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Department of Mathematics

Research Publications (Articles & Books)


2008

Articles

  • Symbolic Dynamics of the Shift Map in R*
    By Abdelkrim Brania and M. Sambandham, Morehouse College
    Proceedings of Dynamic Systems and Applications, Vol. 5 (2008) 68–72.

  • A Probabilistic Model of Cumulative Voting with Implications for Dynamical System Simulation
    By Duane Cooper, Morehouse College
    Proceedings of Dynamic Systems and Applications, Vol. 5 (2008) 125-127.

  • An Approach to Multiscale Modeling of Polymer Viscoelasticity
    By N. G. Medhin, North Carolina State University and M. Sambandham, Morehouse College
    Proceedings of Dynamic Systems and Applications, Vol. 5 (2008) 306-311.

  • On the numerical treatment of hybrid stochastic differential systems
    By S. Pederson and M. Sambandham, Morehouse College
    Proceedings of Dynamic Systems and Applications, Vol. 5 (2008) 380–385.

  • Fuzzy Numbers, Fuzzy Elements, and Their Additive Properties
    By Chuang Peng, Morehouse College
    Proceedings of Dynamic Systems and Applications, Vol. 5 (2008) 386–393.

  • Finite Cyclic Tame Extensions of k_p((t))
    By U. Wilson, Morehouse College
    Journal of Algebra and Its Applications 7 (2008) 61-79.

  • Algebraic Polynomials With Random Coefficients With Binomial And Geometric Progression
    By K. Farahmand, University of Ulster, UK and M. Sambandham, Morehouse College
    Submitted to International Journal of Applied Mathematical Sciences.

  • Morse Theory and Central Configurations in the Spatial N-body Problem
    By John C. Merkel III, Morehouse College
    Accepted for publication in Journal of Dynamics and Differential Equations.

  • On the holonomy of the Coulomb connection over 3-manifolds with boundary
    By William E. Gryc, Morehouse College
    Accepted for publication in Communications in Mathematical Physics.

  • Numerical solution to hybrid stochastic differential systems
    By S. Pederson and M. Sambandham, Morehouse College
    Stochastic Analysis and Applications 26 (2008) 338-356.

  • The Runge-Kutta method for hybrid fuzzy differential equations
    By S. Pederson and M. Sambandham, Morehouse College
    Nonlinear Analysis: Hybrid Systems 2 (2008) 626-634.

  • Projections of hyperbolic mapping classes to simple Dehn twists
    By Chaohui Zhang, Morehouse College
    Accepted for publication in Complex Variables.

  • Remarks on Thurston's construction of pseudo-Anosov maps of Riemann surfaces
    By Chaohui Zhang, Morehouse College
    Chinese Ann. of Mathematics 29, Series B (2008) 85-94.

  • Singularities of quadratic differentials and extremal Teichmuller mappings defined by Dehn twists
    By Chaohui Zhang, Morehouse College
    Accepted for publication in J. Austral. Math. Soc.
  • Hyperbolic lengths of some filling geodesics of Riemann surfaces with punctures
    By Chaohui Zhang, Morehouse College
    Accepted for publication in Osaka J. Math.
  • Pseudo-Anosov maps and fixed points of boundary homeomorphisms compatible with a Fuchsian group
    By Chaohui Zhang, Morehouse College
    Accepted for publication in Osaka J. Math..
  • On lengths of filling closed geodesics of hyperbolic punctured Riemann spheres
    By Chaohui Zhang, Morehouse College
    Accepted for publication in Mathematische Nachrichten.
  • Pseudo-Anosov mapping classes and their representations by products of two Dehn twists
    By Chaohui Zhang, Morehouse College
    Accepted for publication in Chinese Ann. Math. Series AC.
  • Teaching Numerical Analysis with Mathcad
    By D.-T. Wu, Morehouse College
    Accepted for publication in "Transformation: Liberal Arts in Digital Age", ACS.

  • Relative Projectivity to G-sets and its Cohomology
    By Chuang Peng
    submitted to Journal of Algebra.

    Books
  • Proceedings of Dynamic Systems and Applications
    G. S. Ladde, N. G. Medhin, Chuang Peng, and M. Sambandham
    Volume 5, 2008, Dynamic Publishers.


    2007

    Articles

  • The Potential of Cumulative Voting to Yield Fair Representation
    By D. Cooper, Morehouse College
    Journal of Theoretical Politics 19, No. 3, (2007) 277-295.

  • Resolution of some mapping classes
    By Lixin Liu and Chaohui Zhang, Morehouse College
    Acta Math. Sinica 50, No. 5, (2007) 1141-1150.

  • Numerical Solution to Hybrid Fuzzy Systems
    By S. Pederson and M. Sambandham, Morehouse College
    Mathematical and Computer Modelling 45, No. 9-10, (2007) 1133-1144.

  • Hyperbolic mapping classes and their lifts on Bers fiber space
    By Chaohui Zhang, Morehouse College
    Chinese Ann. of Mathematics 28, Series B (2007) 55-66.


    2006

    Articles

  • Numerical Treatment of Hybrid Fuzzy Systems
    By S. Pederson and M. Sambandham, Morehouse College
    Proceedings of the Fifth International Conference on Engineering Computational Technology, Paper 214 (2006).

  • Structure Theorems for Matrix Rings Over Moore-Penrose Two (MP2) Rings
    By Gregory Battle, Morehouse College
    2005 ACRMS Conference Proceedings (2006) 152-161.

  • Covariance of the Number of Real Zeros of a Random Trigonometric Polynomial
    By K. Farahmand, University of Ulster, UK and M. Sambandham, Morehouse College
    International Journal of Mathematics and Mathematical Sciences, 2006, Art. ID 28492.

  • Boundedness Properties of Hybrid Fuzzy Differential Equations
    By M. Sambandham, Morehouse College
    Dynamic Systems and Applications 15 (2006) 149-156.

  • Learning C² and Hölder Functions
    By D. Cooper
    International Journal of Pure and Applied Mathematics 32 (1), 71-82.

  • An Improved Bound for Learning Lipschitz Functions
    By D. Cooper
    Communications in Applied Analysis 10, no. 1, 19-27 (2006).

  • On the Average Number of Real Zeros of Random Hyperbolic Polynomials
    By K. Farahmand, University of Ulster, UK, M. Sambandham and R. Bozeman, Morehouse College,
    Proceedings of Neural, Parallel and Scientific Computations 3 (2006) 57-59.

  • A Study Note on Fuzzy Elements and Operations
    By Chuang Peng
    Proceedings of Neural, Parallel and Scientific Computations 3 (2006) 196-202.

  • Homoclinic trajectories for fuzzy differential equations
    By Steve Pederson
    Proceedings of Neural, Parallel and Scientific Computations 3 (2006) 193-195.



    Books
  • Proceedings of Neural, Parallel & Scientific Computations
    G. S. Ladde, N. G. Medhin, Chuang Peng, and M. Sambandham
    Volume 3, 2006, Dynamic Publishers.

  • An Introduction to Moore-Penrose Rings, Volume I
    By Gregory Battle, Morehouse College
    iUniverse Inc., Lincoln, NE, 2006.


    2005

    Articles

  • Average Number of Points of Inflection of a Random Sum of Orthogonal Polynomials
    By K. Farahmand, University of Ulster, UK, M. Skinner, and M. Sambandham, Morehouse College
    International Journal of Applied Mathematics 18 (2005) 203-211.

  • Representations of Fuzzy Groups and Algebras
    By Chuang Peng
    International J. of Pure and Applied Mathematics 25, No. 2, 215-224 (2005).

  • On the status of the extension of quasiconformal mappings to the boundary
    By A. Brania, Morehouse College, Atlanta, GA
    in Proceedings of The 12th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, 41-48.

  • On Minimizing Sequences for an Optimization Problem Governed by an Integral Equation
    By N. G. Medhin, North Carolina State University, Raleigh, NC and M. Sambandham Morehouse College, Atlanta, Georgia,
    Dynamic Systems and Applications 14 (2005) 607-614.

  • Minimum Degrees of Polynomial Models on Time Series
    By Chuang Peng Morehouse College, Atlanta, Georgia,
    Discrete and Continuous Dynamical Systems, supp. vol. 2005, 270-279.

  • The contribution of technology to education
    By De Ting Wu, Morehouse College
    Fourth iNet online conference
    (go to "New technologies", then "Conference papers") .

  • Modular transformations of Bers fiber spaces
    By Chaohui Zhang, Morehouse College
    Complex Variables- Theory and Application 50 (3) (2005) 217-227.

  • A Moore-Penrose Property Of A Matrix Ring Over A Formal Power Series Quotient Ring
    By Gregory Battle, Morehouse College
    The PI 3 (2005) 25-30.

  • Fuzzy homoclinic orbits and commuting fuzzifications
    By Steve Pederson
    Fuzzy Sets and Systems 155 (3) 361-371.

  • Homoclinic orbits in Self-Mappings of a Space of Fuzzy Sets
    By Steve Pederson
    Proceedings of NAFIPS 2005, Ann Arbor, Michigan, 774-776.


    2004

    Articles

  • Some remarks on Bers fiber spaces
    By Chaohui Zhang, Morehouse College
    Complex Variables- Theory and Application 49 (10) (2004) 731-738.

  • Numerical Estimation of Munitions Payload Using Random Distributions
    By Gregory Battle, Morehouse College
    Journal of Parametrics 24 (2004) 1-20.

  • Modeling Two Dynamical Lane Navigational Problems
    By Gregory Battle, Morehouse College
    Proceedings of the Eighth World Multi-Conference on Systemics, Cybernetics and Informatics, Vol. V (2004) 322-324.

  • A Threefold Treastise On HOSC Performance Metrics, Implementing Full Cost Analysis, And A Competition Matrix For Future Business Planning
    By Gregory Battle, Morehouse College
    The 2004 NASA Faculty Fellowship Program Research Reports, NASA/CR-2005-213847, Marshall Space Flight Center, (2005) III-1 to III-26.

  • Davenport Numbers & Generating Functions over Finite Abelian Groups
    By Chuang Peng
    Proc. Dynamic Systems & App. 4 (2004) 535-541.

  • Spatial Analysis of Cumulative Voting with Modeling for Dynamical System Simulation
    By D. Cooper
    Proc. Dynamic Systems & App. 4 (2004) 596-601.

  • Recommendations for Increasing the Participation and Success of Blacks in Graduate Mathematics Study
    By D. Cooper
    Notices of the American Mathematical Society 51 (5) (2004) 538-543.

  • Keeping a Proper Perspective about Your Students
    By D. Cooper
    in M. Chappelle, J. Choppin, J. Salls (eds.), Empowering the Beginning Teacher of Mathematics in High School. Reston, Va.: National Council of Teachers of Mathematics (2004) p. 12; also in M. Chappelle and T. Pateracki (eds.), Empowering the Beginning Teacher of Mathematics in Middle School, p. 6; also in M. Chappelle, J. Schielack, S. Zagorski (eds.), Empowering the Beginning Teacher of Mathematics in Elementary School, p. 9. Reston, Va.: National Council of Teachers of Mathematics.

  • On the quasisymmetric invariance of a generalized modulus
    By A. Brania, Morehouse College, Atlanta, GA
    Archives of Inequalities and Applications 2 (2004) 85-94.

  • Asymptotically symmetric embeddings and symmetric quasicircles
    By A. Brania and S. Yang
    Proc. of the American Mathematical Society 132 (2004), no. 9, 2671-2678 (electronic).

  • Random and deterministic fixed point theory for generalized contractive maps
    R.P. Agarwal, Florida Institute of Technology, FL
    Donal O'Regan, National University of Ireland, Ireland, and
    M. Sambandham, Morehouse College, GA
    Applicable Analysis 83 (2004) 711-725.

  • Linear Transformations on Polynomial Models of Time Series
    By Aihua Li and Chuang Peng
    International Journal of Pure and Applied Mathematics 17, No. 2 (2004), 235-248.

  • Algebraic and Topological Entropy on Lie Groups
    By Chuang Peng
    Mathematical and Computer Modelling 39, No. 1 (2004) 13-19.

  • Teaching Numerical Analysis with MATHCAD
    By D.-T. Wu, Morehouse College, Atlanta, GA
    ICTCM Proceedings of the 15th Annual International Conference on Technology in Collegiate Mathematics (2004) 328-331.

  • Mathcad's Program Function and Application in Teaching of Math
    By D.-T. Wu, Morehouse College, Atlanta, GA
    Electronic Proceedings of ICTCM 16

  • Cas and Teaching of Calculus
    By D.-T. Wu, Morehouse College, Atlanta, GA
    TSG 12 of ICME-10 (click "Program" then "TSG 12" and Proceedings of ICME-10 will appear)

  • Approximate Schemes For Stochastic Oscillators and Stochastic Resonance of Noninvasive Control
    By D.-T. Wu, Morehouse College, Atlanta, GA
    International Journal of Pure and Applied Mathematics 18 (2) (2004).

  • White Noise Perturbation in a Model Equation for the Viscoelastic Response of Rubber in Tensile Deformation
    By N. Begashaw, Benedict College, Columbia, SC,
    Negash G. Medhin, North Carolina State University, Raleigh, NC, and
    M. Sambandham, Morehouse College, Atlanta, GA
    Proc. Dynamic Systems & App. 4 (2004) 27-33.

  • Method of Vector Lyapunov-Like Functions and Hybrid Fuzzy Differential Systems
    By M. Sambandham, Morehouse College, Atlanta, GA
    Dynamic Systems & App. 13 (2004) 581-591.

  • Homoclinic orbits and bifurcation of entropy-carrying hit-sets
    By Steve Pederson
    Proc. Dynamic Systems & App. 4 (2004) 87-94.

    Books
  • Stochastic versus Deterministic Systems of Differential Equations
    G. S. Ladde and M. Sambandham
    Marcel Dekker, Inc., New York, 2004.

  • Proceedings of Dynamic Systems and Applications
    By G. S. Ladde, N. G. Medhin, and M. Sambandham
    Volume 4, 2004, Dynamic Publishers.


    2003

    Articles

  • Practical Stability of Hybrid Fuzzy Differential Equations
    By A. Brania, C. Finley, and M. Sambandham, Morehouse College
    Mathematical Research 9 (2003) 67-73.

  • Teaching Numerical Analysis with Mathcad
    By D.-T. Wu, Morehouse College, Atlanta, GA
    The International Journal of Computer Algebra in Mathematics Education 10, No. 1 (2003) 55-77.

  • Comparison of actual and analytic computational error estimates to Ito-type stochastic differential equations
    By G.S. Ladde, University of Texas at Arlington,
    S. Pederson, and M. Sambandham, Morehouse College, Atlanta, GA
    International Journal of Computational and Numerical Analysis and Applications 4 (2003) 189-199.

  • The Role of Mathematics Teachers' Content Knowledge in Their Teaching: A Framework for Research Applied to a Study of Student Teaching
    By J. Kahan, D. Cooper, and K. Bethea
    Journal of Mathematics Teacher Education, Vol. 6, No. 3 (2003), 223-252.

  • Numerical Schemes and PC Program for Stochastic Oscillators
    By D.-T. Wu, Morehouse College, Atlanta, GA
    International Journal of Computational and Numerical Analysis and Applications 3, No. 2 (2003) 171-192.

  • Hybrid Fuzzy Systems on Time Scales
    By M. Sambandham, Morehouse College, Atlanta, GA
    Dynamic Sys. Appl. 12 (2003) 217-227.

  • Real zeros of classes of random algebraic polynomials
    By K. Farahmand, University of Ulster, Northern Ireland, UK, and
    M. Sambandham, Morehouse College, Atlanta, GA
    Journal of Applied Mathematics and Stochastic Analysis, 16 (3) 2003, 249-255.

  • On Homoclinic Tangencies in Maps with Entropy-carrying Horseshoes
    By Steve Pederson
    Nonlinear Studies 10 (2003) 177-186.

  • Error Estimates for Random Boundary Value Problems with Applications to a Hanging Cable Problem
    By G. S. Ladde, N. G. Medhin, and M. Sambandham
    Mathematical and Computer Modelling 38 (2003) 1037-1050.


    2002

    Articles

  • A Note on Random Fixed Point Theorems for Single Valued
    Generalized Contractive Random Maps
    R.P. Agarwal, Florida Institute of Technology, FL
    Donal O'Regan, National University of Ireland, Ireland, and
    M. Sambandham, Morehouse College, GA
    Nonlinear Analysis Forum 7 (2002) 231-236.

  • Random fixed point theory for multivalued countably condensing random operators
    By R.P. Agarwal, D. O'Regan, and M. Sambandham
    Stochastic Analysis and Applications 20 (2002) 1157--1168.

  • Random degree and essentiality for countably condensing maps
    By R. P. Agarwal, D. O'Regan, and M. Sambandham
    Stochastic Analysis and Applications 20 (2002) 1169--1176.

  • A Proof and a PC Program for Runge-Kutta Method of Order 3 of ODE
    By De Ting Wu and Robert Bozeman, Morehouse College, Atlanta, GA
    Proceedings of Neural, Parallel, and Scientific Computations, Volume 2 (2002) 193-198.

  • Necessary Conditions on Minimizing Sequences for an Extremal Problem Governed by an Integral Equation
    By N. Begashaw, Negash Medhin, Clark Atlanta University, GA and
    M. Sambandham, Morehouse College, Atlanta, GA
    Proceedings of Neural, Parallel, and Scientific Computations, Volume 2 (2002) 83-86.

  • The importance of Profile Analysis and Covariance Analysis on Four Independent Variables
    By Shirley W. Thompson, Morehouse College, Atlanta, GA
    Proceedings of Neural, Parallel, and Scientific Computations, Volume 2 (2002) 91-94.

  • An Investigation of the Robustness and Stability of the DeChamplain - Gessaroli Approximate Chi-Square Statistic to Assess Fundamental Unidimensionality in Item Response Spaces
    By Padraig McLoughlin, Morehouse College, Atlanta, GA
    Proceedings of Neural, Parallel, and Scientific Computations, Volume 2 (2002) 87-90.

  • The move number of the four-cycle is six
    By Curtis Clark, Morehouse College, Atlanta, GA and Frank Harary and Thomas Storer, New Mexico State University, NM
    Proceedings of Neural, Parallel, and Scientific Computations, Volume 2 (2002) 291-294.

  • Addition Theorems over Finite Groups
    By Chuang Peng, Morehouse College, Atlanta, GA
    Proceedings of Neural, Parallel, and Scientific Computations, Volume 2 (2002) 301-306.

  • Random trigonometric polynomials with stable distribution
    By Maya C. Mukherjee and M. Sambandham, Morehouse College, Atlanta, GA
    Proceedings of Neural, Parallel, and Scientific Computations, Volume 2 (2002) 79-82.

  • Real Zeros of Random Trigonometric Polynomials
    By Robert Bozeman, Morehouse College, Atlanta, GA, K. Farahmand, University of Ulster, Northern Ireland, UK, and M. Sambandham, Morehouse College, Atlanta, GA
    Proceedings of Neural, Parallel, and Scientific Computations, Volume 2 (2002) 75-78.

  • Comparison Theorem for Hybrid Fuzzy Differential Equations
    Abdelkrim Brania, Morehouse College, Atlanta, GA,
    Negash G. Medhin, Clark Atlanta University, GA, and
    M. Sambandham, Morehouse College, Atlanta, GA
    Computational Intelligence and Applications, (2002) 101-106.

  • Perturbing Lyapunov-like functions and hybrid fuzzy differential equations
    By M. Sambandham
    International Journal of Hybrid Systems 2 (2002) 23-34.

  • A continuous 2-parameter family with nonconnected iso-entropy curves
    By Abdelkrim Brania, Morehouse College, Atlanta, GA and
    Steve Pederson, Morehouse College, Atlanta, GA
    Proceedings of Neural, Parallel, and Scientific Computations, Dynamic Publishers, Volume 2 (2002) 249-252.

  • Domains with controlled modulus and quasiconformal mappings
    By A. Brania and S. Yang
    Nonlinear Studies 9 (2002) 57-73.

  • Homoclinic Tangencies in Unimodal Families with Non-constant Topological Entropy
    By Steve Pederson
    Dynamic Systems and Applications 11 (2002) 65-74.

    Books
  • Proceedings of Neural, Parallel & Scientific Computations
    M. P. Bekakos, G. S. Ladde, N. G. Medhin, and M. Sambandham
    Volume 2, 2002, Dynamic Publishers.

  • Computational Intelligence and Applications
    Ajith Abraham, Baikunth Nath, M. Sambandham, and P. Saratchandran
    Dynamic Publishers, 2002.


    2001

    Articles

  • Active and Passive Damping in a Beam
    By N. G. Medhin and M. Sambandham
    Proc. Dynamic Systems & Applications, 3 (2001) 419-426.

  • Destroyable restrictive intervals and two unimodal map models arbitrarily close to homoclinic tangencies
    By Steve Pederson
    Proc. Dynamic Systems & Applications 3 (2001) 505-510.

  • Non-turning Poincare Map and Homoclinic Tangencies in Interval Maps with Non-constant Topological Entropy
    By Steve Pederson
    Proc. of the Third International Conference on Dynamical Systems and Differential Equations, Discrete and Continuous Dynamical Systems, Added Volume 2001, 295-302.

    Books
  • Proceedings of Dynamic Systems and Applications,
    By G. S. Ladde, N. G. Medhin, and M. Sambandham
    Volume 3, 2001, Dynamic Publishers