Coulomb frames in the normal bundle of surfaces in Euclidean spaces : topics from differential geometry and geometric analysis of surfaces / / Steffen Frohlich
| Coulomb frames in the normal bundle of surfaces in Euclidean spaces : topics from differential geometry and geometric analysis of surfaces / / Steffen Frohlich |
| Autore | Frohlich Steffen <1973-> |
| Edizione | [1st ed. 2012.] |
| Pubbl/distr/stampa | Heidelberg ; ; New York, : Springer Verlag, 2012 |
| Descrizione fisica | 1 online resource (XIV, 117 p.) |
| Disciplina | 516.36 |
| Collana | Lecture notes in mathematics |
| Soggetto topico |
Geometry, Differential
Frames (Combinatorial analysis) |
| ISBN | 3-642-29846-X |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Surface Geometry -- Elliptic Systems -- Normal Coulomb Frames in R4 -- Normal Coulomb Frames in Rn+2. |
| Record Nr. | UNINA-9910484159103321 |
Frohlich Steffen <1973->
|
||
| Heidelberg ; ; New York, : Springer Verlag, 2012 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Coulomb frames in the normal bundle of surfaces in Euclidean spaces : topics from differential geometry and geometric analysis of surfaces / Steffen Fröhlich
| Coulomb frames in the normal bundle of surfaces in Euclidean spaces : topics from differential geometry and geometric analysis of surfaces / Steffen Fröhlich |
| Autore | Fröhlich, Steffen |
| Pubbl/distr/stampa | Heidelberg ; New York : Springer Verlag, 2012 |
| Descrizione fisica | xiv, 117 p. : ill. ; 23 cm |
| Disciplina | 516.36 |
| Collana | Lecture notes in mathematics, 0075-8434 ; 2053 |
| Soggetto topico |
Geometry, Differential
Frames (Combinatorial analysis) |
| ISBN | 9783642298455 |
| Classificazione |
AMS 53A07
AMS 53A10 AMS 35J15 AMS 35J47 LC QA3.L38 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991001860379707536 |
Fröhlich, Steffen
|
||
| Heidelberg ; New York : Springer Verlag, 2012 | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Frames and resolvable designs : uses, constructions, and existence / Steven Furino, Miao Ying, Jianxing Yin
| Frames and resolvable designs : uses, constructions, and existence / Steven Furino, Miao Ying, Jianxing Yin |
| Autore | Furino, Steven |
| Pubbl/distr/stampa | Boca Raton, Fla : CRC Press, c1996 |
| Descrizione fisica | 248 p. : ill. ; 25 cm. |
| Disciplina | 511.6 |
| Altri autori (Persone) |
Miao, Yingauthor
Yin, Jianxingauthor |
| Collana | The CRC Press series on discrete mathematics and its applications |
| Soggetto topico |
Block designs
Frames (Combinatorial analysis) |
| ISBN | 0849339847 |
| Classificazione |
AMS 05B05
QA166.25.F87 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Record Nr. | UNISALENTO-991000911639707536 |
Furino, Steven
|
||
| Boca Raton, Fla : CRC Press, c1996 | ||
| Lo trovi qui: Univ. del Salento | ||
| ||
Operator methods in wavelets, tilings, and frames / / Veronika Furst, Keri A. Kornelson, Eric S. Weber, editors
| Operator methods in wavelets, tilings, and frames / / Veronika Furst, Keri A. Kornelson, Eric S. Weber, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
| Descrizione fisica | 1 online resource (177 p.) |
| Disciplina | 511/.6 |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Frames (Combinatorial analysis)
Wavelets (Mathematics) |
| Soggetto genere / forma | Electronic books. |
| ISBN | 1-4704-1957-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Participants""; ""Phase retrieval by vectors and projections""; ""1. INTRODUCTION""; ""2. PHASE RETRIEVAL BY VECTORS""; ""3. PHASE RETRIEVAL BY PROJECTIONS""; ""References""; ""Scalable frames and convex geometry""; ""1. Introduction""; ""2. Preliminaries""; ""3. Scalable Frames and Convex Polytopes""; ""4. Topology of the Set of Scalable Frames""; ""ACKNOWLEDGMENTS""; ""References""; ""Dilations of frames, operator-valued measures and bounded linear maps""; ""1. Introduction""; ""2. Frames, Framings, and Operator-Valued Measures""
""3. Dilations of Operator-Valued Measures""""4. Dilations of Bounded Linear Maps""; ""5. Some Remarks and Problems""; ""References""; ""Images of the continuous wavelet transform""; ""1. Introduction""; ""2. General notations and definitions""; ""3. Wavelets and square-integrable representations""; ""4. Inside _{\overline{ }}( ) for an irreducible ""; ""5. The _{ } as subspaces of â??²( )""; ""References""; ""Decompositions of generalized wavelet representations""; ""1. Introduction""; ""2. Preliminaries""; ""3. Direct Integral Decompositions"" ""4. Irreducibility of the Fiber Representations""""Acknowledgment""; ""References""; ""Exponential splines of complex order""; ""1. Preliminaries on Exponential Splines""; ""2. Brief Review of Polynomial and Exponential B-Splines""; ""3. Polynomial Splines of Complex Order""; ""4. Exponential Splines of Complex Order""; ""5. Summary and Further Work""; ""References""; ""Local translations associated to spectral sets""; ""1. Introduction""; ""2. Local translations""; ""3. Examples""; ""References""; ""Additive spectra of the 1/4 Cantor measure""; ""1. Introduction""; ""2. Background"" ""3. Isometries""""4. Spectral function decompositions""; ""Acknowledgements""; ""References""; ""Necessary density conditions for sampling and interpolation in de Branges spaces""; ""1. Introduction""; ""2. Homogeneous Approximation Property""; ""3. Necessary Conditions for Sampling and Interpolating""; ""4. The Plancherelâ€?Polya Inequality""; ""References""; ""Dynamical sampling in hybrid shift invariant spaces""; ""1. Introduction""; ""2. Constructing a hybrid shift invariant space""; ""3. Dynamical sampling in hybrid shift invariant spaces""; ""4. Main results"" ""5. Conclusions and future work""""6. Appendix""; ""Acknowledgment""; ""References""; ""Dynamical sampling in infinite dimensions with and without a forcing term""; ""1. Introduction""; ""2. Dynamical sampling in infinite dimensions""; ""3. Dynamical Sampling with a Forcing Term""; ""References""; ""Back Cover"" |
| Record Nr. | UNINA-9910478913703321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Operator methods in wavelets, tilings, and frames / / Veronika Furst, Keri A. Kornelson, Eric S. Weber, editors
| Operator methods in wavelets, tilings, and frames / / Veronika Furst, Keri A. Kornelson, Eric S. Weber, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
| Descrizione fisica | 1 online resource (177 p.) |
| Disciplina | 511/.6 |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Frames (Combinatorial analysis)
Wavelets (Mathematics) |
| ISBN | 1-4704-1957-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Participants""; ""Phase retrieval by vectors and projections""; ""1. INTRODUCTION""; ""2. PHASE RETRIEVAL BY VECTORS""; ""3. PHASE RETRIEVAL BY PROJECTIONS""; ""References""; ""Scalable frames and convex geometry""; ""1. Introduction""; ""2. Preliminaries""; ""3. Scalable Frames and Convex Polytopes""; ""4. Topology of the Set of Scalable Frames""; ""ACKNOWLEDGMENTS""; ""References""; ""Dilations of frames, operator-valued measures and bounded linear maps""; ""1. Introduction""; ""2. Frames, Framings, and Operator-Valued Measures""
""3. Dilations of Operator-Valued Measures""""4. Dilations of Bounded Linear Maps""; ""5. Some Remarks and Problems""; ""References""; ""Images of the continuous wavelet transform""; ""1. Introduction""; ""2. General notations and definitions""; ""3. Wavelets and square-integrable representations""; ""4. Inside _{\overline{ }}( ) for an irreducible ""; ""5. The _{ } as subspaces of â??²( )""; ""References""; ""Decompositions of generalized wavelet representations""; ""1. Introduction""; ""2. Preliminaries""; ""3. Direct Integral Decompositions"" ""4. Irreducibility of the Fiber Representations""""Acknowledgment""; ""References""; ""Exponential splines of complex order""; ""1. Preliminaries on Exponential Splines""; ""2. Brief Review of Polynomial and Exponential B-Splines""; ""3. Polynomial Splines of Complex Order""; ""4. Exponential Splines of Complex Order""; ""5. Summary and Further Work""; ""References""; ""Local translations associated to spectral sets""; ""1. Introduction""; ""2. Local translations""; ""3. Examples""; ""References""; ""Additive spectra of the 1/4 Cantor measure""; ""1. Introduction""; ""2. Background"" ""3. Isometries""""4. Spectral function decompositions""; ""Acknowledgements""; ""References""; ""Necessary density conditions for sampling and interpolation in de Branges spaces""; ""1. Introduction""; ""2. Homogeneous Approximation Property""; ""3. Necessary Conditions for Sampling and Interpolating""; ""4. The Plancherelâ€?Polya Inequality""; ""References""; ""Dynamical sampling in hybrid shift invariant spaces""; ""1. Introduction""; ""2. Constructing a hybrid shift invariant space""; ""3. Dynamical sampling in hybrid shift invariant spaces""; ""4. Main results"" ""5. Conclusions and future work""""6. Appendix""; ""Acknowledgment""; ""References""; ""Dynamical sampling in infinite dimensions with and without a forcing term""; ""1. Introduction""; ""2. Dynamical sampling in infinite dimensions""; ""3. Dynamical Sampling with a Forcing Term""; ""References""; ""Back Cover"" |
| Record Nr. | UNINA-9910788255703321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Operator methods in wavelets, tilings, and frames / / Veronika Furst, Keri A. Kornelson, Eric S. Weber, editors
| Operator methods in wavelets, tilings, and frames / / Veronika Furst, Keri A. Kornelson, Eric S. Weber, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , 2014 |
| Descrizione fisica | 1 online resource (177 p.) |
| Disciplina | 511/.6 |
| Collana | Contemporary Mathematics |
| Soggetto topico |
Frames (Combinatorial analysis)
Wavelets (Mathematics) |
| ISBN | 1-4704-1957-2 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Cover""; ""Title page""; ""Contents""; ""Preface""; ""Participants""; ""Phase retrieval by vectors and projections""; ""1. INTRODUCTION""; ""2. PHASE RETRIEVAL BY VECTORS""; ""3. PHASE RETRIEVAL BY PROJECTIONS""; ""References""; ""Scalable frames and convex geometry""; ""1. Introduction""; ""2. Preliminaries""; ""3. Scalable Frames and Convex Polytopes""; ""4. Topology of the Set of Scalable Frames""; ""ACKNOWLEDGMENTS""; ""References""; ""Dilations of frames, operator-valued measures and bounded linear maps""; ""1. Introduction""; ""2. Frames, Framings, and Operator-Valued Measures""
""3. Dilations of Operator-Valued Measures""""4. Dilations of Bounded Linear Maps""; ""5. Some Remarks and Problems""; ""References""; ""Images of the continuous wavelet transform""; ""1. Introduction""; ""2. General notations and definitions""; ""3. Wavelets and square-integrable representations""; ""4. Inside _{\overline{ }}( ) for an irreducible ""; ""5. The _{ } as subspaces of â??²( )""; ""References""; ""Decompositions of generalized wavelet representations""; ""1. Introduction""; ""2. Preliminaries""; ""3. Direct Integral Decompositions"" ""4. Irreducibility of the Fiber Representations""""Acknowledgment""; ""References""; ""Exponential splines of complex order""; ""1. Preliminaries on Exponential Splines""; ""2. Brief Review of Polynomial and Exponential B-Splines""; ""3. Polynomial Splines of Complex Order""; ""4. Exponential Splines of Complex Order""; ""5. Summary and Further Work""; ""References""; ""Local translations associated to spectral sets""; ""1. Introduction""; ""2. Local translations""; ""3. Examples""; ""References""; ""Additive spectra of the 1/4 Cantor measure""; ""1. Introduction""; ""2. Background"" ""3. Isometries""""4. Spectral function decompositions""; ""Acknowledgements""; ""References""; ""Necessary density conditions for sampling and interpolation in de Branges spaces""; ""1. Introduction""; ""2. Homogeneous Approximation Property""; ""3. Necessary Conditions for Sampling and Interpolating""; ""4. The Plancherelâ€?Polya Inequality""; ""References""; ""Dynamical sampling in hybrid shift invariant spaces""; ""1. Introduction""; ""2. Constructing a hybrid shift invariant space""; ""3. Dynamical sampling in hybrid shift invariant spaces""; ""4. Main results"" ""5. Conclusions and future work""""6. Appendix""; ""Acknowledgment""; ""References""; ""Dynamical sampling in infinite dimensions with and without a forcing term""; ""1. Introduction""; ""2. Dynamical sampling in infinite dimensions""; ""3. Dynamical Sampling with a Forcing Term""; ""References""; ""Back Cover"" |
| Record Nr. | UNINA-9910808056003321 |
| Providence, Rhode Island : , : American Mathematical Society, , 2014 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Representations, wavelets, and frames [[electronic resource] ] : a celebration of the mathematical work of Lawrence W. Baggett / / Palle E.T. Jorgensen, Kathy D. Merrill, Judith A. Packer, editors
| Representations, wavelets, and frames [[electronic resource] ] : a celebration of the mathematical work of Lawrence W. Baggett / / Palle E.T. Jorgensen, Kathy D. Merrill, Judith A. Packer, editors |
| Edizione | [1st ed. 2008.] |
| Pubbl/distr/stampa | Boston, : Birkhäuser, 2008 |
| Descrizione fisica | 1 online resource (351 p.) |
| Disciplina | 515.2433 |
| Altri autori (Persone) |
JørgensenPalle E. T. <1947->
MerrillKathy Donovan PackerJudith A BaggettLawrence W. <1939-> |
| Collana | Applied and numerical harmonic analysis |
| Soggetto topico |
Wavelets (Mathematics)
Frames (Combinatorial analysis) Representations of Banach modules |
| Soggetto genere / forma | Electronic books. |
| ISBN |
1-281-86132-4
9786611861322 0-8176-4683-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Classical and Abstract Harmonic Analysis -- Some Riemann Sums Are Better Than Others -- Gelfand Pairs Associated with Finite Heisenberg Groups -- Groups with Atomic Regular Representation -- Wavelet Transforms and Admissible Group Representations -- Frames and Multiresolution Structures -- The Density Theorem and the Homogeneous Approximation Property for Gabor Frames -- Recent Developments on Dual Wavelet Frames -- Characteristic Wavelet Equations and Generalizations of the Spectral Function -- Baggett’s Problem for Frame Wavelets -- Wavelet Sets -- Simple Wavelet Sets for Scalar Dilations in ?2 -- Interpolation Maps and Congruence Domains for Wavelet Sets -- Applications to Dynamical Systems and C*-Algebras -- Orthogonal Exponentials for Bernoulli Iterated Function Systems -- A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice -- Signal and Image Processing -- Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals -- Entropy Encoding in Wavelet Image Compression. |
| Record Nr. | UNINA-9910451725003321 |
| Boston, : Birkhäuser, 2008 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Representations, wavelets, and frames [[electronic resource] ] : a celebration of the mathematical work of Lawrence W. Baggett / / Palle E.T. Jorgensen, Kathy D. Merrill, Judith A. Packer, editors
| Representations, wavelets, and frames [[electronic resource] ] : a celebration of the mathematical work of Lawrence W. Baggett / / Palle E.T. Jorgensen, Kathy D. Merrill, Judith A. Packer, editors |
| Edizione | [1st ed. 2008.] |
| Pubbl/distr/stampa | Boston, : Birkhäuser, 2008 |
| Descrizione fisica | 1 online resource (351 p.) |
| Disciplina | 515.2433 |
| Altri autori (Persone) |
JørgensenPalle E. T. <1947->
MerrillKathy Donovan PackerJudith A BaggettLawrence W. <1939-> |
| Collana | Applied and numerical harmonic analysis |
| Soggetto topico |
Wavelets (Mathematics)
Frames (Combinatorial analysis) Representations of Banach modules |
| ISBN |
1-281-86132-4
9786611861322 0-8176-4683-3 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto | Classical and Abstract Harmonic Analysis -- Some Riemann Sums Are Better Than Others -- Gelfand Pairs Associated with Finite Heisenberg Groups -- Groups with Atomic Regular Representation -- Wavelet Transforms and Admissible Group Representations -- Frames and Multiresolution Structures -- The Density Theorem and the Homogeneous Approximation Property for Gabor Frames -- Recent Developments on Dual Wavelet Frames -- Characteristic Wavelet Equations and Generalizations of the Spectral Function -- Baggett’s Problem for Frame Wavelets -- Wavelet Sets -- Simple Wavelet Sets for Scalar Dilations in ?2 -- Interpolation Maps and Congruence Domains for Wavelet Sets -- Applications to Dynamical Systems and C*-Algebras -- Orthogonal Exponentials for Bernoulli Iterated Function Systems -- A Survey of Projective Multiresolution Analyses and a Projective Multiresolution Analysis Corresponding to the Quincunx Lattice -- Signal and Image Processing -- Sampling and Time-Frequency Localization of Band-Limited and Multiband Signals -- Entropy Encoding in Wavelet Image Compression. |
| Record Nr. | UNINA-9910782094203321 |
| Boston, : Birkhäuser, 2008 | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Wavelets, frames and operator theory : Focused Research Group Workshop on Wavelets, Frames and Operator Theory, January 15-21, 2003, University of Maryland, College Park, Maryland / / Christopher Heil, Palle E.T. Jorgensen, David R. Larson, editors
| Wavelets, frames and operator theory : Focused Research Group Workshop on Wavelets, Frames and Operator Theory, January 15-21, 2003, University of Maryland, College Park, Maryland / / Christopher Heil, Palle E.T. Jorgensen, David R. Larson, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (358 p.) |
| Disciplina | 515/.2433 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Wavelets (Mathematics)
Frames (Combinatorial analysis) Operator theory Electronic books |
| ISBN |
0-8218-7935-9
0-8218-5680-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""List of speakers""; ""How to construct wavelet frames on irregular grids and arbitrary dilations in Rd""; ""An analogue of Bratteli-Jorgensen loop group actions for GMRA's""; ""Examples of wavelets for local fields""; ""The spectral function of shift-invariant spaces on general lattices""; ""Custom building finite frames""; ""Frames of subspaces""; ""The local trace function for super-wavelets""; ""1. Introduction""; ""2. Permutative wavelet representations""; ""3. Shift invariant subspaces""; ""4. The local trace function""
""5. A characterization of super-wavelets""""6. The spectral function and the dimension function""; ""References""; ""Recovery of band-limited functions on manifolds by an iterative algorithm""; ""On a characterization of the local Hardy space by Gabor frames""; ""Riesz bases, multiresolution analyses, and perturbation""; ""The existence of Gabor bases and frames""; ""Co-affine systems in Rd""; ""Rank-one decomposition of operators and construction of frames""; ""An approach to the study of wave packet systems""; ""Convolution for Gabor systems and Newton's method"" ""Wavelets, wavelet sets, and linear actions on Rn""""Orthonormalized coherent states""; ""Localization of stability and p-frames in the Fourier domain""; ""Orthonormal wavelets arising from HDAFs"" |
| Record Nr. | UNINA-9910480986703321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Lo trovi qui: Univ. Federico II | ||
| ||
Wavelets, frames and operator theory : Focused Research Group Workshop on Wavelets, Frames and Operator Theory, January 15-21, 2003, University of Maryland, College Park, Maryland / / Christopher Heil, Palle E.T. Jorgensen, David R. Larson, editors
| Wavelets, frames and operator theory : Focused Research Group Workshop on Wavelets, Frames and Operator Theory, January 15-21, 2003, University of Maryland, College Park, Maryland / / Christopher Heil, Palle E.T. Jorgensen, David R. Larson, editors |
| Pubbl/distr/stampa | Providence, Rhode Island : , : American Mathematical Society, , [2004] |
| Descrizione fisica | 1 online resource (358 p.) |
| Disciplina | 515/.2433 |
| Collana | Contemporary mathematics |
| Soggetto topico |
Wavelets (Mathematics)
Frames (Combinatorial analysis) Operator theory Electronic books |
| ISBN |
0-8218-7935-9
0-8218-5680-4 |
| Formato | Materiale a stampa |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione | eng |
| Nota di contenuto |
""Contents""; ""Preface""; ""List of speakers""; ""How to construct wavelet frames on irregular grids and arbitrary dilations in Rd""; ""An analogue of Bratteli-Jorgensen loop group actions for GMRA's""; ""Examples of wavelets for local fields""; ""The spectral function of shift-invariant spaces on general lattices""; ""Custom building finite frames""; ""Frames of subspaces""; ""The local trace function for super-wavelets""; ""1. Introduction""; ""2. Permutative wavelet representations""; ""3. Shift invariant subspaces""; ""4. The local trace function""
""5. A characterization of super-wavelets""""6. The spectral function and the dimension function""; ""References""; ""Recovery of band-limited functions on manifolds by an iterative algorithm""; ""On a characterization of the local Hardy space by Gabor frames""; ""Riesz bases, multiresolution analyses, and perturbation""; ""The existence of Gabor bases and frames""; ""Co-affine systems in Rd""; ""Rank-one decomposition of operators and construction of frames""; ""An approach to the study of wave packet systems""; ""Convolution for Gabor systems and Newton's method"" ""Wavelets, wavelet sets, and linear actions on Rn""""Orthonormalized coherent states""; ""Localization of stability and p-frames in the Fourier domain""; ""Orthonormal wavelets arising from HDAFs"" |
| Record Nr. | UNINA-9910788666103321 |
| Providence, Rhode Island : , : American Mathematical Society, , [2004] | ||
| Lo trovi qui: Univ. Federico II | ||
| ||