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Dihedral Fourier analysis : data-analytic aspects and applications / Marlos A.G. Viana, Vasudevan Lakshminarayanan.

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Author/Creator:
Viana, Marlos A. G.
Language:
English.
Publication date:
2013
Imprint:
New York : Springer, c2013.
Format:
  • Book
  • xvi, 118 p. : ill. (some col.) ; 24 cm.
Bibliography:
Includes bibliographical references and index.
Contents:
  • Symmetry and experimental data. Introduction ; The flag ranking data ; The orbit invariants as Fourier transforms ; The algebraic framework ; Inference ; Problems ; Appendix A : the flag preference data
  • Algebraic and data-analytic aspects. Introduction ; The dihedral groups ; Dn conjugacy orbits ; Dihedral sets and modules ; Class functions ; Dihedral projections ; Fourier bases ; The center of CDn ; Group rings ; Multivariate normal data ; Selected dihedral bases ; Log-transformed multinomial data ; Additional remarks ; Problems
  • Curvature and refraction data. Introduction ; Dihedral analysis of optical power; The spectral decomposition ; Dihedral analysis of wavefront aberration polynomials ; Dihedral spatial filters ; The algebraic structure of dioptric power matrices ; Problems
  • Symbolic sequences. Introduction ; The dihedral orbit display ; A center of mass display ; Invariant displays ; A class of D4 orbit invariants ; Entropy displays ; Problems ; Appendix A : selected computational tools
  • Symmetry preference and perception. Introduction ; The D2 orbit structure in S4 ; The dihedral D2 summaries ; The dihedral D3 summaries ; Problems
  • Other applications. Normal modes ; Center of mass displacements ; Polarization states ; Decompositions of entropy ; Elementary algebraic surfaces ; Problems
  • References
  • Glossary
  • Index.
Contributor:
Lakshminarayanan, Vasudevan.
Series:
Lecture notes in statistics ; 206
Lecture notes in statistics (Springer-Verlag) ; v. 206.
Subjects:
ISBN:
9781461455615
1461455618
9781461455622
1461455626

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