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Change and invariance : a textbook on algebraic insight into numbers and shapes / / Ilya Sinitsky and Bat-Sheva Ilany
| Change and invariance : a textbook on algebraic insight into numbers and shapes / / Ilya Sinitsky and Bat-Sheva Ilany |
| Autore | Sinitsky Ilya |
| Edizione | [1st ed. 2016.] |
| Pubbl/distr/stampa | Rotterdam, The Netherlands ; ; Boston ; ; Taipei : , : Sense Publishers, , [2016] |
| Descrizione fisica | 1 online resource (XIV, 378 p.) |
| Disciplina | 516.1 |
| Collana | Education Series |
| Soggetto topico |
Symmetry (Mathematics)
Mathematics - Study and teaching Mathematical models Algebra Geometry, Algebraic Mathematics - Philosophy |
| ISBN |
9789463006989
9463006982 |
| Formato | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- Acknowledgements -- The Concept of Invariance and Change: Theoretical Background -- Understanding Phenomena from the Aspect of Invariance and Change -- The Concept of Invariance and Change in the Mathematical Knowledge of Students -- The Basic Interplay between Invariance and Change -- Some Introductory Activities in Invariance and Change -- References -- Invariant Quantities – What Is Invariant and What Changes? -- Introduction: Understanding the Invariance of Quantity as a Basis for Quantitative Thinking -- Activity 2.1: Dividing Dolls between Two Children -- Mathematic and Didactic Analysis of Activity 2.1: Partitioning a Set into Two Subsets: Posing Problems and Partition Methods -- Activity 2.2: How to Split a Fraction. Almost Like Ancient Egypt -- Mathematic and Didactic Analysis of Activity 2.2: Invariance of Quantity and Splitting of Unit Fractions -- Activity 2.3: They Are All Equal, But … -- Mathematic and Didactic Analysis of Activity 2.3: From Equal Addends to Consecutive Addends -- Activity 2.4: Expressing a Natural Number as Infinite Series -- Suggestions for Further Activities -- References -- The Influence of Change -- Introduction: Changes in Quantity and Comparing Amounts -- Activity 3.1: Less or More? -- Mathematical and Didactic Analysis of Activity 3.1: The influence That a Change in One Operand Has on the Value of an Arithmetical Expression -- Activity 3.2: Plus How Much or Times How Much? -- Mathematical and Didactic Analysis of Activity 3.2: Different Ways of Comparing -- Activity 3.3: Markups, Markdowns and the Order of Operations -- Mathematical and Didactic Analysis of Activity 3.3: Repeated Changes in Percentages -- Activity 3.4: Invariant or Not? -- Mathematical and Didactic Analysis of Activity 3.4: Products and Extremum Problems -- Activity 3.5: What Is the Connection between Mathematical Induction and Invariance and Change? -- Mathematical and Didactic Analysis of Activity 3.5: What Is the Connection between Mathematical Induction and Invarianceand Change? -- Suggestions for Further Activities -- References -- Introducing Change for the Sake of Invariance -- Introduction: Algorithms – Introducing Change for the Sake of Invariance -- Activity 4.1: The “Compensation Rule”: What Is It? -- Mathematical and Didactic Analysis of Activity 4.1: Changes in the Components of Mathematical Operations That Ensure the Invariance of the Result -- Activity 4.2: Divisibility Tests -- Mathematical and Didactic Analysis of Activity 4.2: Invariance of Divisibility and Composing of Divisibility Tests -- Activity 4.3: Basket Configuration Problems -- Mathematical and Didactic Analysis of Activity 4.3: Diophantine Problems and Determining the Change and Invariance -- Activity 4.4: Product = Sum? -- Mathematical and Didactic Analysis for the Activities in 4.4: Invariance as a Constraint -- Suggestions for Further Activities -- References -- Discovering Hidden Invariance -- Introduction: Discovering Hidden Invariance as a Way of Understanding Various Phenomena -- Activity 5.1: How to Add Numerous Consecutive Numbers -- Mathematical and Didactic Analysis of Activity 5.1: The Arithmetic Series: Examples of Use of the Interplay between Change and Invariance in Calculations -- Activity 5.2: Solving Verbal Problems: Age, Speed, and Comparing the Concentrations of Chemical Solutions -- Mathematic and Didactic Analysis of Activity 5.2: Solving Verbal Problems by Discovering the Hidden Invariance -- Activity 5.3: Mathematical Magic – Guessing Numbers -- Mathematical and Didactic Analysis of Activity 5.3: Discovering the Invariant in Mathematical “Tricks”: “Guessing Numbers” -- Activity 5.4: “Why Can’t I Succeed?” -- Mathematical and Didactic Analysis of Activity 5.4: Discovering the Hidden Invariance in “Why Can’t I Succeed?” -- Suggestions for Further Activities -- References -- Change and Invariance in Geometric Shapes -- Introduction: Invariance and Change in the World of Geometry -- Activity 6.1: Halving in Geometry – Splitting Shapes -- Mathematical and DidacticAnalysis of Activity 6.1: Invariance and Change When Dividing Polygons -- Activity 6.2: What Can One Assemble from Two Triangles? -- Mathematical and Didactic Analysis of Activity 6.2: Invariance and Change When Constructing Polygons from Triangles -- Activity 6.3: How Can a Parallelogram Change? -- Mathematical and Didactic Analysis of Activity 6.3: Invariance and Change of Dimensions in the Set of Parallelograms -- Activity 6.4: Identical Perimeters -- Mathematical and Didactic Analysis of Activity 6.4: Preserving the Perimeter -- Summary of the Roles of Invariance and Change in Geometrical Shapes -- Suggestions for Further Activities -- References. |
| Record Nr. | UNINA-9910155546803321 |
Sinitsky Ilya
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| Rotterdam, The Netherlands ; ; Boston ; ; Taipei : , : Sense Publishers, , [2016] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Complex symmetries / / György Darvas, editor
| Complex symmetries / / György Darvas, editor |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (268 pages) |
| Disciplina | 516.1 |
| Soggetto topico |
Symmetry (Mathematics)
Mathematics in art Complexity (Philosophy) in art Simetria (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030880590
9783030880583 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466559603316 |
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Complex symmetries / / György Darvas, editor
| Complex symmetries / / György Darvas, editor |
| Pubbl/distr/stampa | Cham, Switzerland : , : Birkhäuser, , [2021] |
| Descrizione fisica | 1 online resource (268 pages) |
| Disciplina | 516.1 |
| Soggetto topico |
Symmetry (Mathematics)
Mathematics in art Complexity (Philosophy) in art Simetria (Matemàtica) |
| Soggetto genere / forma | Llibres electrònics |
| ISBN |
9783030880590
9783030880583 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910520065803321 |
| Cham, Switzerland : , : Birkhäuser, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Conformal Symmetry Breaking Differential Operators on Differential Forms
| Conformal Symmetry Breaking Differential Operators on Differential Forms |
| Autore | Fischmann Matthias |
| Edizione | [1st ed.] |
| Pubbl/distr/stampa | Providence : , : American Mathematical Society, , 2021 |
| Descrizione fisica | 1 online resource (124 pages) |
| Disciplina | 516.3/5 |
| Altri autori (Persone) |
JuhlAndreas
SombergPetr |
| Collana | Memoirs of the American Mathematical Society |
| Soggetto topico |
Differential operators
Conformal geometry Symmetry (Mathematics) Topological groups, Lie groups {For transformation groups, see 54H15, 57Sxx, 58-XX. For abstract harmonic analysis, see 43-XX} -- Lie groups {For the topology of Lie groups and homogeneous spaces, see Partial differential equations -- Elliptic equations and systems [See also 58J10, 58J20] -- Higher-order elliptic equations [See also 31A30, 31B30] Differential geometry {For differential topology, see 57Rxx. For foundational questions of differentiable manifolds, see 58Axx} -- Classical differential geometry -- Conformal differential geometry Special functions (33-XX deals with the properties of functions as functions) {For orthogonal functions, see 42Cxx; for aspects of combinatorics see 05Axx; for number-theoretic aspects see 11-XX; for |
| ISBN |
9781470463397
1470463393 |
| Classificazione | 22E4635J3053A3022E4733C45 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Cover -- Title page -- Chapter 1. Introduction -- Chapter 2. Preliminaries -- 2.1. The -method -- 2.2. Notation and induced representations -- 2.3. A branching problem -- Chapter 3. Singular vectors -- 3.1. The \gol′-equivariance -- 3.2. Families of singular vectors of the first type -- 3.3. Families of singular vectors of the second type -- 3.4. Singular vectors of the third type -- 3.5. Singular vectors of the fourth type -- 3.6. Middle degree cases -- Chapter 4. Conformal symmetry breaking differential operators on differential forms -- 4.1. Families of the first type -- 4.2. Families of the second type -- 4.3. Hodge conjugation -- 4.4. Operators of the third type -- 4.5. Operators of the fourth type -- 4.6. Operators on middle degree forms -- 4.7. Proof of Theorem 3 -- 4.8. Examples -- Chapter 5. Geometric formulas for conformal symmetry breaking operators -- 5.1. Preparations -- 5.2. Even-order families of the first and second type -- 5.3. Odd-order families of the first and second type -- 5.4. Operators of the third and fourth type -- Chapter 6. Factorization identities for conformal symmetry breaking operators -- 6.1. Branson-Gover, gauge companion and -curvature operators -- 6.2. Main factorizations -- 6.3. Supplementary factorizations -- 6.4. Applications -- Appendix: Gegenbauer and Jacobi polynomials -- Bibliography -- Back Cover. |
| Record Nr. | UNINA-9910959539903321 |
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Fischmann Matthias
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| Providence : , : American Mathematical Society, , 2021 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Deformations of space-time symmetries : gravity, group-valued momenta and non-commutative fields / / Michele Arzano, Jerzy Kowalski-Glikman
| Deformations of space-time symmetries : gravity, group-valued momenta and non-commutative fields / / Michele Arzano, Jerzy Kowalski-Glikman |
| Autore | Arzano Michele |
| Pubbl/distr/stampa | Berlin, Heidelberg : , : Springer-Verlag, , [2021] |
| Descrizione fisica | 1 online resource (198 pages) |
| Disciplina | 530.15 |
| Collana | Lecture Notes in Physics |
| Soggetto topico |
Mathematical physics
Symmetry (Mathematics) Noncommutative algebras |
| ISBN | 3-662-63097-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISA-996466847003316 |
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Arzano Michele
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| Berlin, Heidelberg : , : Springer-Verlag, , [2021] | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. di Salerno | ||
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Differential geometry of singular spaces and reduction of symmetry / / J. Śniatycki, Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada [[electronic resource]]
| Differential geometry of singular spaces and reduction of symmetry / / J. Śniatycki, Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, Canada [[electronic resource]] |
| Autore | Śniatycki Jędrzej |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xii, 235 pages) : digital, PDF file(s) |
| Disciplina | 516.3/6 |
| Collana | New mathematical monographs |
| Soggetto topico |
Geometry, Differential
Function spaces Symmetry (Mathematics) |
| ISBN |
1-139-88895-1
1-107-05451-6 1-107-05905-4 1-139-13699-2 1-107-05559-8 1-107-05780-9 1-107-05668-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1. Introduction -- Part I. Differential Geometry of Singular Spaces: 2. Differential structures; 3. Derivations; 4. Stratified spaces; 5. Differential forms -- Part II. Reduction of Symmetries: 6. Symplectic reduction; 7. Commutation of quantization and reduction; 8. Further examples of reduction. |
| Altri titoli varianti | Differential Geometry of Singular Spaces & Reduction of Symmetry |
| Record Nr. | UNINA-9910452484303321 |
|
Śniatycki Jędrzej
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| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Differential geometry of singular spaces and reduction of symmetry [[electronic resource] /] / J. Śniatycki
| Differential geometry of singular spaces and reduction of symmetry [[electronic resource] /] / J. Śniatycki |
| Autore | Śniatycki Jędrzej |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xii, 235 pages) : digital, PDF file(s) |
| Disciplina | 516.3/6 |
| Collana | New mathematical monographs |
| Soggetto topico |
Geometry, Differential
Function spaces Symmetry (Mathematics) |
| ISBN |
1-107-06512-7
1-139-88895-1 1-107-05451-6 1-107-05905-4 1-139-13699-2 1-107-05559-8 1-107-05780-9 1-107-05668-3 |
| Classificazione | MAT038000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1. Introduction -- Part I. Differential Geometry of Singular Spaces: 2. Differential structures; 3. Derivations; 4. Stratified spaces; 5. Differential forms -- Part II. Reduction of Symmetries: 6. Symplectic reduction; 7. Commutation of quantization and reduction; 8. Further examples of reduction. |
| Altri titoli varianti | Differential Geometry of Singular Spaces & Reduction of Symmetry |
| Record Nr. | UNINA-9910779752603321 |
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Śniatycki Jędrzej
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| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Differential geometry of singular spaces and reduction of symmetry [[electronic resource] /] / J. Śniatycki
| Differential geometry of singular spaces and reduction of symmetry [[electronic resource] /] / J. Śniatycki |
| Autore | Śniatycki Jędrzej |
| Pubbl/distr/stampa | Cambridge : , : Cambridge University Press, , 2013 |
| Descrizione fisica | 1 online resource (xii, 235 pages) : digital, PDF file(s) |
| Disciplina | 516.3/6 |
| Collana | New mathematical monographs |
| Soggetto topico |
Geometry, Differential
Function spaces Symmetry (Mathematics) |
| ISBN |
1-107-06512-7
1-139-88895-1 1-107-05451-6 1-107-05905-4 1-139-13699-2 1-107-05559-8 1-107-05780-9 1-107-05668-3 |
| Classificazione | MAT038000 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Preface -- 1. Introduction -- Part I. Differential Geometry of Singular Spaces: 2. Differential structures; 3. Derivations; 4. Stratified spaces; 5. Differential forms -- Part II. Reduction of Symmetries: 6. Symplectic reduction; 7. Commutation of quantization and reduction; 8. Further examples of reduction. |
| Altri titoli varianti | Differential Geometry of Singular Spaces & Reduction of Symmetry |
| Record Nr. | UNINA-9910824597603321 |
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Śniatycki Jędrzej
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| Cambridge : , : Cambridge University Press, , 2013 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Discrete Mathematics and Symmetry / / edited by Angel Garrido
| Discrete Mathematics and Symmetry / / edited by Angel Garrido |
| Pubbl/distr/stampa | Basel : , : MDPI - Multidisciplinary Digital Publishing Institute, , 2020 |
| Descrizione fisica | 1 online resource (458 pages) : illustrations |
| Disciplina | 516.1 |
| Soggetto topico | Symmetry (Mathematics) |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNINA-9910673903003321 |
| Basel : , : MDPI - Multidisciplinary Digital Publishing Institute, , 2020 | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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Dynamics and symmetry [[electronic resource] /] / Michael J. Field
| Dynamics and symmetry [[electronic resource] /] / Michael J. Field |
| Autore | Field Mike |
| Pubbl/distr/stampa | London, : Imperial College Press |
| Descrizione fisica | 1 online resource (492 p.) |
| Disciplina | 515.35 |
| Collana | ICP advanced texts in mathematics |
| Soggetto topico |
Topological dynamics
Lie groups Hamiltonian systems Bifurcation theory Symmetry (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-86756-X
9786611867560 1-86094-854-5 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
Contents; Preface; 1. Groups; 1.1 Definition of a group and examples; 1.2 Homomorphisms, subgroups and quotient groups; 1.2.1 Generators and relations for .nite groups; 1.3 Constructions; 1.4 Topological groups; 1.5 Lie groups; 1.5.1 The Lie bracket of vector fields; 1.5.2 The Lie algebra of G; 1.5.3 The exponential map of g; 1.5.4 Additional properties of brackets and exp; 1.5.5 Closed subgroups of a Lie group; 1.6 Haarmeasure; 2. Group Actions and Representations; 2.1 Introduction; 2.2 Groups and G-spaces; 2.2.1 Continuous actions and G-spaces; 2.3 Orbit spaces and actions
2.4 Twisted products2.4.1 Induced G-spaces; 2.5 Isotropy type and stratification by isotropy type; 2.6 Representations; 2.6.1 Averaging over G; 2.7 Irreducible representations and the isotypic decomposition; 2.7.1 C-representations; 2.7.2 Absolutely irreducible representations; 2.8 Orbit structure for representations; 2.9 Slices; 2.9.1 Slices for linear finite group actions; 2.10 Invariant and equivariant maps; 2.10.1 Smooth invariant and equivariant maps on representations; 2.10.2 Equivariant vector fields and flows; 3. Smooth G-manifolds; 3.1 Proper G-manifolds; 3.1.1 Proper free actions 3.2 G-vector bundles3.3 Infinitesimal theory; 3.4 Riemannianmanifolds; 3.4.1 Exponential map of a complete Riemannian manifold; 3.4.2 The tubular neighbourhood theorem; 3.4.3 Riemannian G-manifolds; 3.5 The differentiable slice theorem; 3.6 Equivariant isotopy extension theorem; 3.7 Orbit structure for G-manifolds; 3.7.1 Closed filtration of M by isotropy type; 3.8 The stratification of M by normal isotropy type; 3.9 Stratified sets; 3.9.1 Transversality to a Whitney stratification; 3.9.2 Regularity of stratification by normal isotropy type 3.10 Invariant Riemannian metrics on a compact Lie group3.10.1 The adjoint representations; 3.10.2 The exponential map; 3.10.3 Closed subgroups of a Lie group; 4. Equivariant Bifurcation Theory: Steady State Bifurcation; 4.1 Introduction and preliminaries; 4.1.1 Normalized families; 4.2 Solution branches and the branching pattern; 4.2.1 Stability of branching patterns; 4.3 Symmetry breaking-theMISC; 4.3.1 Symmetry breaking isotropy types; 4.3.2 Maximal isotropy subgroup conjecture; 4.4 Determinacy; 4.4.1 Polynomial maps; 4.4.2 Finite determinacy; 4.5 The hyperoctahedral family 4.5.1 The representations (Rk,Hk)4.5.2 Invariants and equivariants for Hk; 4.5.3 Cubic equivariants for Hk; 4.5.4 Bifurcation for cubic families; 4.5.5 Subgroups of Hk; 4.5.6 Some subgroups of the symmetric group; 4.5.7 A big family of counterexamples to the MISC; 4.5.8 Examples where P3G (Rk, Rk) = P3H k (Rk, Rk); 4.5.9 Stable solution branches of maximal index and trivial isotropy; 4.5.10 An example with applications to phase transitions; 4.6 Phase vector field and maps of hyperbolic type; 4.6.1 Cubic polynomial maps; 4.6.2 Phase vector field; 4.6.3 Normalized families 4.6.4 Maps of hyperbolic type |
| Record Nr. | UNINA-9910458099103321 |
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Field Mike
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| London, : Imperial College Press | ||
| Materiale a stampa | ||
| Lo trovi qui: Univ. Federico II | ||
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