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MSU Faculty Authors

Author

Education:
  • B. A. (Honors), Austin College, 1972
  • M. Math., University of Waterloo, 1973
  • Ph. D., University of Waterloo, 1977

  • Research Interest:
    Theory of functional equations and their applications to the measurement of information, quantum mechanics, and the social sciences.

    Link to Personal Web Page

    Characterizations of Information Measures

    Ebanks, Bruce R.
    Publisher: World Scientific
    1998
    ISBN: 9810230060
    Collaborators: Prasanna Sahoo and Wolfgang Sander

    How should information be measured? That is the motivating question for this book. The concept of information has become so pervasive that people regularly refer to the present era as the Information Age. Information takes many forms: oral, written, visual, electronic, mechanical, electromagnetic, etc. Many recent inventions deal with the storage, transmission, and retrieval of information. From a mathematical point of view, the most basic problem for the field of information theory is how to measure information. In this book we consider the question: What are the most desirable properties for a measure of information to possess? These properties are then used to determine explicitly the most "natural" (i.e. the most useful and appropriate) forms for measures of information.

    This important and timely book presents a theory which is now essentially complete. The first book of its kind since 1975, it will bring the reader up to the current state of knowledge in this field.




    Ebanks, Bruce R., and Henrik Stetkaer. "Continuous Cocycles on Locally Compact Groups" Aequationes Mathematicae 78.1-2 (2009): 123-145.
    Ebanks, Bruce R. "Functional Equations for Weighted Entropies" Results in Mathematics 55.3-4 (2009): 329-357.
    Ebanks, Bruce R. "General Solution of the 2-Cocycle Functional Equation on Solvable Groups" Aequationes Mathematicae 76.3 (2008): 315-316.
    Ebanks, Bruce R. "Generalized Cauchy Difference Equations. II" Proceedings of the American Mathematical Society 136.11 (2008): 3911-3919.
    Ebanks, Bruce R. "Characterization of Jensen Differences and Related Forms" Aequationes Mathematicae 76.1-2 (2008): 179-190.
    Ebanks, Bruce R., and Peter De Place Friis. "Cauchy Differences Depending on a Product on Rings" Far East Journal of Mathematical Sciences 24.1 (2007): 23-43.
    Ebanks, Bruce R. "General Solution of the 2-Cocycle Functional Equation on Solvable Groups" Aequationes Mathematicae 73.3 (2007): 260-279.
    Ebanks, Bruce R. "Generalized Cauchy Difference Functional Equations" Aequationes Mathematicae 70.1-2 (2005): 154-176.
    Ebanks, Bruce R., and Che Tat Ng. "Tribute to a Distinguished Professor - János Aczél at 80" Aequationes Mathematicae 69.1-2 (2005): 1-5.
    Ebanks, Bruce R. "Inhomogeneous Cauchy Exponential Functional Equations" Publicationes Mathematicae Debrecen 67.3-4 (2005): 437-455.
    Ebanks, Bruce R., and László Székelyhidi. "On Multiplicative and Additive Differences" Aequationes Mathematicae 69.1-2 (2005): 97-113.
    Ebanks, Bruce R., and Peter De Place Friis. "A Class of Functional Equations (Almost) Characterizing Polynomials on Integral Domains" Sarajevo Journal of Mathematics 1.2 (2005): 185-196.
    Ebanks, Bruce R. "Solution of Some Functional Equations Involving Symmetric Means" Publicationes Mathematicae Debrecen 61.3-4 (2002): 579-588.
    Ebanks, Bruce R. "On Some Results of Grzaslewicz Concerning Quadratic Maps and Additive Maps" Mathematical Reports of the Academy of Science of the Royal Society of Canada 24.4 (2002): 132-137.
    Ebanks, Bruce R. "On Heuvers' Logarithmic Functional Equation" Results in Mathematics 42 (2002): 37-41.
    Brillouët-Bellout, Nicole, and Bruce R. Ebanks. "Localizable Composable Measures of Fuzziness - II" Aequationes Mathematicae 60.3 (2000): 233-242.

    Ebanks, Bruce R., Jimmy Solomon, and Tina Straley. "Hiring and Firing Staff and Faculty." Leading the Mathematical Sciences Department: A Resource for Chairs: MMA Notes #64. Ed. Tina H. Straley, Marcia P. Sward, and Jon W. Scott. Washington, DC: Mathematical Association of America, 2005. 106-109.
    Ebanks, Bruce R. "Merit Pay." Leading the Mathematical Sciences Department: A Resource for Chairs: MMA Notes #64. Ed. Tina H. Straley, Marcia P. Sward, and Jon W. Scott. Washington, DC: Mathematical Association of America, 2005. 105.
    Ebanks, Bruce R. "Localizable Functionals." Functional Equations: Results and Advances. Ed. Zoltán Daróczy and Zsolt Páles. London : Kluwer Academic, 2002. 297-304.

    Ebanks, Bruce R. "Continuous Cocycles on Locally Compact Groups." 47th International Symposium on Functional Equations, June 14-20, 2009, Gargnano, Italy. 2009.
    Ebanks, Bruce R. "Characterization of Jensen Differences and Related Forms." 45th International Symposium on Functional Equations, June 24 - July 1, 2007, Bielsko-Biala, Poland. 2007.
    Ebanks, Bruce R. "Generalized Cauchy Difference Equations III." 44th International Symposium on Functional Equations, May 14-20, 2006, Louisville, KY. 2006.
    Ebanks, Burce R. "Cocycles on Solvable Groups." 43rd International Symposium on Functional Equations, May 15-21, 2005, Batz-sur-Mer, France. 2005.
    Ebanks, Bruce R. "Inhomogeneous Cauchy Exponential Functional Equations." 42nd International Symposium on Functional Equations, June 20-27, 2004, Opava, Czech Republic. 2004.
    Ebanks, Bruce R. "On Multiplicative and Additive Differences." 41st International Symposium on Functional Equations, June 8-15, 2003, Noszvaj, Hungary. 2003.
    Ebanks, Bruce R. "Generalized Cauchy Difference Equations for Complex Functions." 40th International Symposium on Functional Equations, August 25 - September 1, 2002, Gronów, Poland. 2002.
    Ebanks, Bruce R. "Solution of Some Generalized Cauchy Difference Equations." 39th International Symposium on Functional Equations, August 12-18, 2001, Sandbjerg Estate, Denmark. 2001.
    Ebanks, Bruce R. "Recent Developments on the Cocycle Equation." 38th International Symposium on Functional Equations, June 11-18, 2000, Noszvaj, Hungary. 2000.