stability -- Algebraic Multiplicity Through Logarithmic Residues -- The Spectral Theorem for Matrix Polynomials -- Further Developments of the Algebraic Multiplicity -- Nonlinear Spectral Theory -- Nonlinear Eigenvalues En línea: http://dx.doi.org/10.1007/978-3-7643-8401-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34714 Algebraic Multiplicity of Eigenvalues of Linear Operators [documento electrónico] / López-Gómez, J ; SpringerLink (Online service) ; Mora-Corral, C . - Basel : Birkhäuser Basel, 2007 . - XXII, 310 p : online resource. - (Operator Theory: Advances and Applications; 177) .
ISBN : 978-3-7643-8401-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Matrix theory Algebra Functional analysis Operator Physics Analysis Linear and Multilinear Algebras, Theory Mathematical Methods in Clasificación: 51 Matemáticas Resumen: This book brings together all the most important known results of research into the theory of algebraic multiplicities, from well-known classics like the Jordan Theorem to recent developments such as the uniqueness theorem and the construction of multiplicity for non-analytic families, which is presented in this monograph for the first time. Part I (the first three chapters) is a classic course on finite-dimensional spectral theory; Part II (the next eight chapters) contains the most general results available about the existence and uniqueness of algebraic multiplicities for real non-analytic operator matrices and families; and Part III (the last chapter) transfers these results from linear to nonlinear analysis. The text is as self-contained as possible. All the results are established in a finite-dimensional setting, if necessary. Furthermore, the structure and style of the book make it easy to access some of the most important and recent developments. Thus the material appeals to a broad audience, ranging from advanced undergraduates (in particular Part I) to graduates, postgraduates and reseachers who will enjoy the latest developments in the real non-analytic case (Part II) Nota de contenido: Finite-dimensional Classic Spectral Theory -- The Jordan Theorem -- Operator Calculus -- Spectral Projections -- Algebraic Multiplicities -- Algebraic Multiplicity Through Transversalization -- Algebraic Multiplicity Through Polynomial Factorization -- Uniqueness of the Algebraic Multiplicity -- Algebraic Multiplicity Through Jordan Chains. Smith Form -- Analytic and Classical Families. Stability -- Algebraic Multiplicity Through Logarithmic Residues -- The Spectral Theorem for Matrix Polynomials -- Further Developments of the Algebraic Multiplicity -- Nonlinear Spectral Theory -- Nonlinear Eigenvalues En línea: http://dx.doi.org/10.1007/978-3-7643-8401-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34714 Ejemplares
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Título : An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem Tipo de documento: documento electrónico Autores: Capogna, Luca ; SpringerLink (Online service) ; Pauls, Scott D ; Danielli, Donatella ; Tyson, Jeremy T Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2007 Colección: Progress in Mathematics num. 259 Número de páginas: XVI, 224 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8133-2 Idioma : Inglés (eng) Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Partial differential equations System theory Differential geometry Complex manifolds Geometry Groups, Groups and Cell Complexes (incl. Diff.Topology) Equations Analysis on Systems Theory, Control Clasificación: 51 Matemáticas Resumen: The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area Nota de contenido: The Isoperimetric Problem in Euclidean Space -- The Heisenberg Group and Sub-Riemannian Geometry -- Applications of Heisenberg Geometry -- Horizontal Geometry of Submanifolds -- Sobolev and BV Spaces -- Geometric Measure Theory and Geometric Function Theory -- The Isoperimetric Inequality in ? -- The Isoperimetric Profile of ? -- Best Constants for Other Geometric Inequalities on the Heisenberg Group En línea: http://dx.doi.org/10.1007/978-3-7643-8133-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34700 An Introduction to the Heisenberg Group and the Sub-Riemannian Isoperimetric Problem [documento electrónico] / Capogna, Luca ; SpringerLink (Online service) ; Pauls, Scott D ; Danielli, Donatella ; Tyson, Jeremy T . - Basel : Birkhäuser Basel, 2007 . - XVI, 224 p : online resource. - (Progress in Mathematics; 259) .
ISBN : 978-3-7643-8133-2
Idioma : Inglés (eng)
Palabras clave: Mathematics Topological groups Lie Global analysis (Mathematics) Manifolds Partial differential equations System theory Differential geometry Complex manifolds Geometry Groups, Groups and Cell Complexes (incl. Diff.Topology) Equations Analysis on Systems Theory, Control Clasificación: 51 Matemáticas Resumen: The past decade has witnessed a dramatic and widespread expansion of interest and activity in sub-Riemannian (Carnot-Caratheodory) geometry, motivated both internally by its role as a basic model in the modern theory of analysis on metric spaces, and externally through the continuous development of applications (both classical and emerging) in areas such as control theory, robotic path planning, neurobiology and digital image reconstruction. The quintessential example of a sub Riemannian structure is the Heisenberg group, which is a nexus for all of the aforementioned applications as well as a point of contact between CR geometry, Gromov hyperbolic geometry of complex hyperbolic space, subelliptic PDE, jet spaces, and quantum mechanics. This book provides an introduction to the basics of sub-Riemannian differential geometry and geometric analysis in the Heisenberg group, focusing primarily on the current state of knowledge regarding Pierre Pansu's celebrated 1982 conjecture regarding the sub-Riemannian isoperimetric profile. It presents a detailed description of Heisenberg submanifold geometry and geometric measure theory, which provides an opportunity to collect for the first time in one location the various known partial results and methods of attack on Pansu's problem. As such it serves simultaneously as an introduction to the area for graduate students and beginning researchers, and as a research monograph focused on the isoperimetric problem suitable for experts in the area Nota de contenido: The Isoperimetric Problem in Euclidean Space -- The Heisenberg Group and Sub-Riemannian Geometry -- Applications of Heisenberg Geometry -- Horizontal Geometry of Submanifolds -- Sobolev and BV Spaces -- Geometric Measure Theory and Geometric Function Theory -- The Isoperimetric Inequality in ? -- The Isoperimetric Profile of ? -- Best Constants for Other Geometric Inequalities on the Heisenberg Group En línea: http://dx.doi.org/10.1007/978-3-7643-8133-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34700 Ejemplares
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Título : An Introduction to the Theory of Functional Equations and Inequalities : Cauchy’s Equation and Jensen’s Inequality Tipo de documento: documento electrónico Autores: Kuczma, Marek ; SpringerLink (Online service) ; Gilányi, Attila Editorial: Basel : Birkhäuser Basel Fecha de publicación: 2009 Número de páginas: XIV, 595 p Il.: online resource ISBN/ISSN/DL: 978-3-7643-8749-5 Idioma : Inglés (eng) Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Clasificación: 51 Matemáticas Resumen: Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik) Nota de contenido: Preliminaries -- Set Theory -- Topology -- Measure Theory -- Algebra -- Cauchy’s Functional Equation and Jensen’s Inequality -- Additive Functions and Convex Functions -- Elementary Properties of Convex Functions -- Continuous Convex Functions -- Inequalities -- Boundedness and Continuity of Convex Functions and Additive Functions -- The Classes A, B, ? -- Properties of Hamel Bases -- Further Properties of Additive Functions and Convex Functions -- Related Topics -- Related Equations -- Derivations and Automorphisms -- Convex Functions of Higher Orders -- Subadditive Functions -- Nearly Additive Functions and Nearly Convex Functions -- Extensions of Homomorphisms En línea: http://dx.doi.org/10.1007/978-3-7643-8749-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34084 An Introduction to the Theory of Functional Equations and Inequalities : Cauchy’s Equation and Jensen’s Inequality [documento electrónico] / Kuczma, Marek ; SpringerLink (Online service) ; Gilányi, Attila . - Basel : Birkhäuser Basel, 2009 . - XIV, 595 p : online resource.
ISBN : 978-3-7643-8749-5
Idioma : Inglés (eng)
Palabras clave: Mathematics Mathematical analysis Analysis (Mathematics) Clasificación: 51 Matemáticas Resumen: Marek Kuczma was born in 1935 in Katowice, Poland, and died there in 1991. After finishing high school in his home town, he studied at the Jagiellonian University in Kraków. He defended his doctoral dissertation under the supervision of Stanislaw Golab. In the year of his habilitation, in 1963, he obtained a position at the Katowice branch of the Jagiellonian University (now University of Silesia, Katowice), and worked there till his death. Besides his several administrative positions and his outstanding teaching activity, he accomplished excellent and rich scientific work publishing three monographs and 180 scientific papers. He is considered to be the founder of the celebrated Polish school of functional equations and inequalities. "The second half of the title of this book describes its contents adequately. Probably even the most devoted specialist would not have thought that about 300 pages can be written just about the Cauchy equation (and on some closely related equations and inequalities). And the book is by no means chatty, and does not even claim completeness. Part I lists the required preliminary knowledge in set and measure theory, topology and algebra. Part II gives details on solutions of the Cauchy equation and of the Jensen inequality [...], in particular on continuous convex functions, Hamel bases, on inequalities following from the Jensen inequality [...]. Part III deals with related equations and inequalities (in particular, Pexider, Hosszú, and conditional equations, derivations, convex functions of higher order, subadditive functions and stability theorems). It concludes with an excursion into the field of extensions of homomorphisms in general." (Janos Aczel, Mathematical Reviews) "This book is a real holiday for all the mathematicians independently of their strict speciality. One can imagine what deliciousness represents this book for functional equationists." (B. Crstici, Zentralblatt für Mathematik) Nota de contenido: Preliminaries -- Set Theory -- Topology -- Measure Theory -- Algebra -- Cauchy’s Functional Equation and Jensen’s Inequality -- Additive Functions and Convex Functions -- Elementary Properties of Convex Functions -- Continuous Convex Functions -- Inequalities -- Boundedness and Continuity of Convex Functions and Additive Functions -- The Classes A, B, ? -- Properties of Hamel Bases -- Further Properties of Additive Functions and Convex Functions -- Related Topics -- Related Equations -- Derivations and Automorphisms -- Convex Functions of Higher Orders -- Subadditive Functions -- Nearly Additive Functions and Nearly Convex Functions -- Extensions of Homomorphisms En línea: http://dx.doi.org/10.1007/978-3-7643-8749-5 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34084 Ejemplares
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