Quaternion References  

This page contains a bibliography of quaternions and their applications.  If you have authored or are aware of material written on quaternions and their application that is not contained within this list, please contact me via email with the reference. I will be glad to include it the next time I update this list. T. A. Ell   

A

  1. Abbott, Edwin A.: FLATLAND: A Romance of Many Dimensions. Basil Blackwell-Oxford, 1962.
  2. Abdel-khalek, Khaled: Quaternion Analysis, Dipartimento di Fisica-Universita di Lecce-Lecce, 73100, Italy, 1996.
  3. Abonyi, I.: Quaternion Representation of Lorentz Group for Classical Physics. J. Phys. A. Math. & Gen. 24,14 (July 1991), 3245-3254.
  4. Abraham, Max: Ueber einige bei Schwingungsproblemen auftretende Differentialgleichungen. Math. Ann. 52, p. 81—112, 1899.
  5. Abraham, Max: Geometrisehe Grundbegriffe. Encykl. d. math, Wiss., 4, p. 3—47, 1901
  6. Acheson, Paulette Bootz: Multimedia Application Of Quaternions (Object Rotation), M.Sc. dissertation, University Of Southern California 1997.
  7. Alder,Stephen L.; "Quaternionic quantum field theory" Commun. Math. Phys. 104 (1986) 611-656.
  8. Adler,S. L.; "Quaternionic quantum mechanics and quantum fields" New York: Oxford University Press (1995).
  9. Adler, S. L.; Emch, G. G. "A rejoinder on quaternionic projective representations" J. Math. Phys. 38 (1997) 4758-4762.
  10. Aeberli, G.: Der Zusammenhang Zwischen quaternaeren quadratischen Formen und Idealen in Quaternionenringen. Comment. Math. Helv. 33 (1959), 212-239.
  11. Agrawal, Om Prakash: Quaternions, Hamilton Operators, and Kinematics of Mechanical Systems Advances in Design Automation -1987, Vol. 2, Robotics, Mechanisms, and Machine Systems, Edited by S. S. Rao (1987) pp. 317-322, 1987.
  12. Agrawal, Om Prakash: Hamilton Operators and Dual-Number Quaternions in Spatial Kinematics, Mechanisms and Machine Theory, Vol. 22, Number 6, pp. 569-575, 1987.
  13. Ahlfors, L.V.: Moebius transformations of Rn expressed through 2x2 matrices of Clifford numbers. Complex Variables 5 (1986), 215-224.
  14. Aitken, V.C.; Schwartz, H.M.: A comparison of rotational representations in structure and motion estimation for manoeuvring objects, Image Processing, IEEE Transactions on, Volume: 4 4 , Page(s): 516 -520.
  15. Albert, A.A. Absolute Valued Real Algebras. Ann. of Math. 48,2 (April 1947), 495-501.
  16. Albrecht, K. L.: The Use of Quaternions in the Modeling of Non-Local Contact in Proteins. Master's thesis. Washington State University, December 1995.
  17. Albrecht, K.; Hart, J.; Shaw, A.; Dunker, A.K.: Quaternion Contact Ribbons: a New Tool for Visualizing Intra- and Intermolecular Interactions in Proteins, Department of Electrical Engineering and Computer Science, Department of Biochemistry and Biophysics, Washington State University, Pullman, WA 99164-4660.
  18. Alekseevsky, Dimitry: Gradient Quaternionic Vector Fields and a Characterization of the Quaternionic Projective Space, The Erwin Schrodinger International Institute for Mathematical Physics, Vienna Preprint ESI 138 (1994), Available at http://web.archive.org/web/20080509143855/ftp://ftp.esi.ac.at/.
  19. Alekseevsky, Dimitry; Marchiafava, Stefano: Quaternionic Transformations and First Eiganvalues of Laplacian on a Quaternionic Kahler Manifold, The Erwin Schrodinger International Institute for Mathematical Physics, Preprint ESI 150 (October 24, 1994), Available at http://web.archive.org/web/20080509143855/ftp://ftp.esi.ac.at/.
  20. Alekseevsky, Dimitry; Cortes, Vincente: Isometry Groups of Homogeneous Quaternionic Kahler Manifolds, The Erwin Schrodinger International Institute for Mathematical Physics, Vienna Preprint ESI 230 (May 30, 1995), Available at http://web.archive.org/web/20080509143855/ftp://ftp.esi.ac.at/.
  21. Alekseevsky, Dimitry; Marchiafava, Stefano; Pontecorvo, Massimiliano: Compatible Complex Structures on Almost Quaternionic Manifolds, The Erwin Schrodinger International Institute for Mathematical Physics, Vienna Preprint ESI 404 (December 5, 1996) Available at http://web.archive.org/web/20080509143855/ftp://ftp.esi.ac.at/.
  22. Alekseevsky, Dimitry; Podesta, F.: -Compact Cohomogeneity One Riemannian Manifolds of Positive Euler Characteristic and QuaternionKahler Manifolds, The Erwin Schrodinger International Institute for Mathematical Physics, Vienna Preprint ESI 466 (June 27, 1997) Available at http://web.archive.org/web/20080509143855/ftp://ftp.esi.ac.at/
  23. Alekseevsky, Dimitry; Marchiafava, Stefano; Pontecorvo, Massimiliano: -Compatible Almost Complex Structures on QuaternionKahler Manifolds, The Erwin Schrodinger International Institute for Mathematical Physics, Vienna Preprint ESI 419 (January 10, 1997) Available at http://web.archive.org/web/20080509143855/ftp://ftp.esi.ac.at/
  24. ALLARDICE, ROBERT EDGAR: Note on a formula in quaternions, Edinb. M. S. Proc., 7, pp. 8—12, 1889.
  25. ALLÉ, MORIZ: Ueber die Ableitung der Gleichungen der drehenden Bewegung eines starren Korpers nach der Grassmann’schen Analyse, Prag Math. Ges., 64—69, 1892.
  26. ALLÉGRET, ALEXANDRE: Essai sur le calcul des quaternions de M. W. Hamilton, Paris: Gauthier—Villars. 7+72, 4°, 1862.  (This article reviewed by M. Prouhet. Nouv. Ann., (2), 2, pp. 833—834, 1868).
  27. Alonso, Roberto; Shuster, Malcolm D.: TWOSTEP: A Fast Robust Algorithm for Attitude-Independent Magnetometer-Bias Determination, The Journal of Astronautical Sciences, October - December, 2002, Vol. 50, No. 4. 
  28. Alonso, Roberto; Shuster, Malcolm D.: Attitude-Independent Magnetometer-Bias Determination: A Survey, The Journal of Astronautical Sciences, October - December, 2002, Vol. 50, No. 4. 
  29. Alonso, Roberto; Shuster, Malcolm D.: Complete Linear Attitude-Independent Magnetometer Calibration, The Journal of Astronautical Sciences, October - December, 2002, Vol. 50, No. 4.
  30. Althoen, S.C., et al.: Rotational Scaled Quaternion Division Algebras, J. Algebra 146,1 (Feb. 1992), 124-143.
  31. Altmann, Simon L.: Icons and Symmetries, Clarendon Press - Oxford, 1992.
  32. Altmann, Simon L.: Hamilton, Rodrigues, and the quaternion scandal,  Mathematics Magazine v. 62, No. 5, p. 291-308, Dec. 1989
  33. Altmann, Simon L.: Rotations, Quaternions, and Double Groups, Clarendon Press, Oxford 1986.
  34. ANTRONY, EDWYN: Notes on quaternions. Messenger (2), 10, pp. 66—72, 1881.
  35. Araneda, J.E.A.: Dimensional-directional Analysis by a Quaternionic Representation of Physical Quantities, Journal Of The Franklin Institute, Volume 333B, Issue 1, January 1996, ISSN: 00160032
  36. Aramanovitch, L.: Spacecraft orientation based on space object observations by means of quaternion algebra, Journal of Guidance, Control, and Dynamics v. 18 (July/Aug. '95) p. 859-66
  37. Arena, P., Fortuna, L., Muscato, G., Xibilia, M.G.: Multilayer Perceptrons to Approximate Quaternion Valued Functions, Neural Networks, Volume 10, Issue 2, March 1997, p. 335-42, ISSN: 08936080
  38. Arena, P.; Baglio, S.; Fortuna, L.; Xibilia, M.G.: Chaotic time series prediction via quaternionic multilayer perceptrons, Systems, Man and Cybernetics, 1995. Intelligent Systems for the 21st Century., IEEE International Conference on Volume: 2 , Page(s): 1790 -1794
  39. ARGAND, JEAN—ROBERT: Essai sur une maniére de représenter les quantités imaginaires dans les constructions géométriques. (Anonymous.) Paris 78. Small 8°, 1806.
  40. ARGAND, JEAN—ROBERT: Essai sur une manière do reprèsenter les quantités imaginaires dans les constructions gèométriques. Ann. de Math, de Gergonne, 4, pp. 133—147, 1814.
  41. ARGAND, JEAN—ROBERT: Réfiexions sur la nouvelle théorie des imaginaires, suivies d’une application à la démonstration d’un théorème d’analyse. Ann. de Math. De Gergonne, 5, 197—209, 1815.
  42. ARGAND, JEAN—ROBERT: Essai sur une manière, etc. 2° edition, précedée d’une préface par M. J. Hoüol et suivie d’un appendico contenant des extraits des Annales de Gergonne relatifs à la question des imaginaires. Paris Gauthier—Villars, 19+126. 8°, 1874.
  43. ARGAND, JEAN—ROBERT: Imaginary Quantities. The second edition of the above translated into English by A. S. Hardy. New York: Van Nostrand, 1881.
  44. Artin, E.: Geometric Algebra. Interscience Publs., NY 1957.
  45. Artmann, Benno: The Concept of Number: from Quaternions to Monads and Topological Fields. Ellis Horwood series in Mathematics and Its Applications. Ellis Horwood, Halsted, Chichester, 1988. Translation of: Der Zahlbeginff, Gottigen: Vandenhoeck & Rupprecht, 1983. Translated with additional exercises and material by H.B. Griffiths.
  46. Aslaksen, H.: Quaternionic determinants, Mathematics Intelligencer, Vol. 18(3), pp.57-65, 1996.
  47. Aspragathos, N.A.; Dimitros, J.K.: A comparative study of three methods for robot kinematics, Systems, Man and Cybernetics, Part B, IEEE Transactions on, Volume: 28 2 , Page(s): 135 -145

B

  1. Bacakoglu, H.; Kamel, M.: An optimized two-step camera calibration method, Robotics and Automation, 1997. Proceedings., 1997 IEEE International Conference on, Volume: 2 , Page(s): 1347 -1352 vol.2
  2. Bach, Ralph ; Paielli, Russell: Linearization of Attitude-Control Error Dynamics, IEEE Transactions on Automatic Control, Vol 38 No. 10, pp.1521-1525, October, 1993.
  3. Bach, Ralph.; Paielli, Russell. : Linearization of attitude-control error dynamics, IEEE Transactions on Automatic Control v. 38 (Oct. '93) p. 1521-5.
  4. Bachoc, Christine: Applications of Coding Theory to the Construction of Modular Lattices, Journal of Combinatorial Theory, Series A, v 78, n 1, Apr 1997, p 92-119
  5. Badorff: Beitrag zur Geometrie des Kreises und der Kugel Pr. Baden, 1877.
  6. BAKER, ALFRED: The principles at the base of quaternion analysis. Trans. R. S. C., Section III, (2), 7, pp. 17-20, 1901.
  7. Baker, Arthur Latham.: Quaternions as the Result of Algebraic Operations. New York: D. Van Nostrand Company, 1911. 92 p. QA257 .B3.
  8. Bakkesa Swamy, K.E., Nagaraj, M.: Conformality, Differentiability and Regularity of Quaternion Functions, Indian Journal of Pure and Applied Mathematics, Vol. 47, pp. 21-30, 1983.
  9. BALBIN, VALENTIN: Elementos de calculo de los cuaterniones y sus aplicaciones principales á la geometria al analysis y á la mecanica. Buenos Aires. 19 + 359. 8°, 1888.
  10. BALL, Sir ROBERT STAWELL: The theory of screws: a study in the dynamics of a rigid body. Dublin Hodges, Foster, & Co. 24 + 194. 8°, 1876.
  11. BALL, Sir ROBERT STAWELL: The discussion on quaternions. Nature, 48, 391, 1893.
  12. BALL, Sir ROBERT STAWELL: A treatise on the theory of screws. Cambridge University Press. 19 + 544. Royal 8°. 1900.
  13. BALLAUFF, L.: Beiträge zur systematisehen Darstellung der allgemeinen Arithmetik. Grunert Arch., 5, 259—, 1844.
  14. BALLAUFF, L.: Ueber die Potenzen mit imaginären Exponenten. Grunert Arch., 6, 409—, 1845.
  15. BALTZER, Richard: Ueber die Einführung der complexen Zahlen. J. für Math., 94, 87—92., 1883.
  16. Balzarotti, Giorgio; Marsiglia, Gianluca: Quaternions in line-of-sight control, Opt. Eng. Vol. 44, 103003 (Oct. 21, 2005)
  17. Barberis, Maria Laura: Hypercomplex structures on four-dimensional Lie groups. Proc. Am. Math. Soc. 125, No.4, 1043-1054 (1997).
  18. BARISIEN, Napoleon—Ernest: Application de la méthode de Grassmann à une démonstration de deux théorèmes do géométrie différentielle. Nouv. Ann., (4), 1, 1901.
  19. Bar-Itzhack, Itzhack Y.: Optimum Normalization of a Computed Quaternion of Rotation, IEEE Transactions on Aerospace and Electronic Systems, pp.401-402, March, 1971.
  20. Bar-Itzhack, Itzhack Y.; Deutschmann, J.; Markley, F.L.: Quaternion Normalization in Additive EKF for Spacecraft Attitude Determination, AIAA Guidance, Navigation and Control Conference, New Orleans, Aug. 12-14, 1991, pp. 908-916.
  21. Bar-Itzhack, Itzhack Y.: REQUEST: A Recursive QUEST Algorithm for Sequential Attitude Determination, Journal of Guidance, Control, and Dynamics, Vol. 19, No. 5, September-October 1996, pp. 1034-1038.
  22. Barr, Alan H.; Currin, Bena; Gabriel, Steven; Hughes, John F.: Smooth Interpolation of Orientations with Angular Velocity Constraints Using Quaternions, 19th Annual ACM Conference on Computer Graphics and Interactive Techniques - SIGGRAPH '92, Computer Graphics (ACM) Vol. 26 No 2, pp. 313-320, July 1992.
  23. Bartocci, C.; Bruzzo, U.; Ruiperez, D.H.: A hyperkahler Fourier transform, Differential Geometry and its Applications, Volume 8, Issue 3, June 1998, ISSN: 09262245
  24. Battaglia, Fiammetta: $S^1$-quotients of quaternion-Kähler manifolds. Proc. Amer. Math. Soc. 124 (1996), pp. 2185-2192.
  25. Battaglia, Fiammetta: A hypercomplex Stiefel manifold. Differ. Geom. Appl. 6, No.2, 121-128 (1996). [ISSN 0926-2245]
  26. Battilotti, S.; Di Gennaro, S.; Lanari, L.: Output feedback stabilization of a rigid spacecraft with unknown disturbances, Decision and Control, 1994., Proceedings of the 33rd IEEE Conference on, Volume: 1 , Page(s): 916 -920 vol.1
  27. Bayen, Dilip; Bruner, Robert R.: Real connective K-theory and the quaternion group. Trans. Amer. Math. Soc. 348 (1996), pp. 2201-2216.
  28. Bedding, Stephen; Briggs, Keith: Iteration of quaternion functions, The American Mathematical Monthly v. 103 (Oct. '96) p. 654-64
  29. Bedding, Stephen; Briggs, Keith: Regularly Iterable Linear Quaternion Maps, Dept. of Applied Maths, University of Adelaide, South Australia, May 31, 1995.
  30. Bedding, Stephen; Briggs, Keith: Iteration of Quaternion Maps, Dept. of Applied Maths, University of Adelaide, South Australia, July 22, 1994.
  31. BEEBE, WILLIAM; Phillips, A. W.: The orbit of Swift’s comet 1880 V determined by Gibbs’s vector method, Astronomical Journal, 9, 113—117 and 121—124, 1890.
  32. Beeler, M.; Gosper, R. W.; Schroeppel, R.: HAKMEM. Cambridge, MA: Mass. Institute of Technology Artificial Intelligence Laboratory, Memo AIM-239, Item 107, Feb. 1972.
  33. BEEZ, R.: Ueber conforme Abbildung von Mannigfaltigkeiten höberer Ordnung. Schlömilch Z., 20, 253—270, 1875.
  34. BEEZ, R.: Zur Theorie der Vectoren und Quaternionen, Schlömilch Z., 41, 85—57 and 65—84, 1896.
  35. Bell, S.B.M., Diaz, B.M. and Holroyd, F.C. (1986). Tesseral quaternions for 3-D. Spatial Data Processing using Tesseral Methods, B.M. Diaz and S.B.M. Bell (Eds), NERC Unit for Thematic Information Systems, Reading, 265-284.
  36. Bell, S.B.M.; Mason, D.C.: Tesseral Quaternions for the Octtree, The Computer Journal, Vol. 33, No 5, pp.386-397, October 1990.
  37. Bellavitis, Giusto: Sulla geometria denivata. Ann. Lomb. Veneto, 2, 250—258, 1832.
  38. Bellavitis, Giusto: Sopra alcune applicazioní di un nuovo metodo di geometria analitica. Poligrafo di Verona, 13, 53—61, 1833.
  39. Bellavitis, Giusto: Saggio di applicazioni di un nuovo metodo di geometria analitica (Calcolo delle equipollenze). Ann. Lomb. Veneto, 5, 244—250, 1835.
  40. Bellavitis, Giusto: Teoria delle figure inverse e loro uso nella geometria elementare. Ann. Lomb. Veneto, 6, 136—141, 1836.
  41. Bellavitis, Giusto: Memoria sul metodo delle equipollenze. Ann. Lomb. Veneto, 7, 248—261 8, 17—37 and 85—121, 1887—8.
  42. Bellavitis, Giusto: Soluzioni grafiche di alcuni problemi geometrici del primo e del secondo grado trovato col metodo delle equipollenze. Von. 1st. Mem., 1, 225—267, 1843.
  43. Bellavitis, Giusto: Dimostrazione col metodo delle equipollenze di alcuni teoremi in parte considerati dai sig. Bellati e Ridolfi. Von. 1st. Atti, (1), 6, 53—59, 1847.
  44. Bellavitis, Giusto: Saggio sull’ algebra degli immaginarie. Von. 1st. Mom., 4, 243—344, 1852.
  45. Bellavitis, Giusto: Sposiziono del metodo delle equipollenze. Mem. Soc. Ital., 25, 225—309. Published separately at Modena, 1854. Translated by C. A. Laisant, Paris. 1874.
  46. Bellavitis, Giusto: Sposizione dei nuovi metodi di geometria analitica. Ven 1st. Mem. 159 pages, 1880.
  47. Bellavitis, Giusto: Sul calcolo dei quaternioni. Undecima Rivista di Giornali. Ven. 1st. Atti, (2), 204, 1871.
  48. Bellavitis, Giusto: Sul calcolc dci quaternioni ossia teoria dei rapporti geometrici nello spazio. Duodecima Rivista di Giornali. Ven. 1st. Atti, (2), 69, 1878.
  49. Bellavitis, Giusto: Exposition de Ia méthode des Équipollences de Giusto Bellavitis: traduction par C. A. Laisant, Nouv. Ann. (2), 12 and 13, 1873—4.
  50. Bellavitis, Giusto: Sulle origini del metodo delle equipollenze. Ven. 1st, Mem., 19, 449—491, 1876.
  51. Bellavitis, Giusto: Sur la thèse de M. Laisant relative au calcul dos quaternions. Quattuor dicesima Rivista di Giornali, Ven. 1st. Atti. (2), 116, 1878.
  52. BEMAN , WOOSTER WOODRUFF: A brief account of the essential features of Grassmann’s extensive algebra. Translation of Grassmann’s “Kurzo Uebersicht” in Grunert’s Archiv. Analyst, 8, 96—97, and 114—124, 1881.
  53. BEMAN , WOOSTER WOODRUFF: A chapter in the history of mathematics. Amer. Assoc. Proc.,46, 33—50, 1897.
  54. Beniac, D.R.; Czarnota, G.J.; Rutherford, B.L.; Ottensmeyer, F.P.; Harauz, G.:Three-dimensional Architecture of Thermomyces lanuginosus Small Subunit Ribosomal RNA, Micron, Volume 28, Issue 1, February 1997, ISSN: 09684328
  55. Benn, I.W., and Tucker, R.W. An Introduction to Spinors and Geometry. Adam Hilger, Bristol, 1988.
  56. Berezanskii, Iu. M., Kaliuzhnyi, A. A.: Harmonic Analysis in Hypercomplex Systems (Mathematics and Its Applications (Kluwer Academic Publishers), V. 434.) Vol 434 (May 1998) Kluwer Academic Pub; ISBN: 0792350294
  57. BERLOTY , B.: Théorie des quantités complexes à n unités principales. Thèse. Paris: Gauthier—Villars. 12 pp. 4°., 1886
  58. Bernstein, Dennis S.; So, Wasin: Some Explicit Formulas for the Martix Exponential, IEEE Transactions on Automatic Control, Vol 38 No. 8, pp. 1228-1231, August, 1993.
  59. Bharathi, K., Nagaraj, M.: Geometry of Quaternionic and Pseudo-Quaternionic Multiplications, Indian Journal of Pure and Applied Mathematics, Vol. 16, No 7, pp. 741-756, July 1985.
  60. Bharathi, K., Nagaraj, M.: Regularity for Quaternion Functions of Several Complex Variables, Indian Journal of Pure and Applied Mathematics, Vol. 18, No 8, pp. 679-704, August 1987.
  61. Bharathi, K., Nagaraj, M.: Quaternion Valued Function of a Real Variable Serret-Frenet Formula, Indian Journal of Pure and Applied Mathematics, Vol. 18, No 6, pp. 507-511, 1987.
  62. BIGELOW, FRANK HAGAR: Eclipse meteorology and allied problems. Chap. V., Fundamental physical relations, p. 135—166. Bulletin of the United States Weather Bureau, 1902.
  63. BIGELOW, FRANK HAGAR: Studies on the statics and kinematics of the atmosphere in the United States. Bulletin of the United States Weather Bureau, 1902.
  64. BJERKNES, V: Zur Theorie gewisser Vectorgrössen. Christiania. 27 pp. 8°, 1898.
  65. BJERKNES, V: Vorlesungen über hydrodynamische Fernkräfte. Bd. I. Leipzig, 1900.
  66. Björling, CARL F. E.: Ueber eine vollständige geometrische Darstellung einer Gleichung zwischen zwei veränderlichen Grössen. Stockholm Akad. Handl., 13, No. 4, 1876.
  67. Blaschke, W.: Kinematik und Quaternionen. VEB Deutscher Verlag der Wiss, 1960.
  68. Bobrysheva, A.I.; Moskalenko, S.A.; Misko, V.R.; Negru, S.I.: Spontaneous and light induced Bose-Einstein condensation of biexcitons, Semiconductor Conference, 1995. CAS'95 Proceedings., 1995 International , Page(s): 263 -266
  69. BÔCHER, MAXIME: The geometric representation of imaginaries. Annals of Math., 7, 70—72, 1893.
  70. Boecherer, Siegfried; Schulze-Pillot, Rainer: Siegel Modular Forms and Theta Series Attached to Quaternion Algebras. 
  71. Boguslawsky, A. J.: Algebra of the plane and of space, (Russian.) Mosk. Math. Samml, 14—16, 1891—2.
  72. Boguslawsky, A. J.: Calculus of position. (Russian.), Charkow Ges. (2), 4, 86—96, 1893.
  73. Böklen, Otto: Die Rechnung mit Vectoren. Correspondenzbl. f. Gel. u. Realschule, 1882.
  74. Bolker, E.: The spinor spanner. Am. Math. Month. 80, 9 (Nov. 1973), 977-984.
  75. Bonan, Edmond: Isoporphismes Sur Une Variete Presque Hermitienne Quaternionique, Quaternionic Structures in Mathematics and Physics, SISSA - Trieste, 5-9 September 1994.
  76. Boole G.: Notes on Quaternions, Philosophical Magazine, Vol. 33, No. 3, pp. 278—280, 1847.
  77. Boole, George: Application of the method of Quaternions to the solution of the partial differential equation Ñ2u = 0. Dublin Proc., 6, 375—385, 1856.
  78. Bottasso, C.: A Non-Linear Beam Space-Time Finite Element Formulation Using Quaternion Algebra: Interpolation of the Lagrange Multipliers and the Appearance of Spurious Modes, Computational Mechanics, Vol. 10 No 5, pp. 359-368, 1992.
  79. Boyer, Charles P.; Galicki, Krzysztof; Mann, Benjamin M.: Quaternionic Geometry and 3-Sasakian Manifolds , Quaternionic Structures in Mathematics and Physics, SISSA-Trieste, 5-9 September 1994.
  80. Brackx, F.F., Delanghe, R, and Sommen, F. Clifford Analysis. Pitman, 1983.
  81. Bragdon, Claude: A Primer of Higher Space. Omen Press, Tucson, AZ, 1972.
  82. Brand, Louis: The Roots of a Quaternion, The American Mathematical Monthly, Vol. 49, No. 8, pp. 519-520, Oct. 1942.
  83. Brand, Louis: Vector and Tensor Analysis, John Wiley and Sons, 1947
  84. Branets, V.N., Shmyglevskiy, I.P.: Primeneniye Kvaternionov v Zadachakh Orientatsii Tverdogn Tela (Application of Quaternions to Rigid Body Rotation Problems), Nauka Press, 1973.
  85. Breure, A.: Die Gauss’sche Darstellung complexer Zahlen in geometrischer Beleuchtung. Hoppe Arch., (2), 12, 337—344, 1893.
  86. Bricard, R.: Sur la similitude directe dans le plan. Application do la méthode des équipollences. Nouv. Ann., (4), 1, 112—120, 1901.
  87. Brill, John: On the application of the theory of complex quantities to plane geometry, Mesenger, (2), 16, 8—20, 1886.
  88. Brill, John: A new method for the graphical representation of complex quantities. Messenger, (2), 17, 80—93, 1887.
  89. Brill, John: A new geometrical representation of the quaternion analysis. Cambr. Proc., 6, 156—169, 1889.
  90. Brill, John: Note on the application of quaternions to the discussion of Laplace’s equation. Cambr, Proc., 7, 120—125 and 151—156, 1892.
  91. Brill, John: Note on the application of analysis to geometry. Messenger, (2), 25, 49—59, 1895.
  92. Brill, John: On the generalization of certain properties of the tetrahedron. Cambr. Proc., 9, 98—108, 1896.
  93. BROCA , André: Champs de vecteur et champs de force, Action réciproque des masses scalaires et vectorielles. C.R. 130, 109—112, 1900.
  94. BROCA , André: Sur les masses vectorielles de discontinuité, C. R. 130, 317—319, 1900.
  95. BROCARD, HENRI: Applications mécaniques du calcul des quaternions, par C. A. Laisant. Compte rendu bibliographique. Nouv. Corresp. Math. 4, 115—116, 1877.
  96. BROCARD, HENRI: Introduction à la méthode des quaternions, par C. A. Laisant. Compte rendu bibliographique. Nouv. Ann., (3), 1, 332—385, and Mathesis, 2, 32—84, 1882.
  97. BROCARD, HENRI: Théorie et applications des Équipollences, par C. A. Laisant. Compte rendu bibliographique. Mathesis, 7, 184—185, 1887.
  98. Brown, D.M. Arithmetics of rational generalized quaternion algebras.Bull. Amer. Math. Soc. 46 (1940), 899-908.
  99. Brumby, S.P., Joshi, G.C.: Experimental Status of Quaternionic Quantum Mechanics, Chaos, Solitons And Fractals, Volume 7, Issue 5, May 1996, ISSN: 09600779
  100. Brumby, S.P., Hanlon, B.E., Joshi, G.C.: Implications of quaternionic dark matter, Physics Letters B, Volume 401, Issue 3-4 , 29 May 1997, ISSN: 03702693
  101. Bryukhov, D.A. Hypercomplex Numbers in Geometry and Physics, 2 (14), Vol 7, 2010, с. 1-12.

  102. BUCHERER , A. H.: Elemente der Vectoranalysis. Leipzig: Teubner, 6 + 91 pp. 8 Vo., 1908.
  103. BUCHHEIM, ARTHUR: On the application of quaternions to the theory of the linear complex and the linear congruence. Messenger, (2), 12, 129—130, 1883.
  104. BUCHHEIM, ARTHUR: On the quaternion treatment of the linear complex. Messenger, (2) 13, 120—124, 1883.
  105. BUCHHEIM, ARTHUR: On the theory of screws in elliptic space. Lond. M. S. PrOc., 15, 88-98 ; 16, 15—27 ; 17, 240-254; 18, 88—96, 1884-7.
  106. BUCHHEIM, ARTHUR: On the theory of matrices. Lond. M. S. Proc., 16, 63—82, 1885.
  107. BUCHHEIM, ARTHUR: A memoir on biquaternions. American J., 7, 293—326, 1885.
  108. BUCHHEIM, ARTHUR: On Clifford’s theory of graphs. Lond. M. S. Proc., 17, 80-106, 1886.
  109. Buée, L’Abbé: Mémoire sur les quantités imaginaires. Lond. Phil. Trans. 96, 28—88, 1806.
  110. BUNKHOFER, WILHELM: Zahlenbüschel, &c. Pr. Bruchsal, 1878.
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Z

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