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Biblioteca

MARC Lista (tabellare)
(Mostly) commutative algebra / / Antoine Chambert-Loir
(Mostly) commutative algebra / / Antoine Chambert-Loir
Autore Chambert-Loir Antoine
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (471 pages)
Disciplina 512.24
Collana Universitext
Soggetto topico Commutative algebra
Àlgebra commutativa
Soggetto genere / forma Llibres electrònics
ISBN 3-030-61595-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466546403316
Chambert-Loir Antoine  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
(Mostly) commutative algebra / / Antoine Chambert-Loir
(Mostly) commutative algebra / / Antoine Chambert-Loir
Autore Chambert-Loir Antoine
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (471 pages)
Disciplina 512.24
Collana Universitext
Soggetto topico Commutative algebra
Àlgebra commutativa
Soggetto genere / forma Llibres electrònics
ISBN 3-030-61595-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910483721503321
Chambert-Loir Antoine  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Algebraic geometry and commutative algebra / / Siegfried Bosch
Algebraic geometry and commutative algebra / / Siegfried Bosch
Autore Bosch S (Siegfried), <1944->
Edizione [Second edition.]
Pubbl/distr/stampa London, England : , : Springer-Verlag, , [2022]
Descrizione fisica 1 online resource (508 pages)
Disciplina 516.35
Collana Universitext
Soggetto topico Geometry, Algebraic
Commutative algebra
Algebra
Geometria algebraica
Àlgebra commutativa
Soggetto genere / forma Llibres electrònics
ISBN 9781447175230
9781447175223
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996472037103316
Bosch S (Siegfried), <1944->  
London, England : , : Springer-Verlag, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Algebraic geometry and commutative algebra / / Siegfried Bosch
Algebraic geometry and commutative algebra / / Siegfried Bosch
Autore Bosch S (Siegfried), <1944->
Edizione [Second edition.]
Pubbl/distr/stampa London, England : , : Springer-Verlag, , [2022]
Descrizione fisica 1 online resource (508 pages)
Disciplina 516.35
Collana Universitext
Soggetto topico Geometry, Algebraic
Commutative algebra
Algebra
Geometria algebraica
Àlgebra commutativa
Soggetto genere / forma Llibres electrònics
ISBN 9781447175230
9781447175223
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910564691103321
Bosch S (Siegfried), <1944->  
London, England : , : Springer-Verlag, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Commutative algebra : expository papers dedicated to David Eisenbud on the occasion of his 65th birthday / / edited by Irena Peeva
Commutative algebra : expository papers dedicated to David Eisenbud on the occasion of his 65th birthday / / edited by Irena Peeva
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (898 pages)
Disciplina 512.24
Soggetto topico Àlgebra commutativa
Anells commutatius
Commutative algebra
Soggetto genere / forma Llibres electrònics
ISBN 9783030896942
9783030896935
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNISA-996466556503316
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Commutative algebra : expository papers dedicated to David Eisenbud on the occasion of his 65th birthday / / edited by Irena Peeva
Commutative algebra : expository papers dedicated to David Eisenbud on the occasion of his 65th birthday / / edited by Irena Peeva
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (898 pages)
Disciplina 512.24
Soggetto topico Àlgebra commutativa
Anells commutatius
Commutative algebra
Soggetto genere / forma Llibres electrònics
ISBN 9783030896942
9783030896935
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910547291403321
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Determinants, Gröbner bases and cohomology / / Winfried Bruns [and three others]
Determinants, Gröbner bases and cohomology / / Winfried Bruns [and three others]
Autore Bruns Winfried
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (514 pages)
Disciplina 512.55
Collana Springer monographs in mathematics
Soggetto topico Algebra, Homological
Algebraic geometry
Commutative algebra
Àlgebra homològica
Geometria algebraica
Àlgebra commutativa
Soggetto genere / forma Llibres electrònics
ISBN 3-031-05480-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Gröbner Bases, Initial Ideals and Initial Algebras -- 1.1 Monomial Orders -- 1.2 Gröbner Bases -- 1.3 Sagbi Bases -- 1.4 Initial Subspaces and Gradings -- 1.5 Initial Subspaces for Weights. Homogenization -- 1.6 Deformation to the Initial Object -- 2 More on Gröbner Deformations -- 2.1 Minimal and Associated Primes -- 2.2 Connectedness -- 2.3 Optimal Gröbner Deformations -- 2.4 Square-Free Gröbner Deformations -- 3 Determinantal Ideals and the Straightening Law -- 3.1 Minors and Determinantal Ideals -- 3.2 Standard Bitableaux and the Straightening Law -- 3.3 Refinement of the Straightening Law -- 3.4 Determinantal Rings -- 3.5 Powers and Products of Determinantal Ideals -- 3.6 Representation Theory -- 4 Gröbner Bases of Determinantal Ideals -- 4.1 An Instructive Case: the Ideal of 2-Minors -- 4.2 The Robinson-Schensted-Knuth Correspondence -- 4.3 RSK and Gröbner Bases of Ideals -- 4.4 Cohen-Macaulayness and Hilbert Series of Determinantal Rings -- 4.5 Gröbner Bases via Secants -- 4.6 Multigraded Structures and the Multidegree -- 5 Universal Gröbner Bases -- 5.1 Universal Gröbner Bases -- 5.2 Universal Gröbner Bases for Maximal Minors -- 5.3 Universal Gröbner Bases for 2-Minors -- 6 Algebras Defined by Minors -- 6.1 A Recap of Toric Algebra -- 6.2 Algebras Defined by Maximal Minors -- 6.3 Rees Algebras of Determinantal Ideals -- 6.4 The Algebra of Minors -- 6.5 Algebraic Relations between Minors -- 6.6 Exterior Powers of Linear Maps -- 6.7 Sagbi Deformations of Determinantal Rings -- 7 F-singularities of Determinantal Rings -- 7.1 F-purity -- 7.2 F-regularity -- 7.3 F-rationality and Gröbner Deformations -- 7.4 Equivariant Deformations -- 7.5 F-pure Thresholds -- 8 Castelnuovo-Mumford Regularity -- 8.1 Castelnuovo-Mumford Regularity over General Base Rings.
8.2 Castelnuovo-Mumford Regularity and Multigraded Structures -- 8.3 Vanishing over Nonstandard Multigraded Rings -- 8.4 Regularity of Powers and Products of Ideals -- 8.5 Linear Powers and Linear Products -- 8.6 A Family of Determinantal Ideals with Linear Products -- 8.7 Maximal Minors of Matrices of Linear Forms and Linear Powers -- 9 Grassmannians, Flag Varieties, Schur Functors and Cohomology -- 9.1 Fundamental Multilinear Algebra Constructions -- 9.2 Affine and Projective Bundles, Grassmannians, Flag Varieties -- 9.3 Basic Calculus with Direct Images -- 9.4 The Kempf Vanishing Theorem -- 9.5 Characteristic-Free Vanishing for some Nondominant Weights -- 9.6 A Sharp Characteristic-Free Vanishing on Projective Bundles -- 9.7 Algebraic Groups and Representations -- 9.8 Schur Functors -- 9.9 Grothendieck Duality -- 9.10 Cohomology Vanishing on Grassmannians -- 10 Asymptotic Regularity for Symbolic Powers of Determinantal Ideals -- 10.1 Quotients of Ideals Defined by Shape -- 10.2 Filtrations Associated with Ideals Defined by Shape -- 10.3 An algorithm to Compute Z(Σ) -- 10.4 The Filtration for Symbolic Powers of Determinantal Ideals -- 10.5 Sheaves Defined by Shape and Their Quotients -- 10.6 A Geometric Realization of the Modules J(σ)l -- 10.7 Regularity of Symbolic Powers of Determinantal Ideals -- 10.8 Some Geometric Properties of Determinantal Varieties -- 11 Cohomology and Regularity in Characteristic Zero -- 11.1 The Borel-Weil-Bott Theorem -- 11.2 The Optimality of Theorem 9.5.1摥映數爠eflinkthm:charspsfreespsvanishing9.5.19 -- 11.3 Borel-Weil-Bott on Grassmannians -- 11.4 Effective Vanishing of Cohomology in Characteristic Zero -- 11.5 Cauchy's Formula Revisited -- 11.6 Explicit Description of `3́9`42`"̇613A``45`47`"603AExt Modules for J(σ)l -- 11.7 `3́9`42`"̇613A``45`47`"603AExt Modules for Symbolic Powers.
11.8 The Basics on `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.9 `3́9`42`"̇613A``45`47`"603AExt Modules for `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.10 Local Cohomology with Determinantal Support -- 11.11 Syzygies of `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- Appendix List of Symbols -- References -- -- Index.
Record Nr. UNINA-9910633915903321
Bruns Winfried  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Determinants, Gröbner bases and cohomology / / Winfried Bruns [and three others]
Determinants, Gröbner bases and cohomology / / Winfried Bruns [and three others]
Autore Bruns Winfried
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2022]
Descrizione fisica 1 online resource (514 pages)
Disciplina 512.55
Collana Springer monographs in mathematics
Soggetto topico Algebra, Homological
Algebraic geometry
Commutative algebra
Àlgebra homològica
Geometria algebraica
Àlgebra commutativa
Soggetto genere / forma Llibres electrònics
ISBN 3-031-05480-6
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Preface -- Contents -- 1 Gröbner Bases, Initial Ideals and Initial Algebras -- 1.1 Monomial Orders -- 1.2 Gröbner Bases -- 1.3 Sagbi Bases -- 1.4 Initial Subspaces and Gradings -- 1.5 Initial Subspaces for Weights. Homogenization -- 1.6 Deformation to the Initial Object -- 2 More on Gröbner Deformations -- 2.1 Minimal and Associated Primes -- 2.2 Connectedness -- 2.3 Optimal Gröbner Deformations -- 2.4 Square-Free Gröbner Deformations -- 3 Determinantal Ideals and the Straightening Law -- 3.1 Minors and Determinantal Ideals -- 3.2 Standard Bitableaux and the Straightening Law -- 3.3 Refinement of the Straightening Law -- 3.4 Determinantal Rings -- 3.5 Powers and Products of Determinantal Ideals -- 3.6 Representation Theory -- 4 Gröbner Bases of Determinantal Ideals -- 4.1 An Instructive Case: the Ideal of 2-Minors -- 4.2 The Robinson-Schensted-Knuth Correspondence -- 4.3 RSK and Gröbner Bases of Ideals -- 4.4 Cohen-Macaulayness and Hilbert Series of Determinantal Rings -- 4.5 Gröbner Bases via Secants -- 4.6 Multigraded Structures and the Multidegree -- 5 Universal Gröbner Bases -- 5.1 Universal Gröbner Bases -- 5.2 Universal Gröbner Bases for Maximal Minors -- 5.3 Universal Gröbner Bases for 2-Minors -- 6 Algebras Defined by Minors -- 6.1 A Recap of Toric Algebra -- 6.2 Algebras Defined by Maximal Minors -- 6.3 Rees Algebras of Determinantal Ideals -- 6.4 The Algebra of Minors -- 6.5 Algebraic Relations between Minors -- 6.6 Exterior Powers of Linear Maps -- 6.7 Sagbi Deformations of Determinantal Rings -- 7 F-singularities of Determinantal Rings -- 7.1 F-purity -- 7.2 F-regularity -- 7.3 F-rationality and Gröbner Deformations -- 7.4 Equivariant Deformations -- 7.5 F-pure Thresholds -- 8 Castelnuovo-Mumford Regularity -- 8.1 Castelnuovo-Mumford Regularity over General Base Rings.
8.2 Castelnuovo-Mumford Regularity and Multigraded Structures -- 8.3 Vanishing over Nonstandard Multigraded Rings -- 8.4 Regularity of Powers and Products of Ideals -- 8.5 Linear Powers and Linear Products -- 8.6 A Family of Determinantal Ideals with Linear Products -- 8.7 Maximal Minors of Matrices of Linear Forms and Linear Powers -- 9 Grassmannians, Flag Varieties, Schur Functors and Cohomology -- 9.1 Fundamental Multilinear Algebra Constructions -- 9.2 Affine and Projective Bundles, Grassmannians, Flag Varieties -- 9.3 Basic Calculus with Direct Images -- 9.4 The Kempf Vanishing Theorem -- 9.5 Characteristic-Free Vanishing for some Nondominant Weights -- 9.6 A Sharp Characteristic-Free Vanishing on Projective Bundles -- 9.7 Algebraic Groups and Representations -- 9.8 Schur Functors -- 9.9 Grothendieck Duality -- 9.10 Cohomology Vanishing on Grassmannians -- 10 Asymptotic Regularity for Symbolic Powers of Determinantal Ideals -- 10.1 Quotients of Ideals Defined by Shape -- 10.2 Filtrations Associated with Ideals Defined by Shape -- 10.3 An algorithm to Compute Z(Σ) -- 10.4 The Filtration for Symbolic Powers of Determinantal Ideals -- 10.5 Sheaves Defined by Shape and Their Quotients -- 10.6 A Geometric Realization of the Modules J(σ)l -- 10.7 Regularity of Symbolic Powers of Determinantal Ideals -- 10.8 Some Geometric Properties of Determinantal Varieties -- 11 Cohomology and Regularity in Characteristic Zero -- 11.1 The Borel-Weil-Bott Theorem -- 11.2 The Optimality of Theorem 9.5.1摥映數爠eflinkthm:charspsfreespsvanishing9.5.19 -- 11.3 Borel-Weil-Bott on Grassmannians -- 11.4 Effective Vanishing of Cohomology in Characteristic Zero -- 11.5 Cauchy's Formula Revisited -- 11.6 Explicit Description of `3́9`42`"̇613A``45`47`"603AExt Modules for J(σ)l -- 11.7 `3́9`42`"̇613A``45`47`"603AExt Modules for Symbolic Powers.
11.8 The Basics on `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.9 `3́9`42`"̇613A``45`47`"603AExt Modules for `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- 11.10 Local Cohomology with Determinantal Support -- 11.11 Syzygies of `3́9`42`"̇613A``45`47`"603AGL-Invariant Ideals -- Appendix List of Symbols -- References -- -- Index.
Record Nr. UNISA-996503552303316
Bruns Winfried  
Cham, Switzerland : , : Springer, , [2022]
Materiale a stampa
Lo trovi qui: Univ. di Salerno
Opac: Controlla la disponibilità qui
Monogenic Functions in Spaces with Commutative Multiplication and Applications / / by Sergiy A. Plaksa, Vitalii S. Shpakivskyi
Monogenic Functions in Spaces with Commutative Multiplication and Applications / / by Sergiy A. Plaksa, Vitalii S. Shpakivskyi
Autore Plaksa Sergiy A
Edizione [1st ed. 2023.]
Pubbl/distr/stampa Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2023
Descrizione fisica 1 online resource (548 pages)
Disciplina 515.9
Altri autori (Persone) ShpakivskyiVitalii S
Collana Frontiers in Mathematics
Soggetto topico Functions of complex variables
Functions of a Complex Variable
Àlgebra commutativa
Problemes de contorn
Soggetto genere / forma Llibres electrònics
ISBN 3-031-32254-1
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Nota di contenuto Intro -- Foreword -- Preface -- Contents -- 1 Introduction -- References -- Part I Differentiable Mapping in Vector Spaces -- 2 Differentiation in Vector Spaces -- 2.1 Fréchet Differential -- 2.2 Gâteaux Differential -- 2.2.1 Gâteaux Differential and its Properties -- 2.2.2 Examples -- 2.2.3 Relation to the Fréchet derivative -- References -- 3 Monogenic Functions in Vector Spaces with Commutative Multiplication -- 3.1 Differentiability in the Sense of Lorch and in the Sense of Gâteaux in Commutative Banach Algebras -- 3.1.1 Differentiability in the Sense of Lorch -- 3.1.2 Principal Extensions of Holomorphic Functions of a Complex Variable -- 3.1.3 Differentiability in the Sense of Gâteaux -- 3.2 Monogenic Functions -- 3.3 Weakening of Monogeneity Conditions in the Complex Plane -- References -- Part II Monogenic Functions in a Three-Dimensional Commutative Algebra with Two-Dimensional Radical -- 4 Three-Dimensional Harmonic Algebra with Two-Dimensional Radical -- 4.1 Three-Dimensional Harmonic Algebra A3 -- 4.2 Harmonic Bases in the Algebra A3 -- References -- 5 Algebraic-Analytic Properties of Monogenic Functions in the Three-Dimensional Harmonic Algebra with Two-Dimensional Radical -- 5.1 Cauchy-Riemann Conditions for Functions Taking Values in the Algebra A3 -- 5.2 Principal Extensions of Holomorphic Functions of a Complex Variable into the Algebra A3 -- 5.3 Constructive Description of Monogenic Functions Taking Values in the Algebra A3 -- 5.3.1 Main Lemma -- 5.3.2 Main Results -- 5.3.3 Principal Corollaries -- 5.3.4 Monogenic Functions and Solutions of Three-Dimensional Laplace Equation -- 5.4 Isomorphism of Algebras of Monogenic Functions -- References -- 6 Integral Theorems and Series in the Three-Dimensional Harmonic Algebra with Two-Dimensional Radical -- 6.1 Gauss-Ostrogradsky Formula and Cauchy Theorem for a Surface Integral.
6.1.1 Hyperholomorphic Functions -- 6.1.2 Gauss-Ostrogradsky Formula in the Algebra A3 -- 6.1.3 Cauchy Theorem for a Surface Integral -- 6.2 Stokes Formula and Cauchy Theorem for a Curvilinear Integral -- 6.2.1 Stokes Formula in the Algebra A3 -- 6.2.2 Cauchy Theorem for a Curvilinear Integral -- 6.3 Morera Theorem -- 6.4 Cauchy Integral Formula -- 6.5 Power Series and Monogenic Functions -- 6.5.1 Taylor Theorem for Monogenic Functions -- 6.5.2 Uniqueness Theorem for Monogenic Functions -- 6.6 Laurent Series and a Classification of Singular Points of Monogenic Functions -- 6.6.1 Laurent Theorem for Monogenic Functions -- 6.6.2 Classification of Singular Points of Monogenic Functions -- 6.7 Logarithmic Residue of Monogenic Functions -- 6.8 Different Equivalent Definitions of Monogenic Functions and Weakening of Monogeneity Conditions -- 6.8.1 Equivalent Definitions of Monogenic Functions -- 6.8.2 Weakening of the Continuity Condition for a Function -- 6.8.3 An Analog of the Menchov-Trokhimchuk Theorem -- References -- 7 Hypercomplex Cauchy-Type Integral -- 7.1 On the Existence of Limiting Values of Cauchy-Type Integrals in the Complex Plane -- 7.2 Existence of Limiting Values of Hypercomplex Cauchy-Type Integrals on the Line of Integration -- 7.3 Existence of Limiting Values of Hypercomplex Cauchy-Type Integral on the Boundary of Domain -- References -- Part III Monogenic Functions in a Finite-Dimensional Commutative Associative Algebra -- 8 Constructive Description of Monogenic Functions in a Finite-Dimensional Commutative Algebra -- 8.1 Cartan Basis in a Finite-Dimensional Commutative Associative Algebra -- 8.2 Monogenic Functions in Special Subspaces of Algebra -- 8.3 Expansion of Resolvent -- 8.4 Constructive Description of Monogenic Functions -- 8.4.1 Auxiliary Results.
8.4.2 Representation of Monogenic Functions via Holomorphic Functions of Complex Variables -- 8.4.3 Principal Corollaries -- 8.5 Special Cases -- 8.5.1 A Case Where um+1=um+2=…=un -- 8.5.2 A Case Where Br, p0 -- 8.5.3 A Case Where n=m -- 8.6 Some Relations Between Monogenic Functions and PDEs -- References -- 9 Contour Integral Theorems for Monogenic Functions in a Finite-Dimensional Commutative Algebra -- 9.1 Cauchy Theorem and Morera Theorem for a Curvilinear Integral -- 9.2 Cauchy Integral Formula -- 9.2.1 Main Result -- 9.2.2 On a Constant λ -- 9.2.3 Taylor Theorem -- 9.3 Equivalent Definitions of Monogenic Functions -- 9.4 Brief Review of Some Other Results -- References -- 10 Cauchy Theorem for a Surface Integral in a Finite-Dimensional Commutative Algebra -- 10.1 Surface Integrals on Quadrable Surfaces -- 10.2 Hyperholomorphic Functions and Auxiliary Statements -- 10.3 Cauchy Theorem for a Surface Integral -- 10.3.1 Main Result -- 10.3.2 Some Remarks -- References -- 11 On Monogenic Functions Given in Various Commutative Algebras -- 11.1 Characteristic Equation -- 11.1.1 Characteristic Equation in Various Commutative Algebras -- 11.1.2 Linear Independence of Vectors 1,e"0365e2(u),e"0365e3(u) -- 11.2 Monogenic Functions Given in Various Commutative Algebras -- References -- 12 Monogenic Functions on Extensions of a Commutative Algebra -- 12.1 Characteristic Equation in the Algebras An -- 12.2 Extensions of an Algebra and Their Properties -- 12.3 Monogenic Functions on Extensions of the Algebra An -- References -- 13 Hypercomplex Method for Solving Linear Partial Differential Equations with Constant Coefficients -- 13.1 Monogenic Functions in Domains of a Special Space Ed -- 13.2 Families of Solutions of Linear Partial Differential Equations with Constant Coefficients -- 13.2.1 An Equation with Partial Derivatives of Highest Order Only.
13.2.2 An Arbitrary Linear Partial Differential Equation with Constant Coefficients -- 13.3 Families of Solutions Generated by a Sequence of Extensions {Eρn}n=1∞ -- 13.3.1 Solutions of Linear Partial Differential Equations with Constant Coefficients -- 13.3.2 Solutions of Equations with Partial Derivatives of Highest Order Only -- 13.4 Examples -- 13.4.1 Solutions of One Hydrodynamic Equation -- 13.4.2 Solutions of the Three-Dimensional Laplace Equation -- 13.4.3 Solutions of the Wave Equation -- 13.4.4 Solutions of the Equation of Transverse Oscillation of an Elastic Rod -- 13.4.5 Solutions of the Generalized Biharmonic Equation -- 13.4.6 Solutions of the Two-Dimensional Helmholtz Equation -- 13.4.7 Final Remarks -- References -- Part IV Monogenic Functions in Infinite-Dimensional Vector Spaces Associated with the Three-Dimensional Laplace Equation -- 14 Description of Spatial Potential Fields by Means of Monogenic Functions in Infinite-Dimensional Spaces with Commutative Multiplication -- 14.1 Infinite-Dimensional Harmonic Algebra F -- 14.2 Monogenic Functions in the Algebra F -- 14.3 Monogenic Functions in the Topological Vector Space F"0365F Containing the Algebra F -- 14.4 Relation Between Monogenic Functions in F"0365F and Harmonic Vectors -- 14.4.1 Some Conditions for the Existence of Harmonic Vectors -- 14.4.2 Relation Between Monogenic Functions and Harmonic Vectors -- 14.4.3 Monogeneity of Gâteaux Derivatives -- 14.5 Infinite-Dimensional Harmonic Algebra G and Monogenic Functions in G -- 14.6 Monogenic Functions in the Topological Vector Space G"0365G Containing the Algebra G and Relation to Harmonic Vectors -- References -- 15 Monogenic Functions in Complexified Infinite-Dimensional Spaces with Commutative Multiplication -- 15.1 Monogenic and Analytic Functions in the Algebra FC -- 15.2 Integral Theorems for Monogenic Functions in FC.
15.3 Monogenic Functions in the Topological Vector Space F"0365FC and Relation to Spatial Potentials -- 15.3.1 An Extension of Monogenic Functions in F"0365FC -- 15.3.2 Relations to Spatial Potentials -- 15.4 Integral Theorems for Monogenic Functions in F"0365FC -- References -- Part V Monogenic Functions in an Infinite-Dimensional Vector Space Associated with Axial-Symmetric Potential Fields -- 16 Monogenic Functions in an Infinite-Dimensional Commutative Banach Algebra Associated with Axial-Symmetric Potential Fields -- 16.1 Spatial Stationary Axial-Symmetric Potential Solenoidal Fields -- 16.2 Infinite-Dimensional Commutative Banach Algebra HC -- 16.3 Monogenic and Analytic Functions in ``Meridian'' Plane μ -- 16.4 Relation to Axial-Symmetric Potential Fields -- 16.4.1 Relation of Monogenic Functions in Proper Domains to Axial-Symmetric Potential Fields -- 16.4.2 Integral Expression for the Axial-Symmetric Potential in a Proper Domain -- 16.4.3 Integral Expression for Stokes' Flow Function in a Proper Domain -- 16.5 Relation to Elliptic Equations Degenerating on an Axis -- 16.6 Monogenic Functions and Principal Extensions of Holomorphic Functions into Three-Dimensional Linear Manifold M -- 16.7 Integral Theorems for Monogenic Functions Taking Values in the Algebra HC -- References -- 17 Monogenic Functions in a Topological Vector Space Associated with Axial-Symmetric Potential Fields -- 17.1 Monogenic Functions Taking Values in a Topological Vector Space H"0365HC Containing the Algebra HC -- 17.2 Integral Theorems for Monogenic Functions Taking Valuesin H"0365HC -- 17.3 Relation to Axial-Symmetric Potential Fields -- References -- Part VI Boundary Value Problems for Axial-Symmetric Potential Fields -- 18 Integral Representations for the Axial-Symmetric Potential and Stokes' Flow Function in an Arbitrary Simply-Connected Domain.
18.1 Direct Theorems.
Record Nr. UNINA-9910735090403321
Plaksa Sergiy A  
Cham : , : Springer Nature Switzerland : , : Imprint : Birkhäuser, , 2023
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui
Recent developments in commutative algebra : levico terma, trento 2019 / / Claudia Polini, 3 others
Recent developments in commutative algebra : levico terma, trento 2019 / / Claudia Polini, 3 others
Autore Polini Claudia <1966->
Edizione [1st ed. 2021.]
Pubbl/distr/stampa Cham, Switzerland : , : Springer, , [2021]
Descrizione fisica 1 online resource (XI, 118 p. 17 illus., 1 illus. in color.)
Disciplina 512.44
Collana C.I.M.E. Foundation Subseries
Soggetto topico Commutative algebra
Geometry, Algebraic
Àlgebra commutativa
Geometria algebraica
Soggetto genere / forma Llibres electrònics
ISBN 3-030-65064-2
Formato Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione eng
Record Nr. UNINA-9910484461703321
Polini Claudia <1966->  
Cham, Switzerland : , : Springer, , [2021]
Materiale a stampa
Lo trovi qui: Univ. Federico II
Opac: Controlla la disponibilità qui