Jess & Mildred Fisher College of Science & Mathematics


Department of Mathematics

Faculty Research and Scholarship

Applied Mathematics

Dr. Sergiy Borodachov's current research interests are in the fields of approximation theory, discrete minimum energy problems as well as quantization and fractal analysis.

Some of Dr. Borodachov's publications include:

  • Sergiy Borodachov, Edward Staff and Douglas Hardin, Low complexity methods for discretizing manifolds via Riesz energy minimization, Foundations of Computational Mathematics (to appear).
  • Sergiy Borodachov, Tim Bedford and Jeff Geronimo, A topological separation condition for fractal attractors, Journal of Fractal Geometry (to appear).
  • Sergiy Borodachov and Nattapong Bosuwan, Asymptotics of discrete Riesz d-polarization on subsets of d-dimensional manifolds, Potential Analysis (to appear).
  • Sergiy Borodachov and Tatyana Sorokina, Optimal recovery of twice differentiable functions based on symmetric splines, Journal of Approximation Theory 164 (No. 10, 2012), 1443–1459.
  • Sergiy Borodachov, Lower order terms of the discrete minimal Riesz energy on smooth closed curves, Canadian Journal of Mathematics 64 (2012), 24–43.
  • Vladyslav Babenko, Sergiy Borodachov, and Dmytro Skorokhodov, Optimal cubature formulas related to tomography for certain classes of functions defined on a cube, Jaen Journal on Approximations 3 (No. 2, 2011), 143–160.
  • Sergiy Borodachov, Asymptotics for the minimum Riesz energy and best-packing on sets of finite packing premeasure, Publicacions Matemàtiques minimum Riesz energy and best-packing on sets of finite packing premeasure, Publicacions Matemàtiques 56 (No. 1, 2011), 225–254.
  • Sergiy Borodachov and Yuliya Babenko, Inequalities for the norms of finite difference operators of multiply monotone sequences, Mathematical Inequalities and Applications 15 (No. 2, 2012), 247–269.
  • Sergiy Borodachov and Tatyana Sorokina, An optimal multivariate spline method of recovery of twice differentiable functions, BIT Numerical Mathematics 51 (No. 3, 2011), 497–511.
  • Vladyslav Babenko, Sergiy Borodachov, and Dmytro Skorokhodov, Optimal cubature formulas for tensor products of certain classes of functions, Journal of Complexity, 27 (No. 6, 2011),
    519–530.


Dr. Raouf Boules' current research interests are in the fields of spectral estimation theory, Fourier analysis, optimal filtering and electrodynamics.

Some of Dr. Boules' publications include:

  • R. Boules, G.R. Goodson, O. Kim and M. O'Leary, Laboratory Manuals for Single Variable and Multivariable Calculus,  Harcourt Publishing Company, 2000.
  • Raouf Boules, Numerical Analysis Using Mathematica, 3rd ed., Towson University Printing Services, August 1999.
  • R. Boules,, H. Harmuth and M. Hussain, Electromagnetic Signals: Reflection, Transmission, Focusing, Distortion, and Their Practical Applications, Kluwer Academic/Plenum Publishers, New York, 1999.

Some of Dr. Boules' recent presentations at conferences include:

  • “Using computer algebra systems in the teaching of mathematics”, The Tenth International Congress on Mathematics Education (ICME-10), Copenhagen, July 2004.


Dr. Elizabeth Goode's current research interests are in the fields of splicing systems and DNA computing.

Some of Dr. Goode's recent publications include:

  • Elizabeth Goode and William DeLorbe, DNA splicing systems: an ordinary differential equations model and simulation, Springer-Verlag's Lecture Notes in Computer Science 4848 (2008), 236–245.
  • Elizabeth Goode, Recognizing splicing languages: syntactic monoids and simultaneous pumping, Discrete Applied Mathematics Journal, (to appear).
  • E. Goode and D. Pixton, “Splicing to the limit”, Aspects of molecular computing - essays dedicated to Tom Head on the occasion of his 70th birthday, N. Jonoska, G. Paun & G. Rozenberg, Eds. , Springer, Lecture Notes in Computer Science 2950 (2004), 189–201.
  • E. Goode, T. Head and D. Pixton, “Splicing systems: regularity and below”, DNA Computing, 8th International Workshop on DNA-Based Computers, M. Hagiya & A. Ohuchi, Eds., Springer, Lecture Notes in Computer Science 2568 (2003), 262–268.
  • E. Goode and G. Trajkovsky, Napoleon's soldiers, CCSC, Journal of Computing Sciences in Colleges 18 (2003), 193–197.


Dr. Ge Han's current research interests are in the fields of applied mathematics, financial mathematics and differential equations.

Some of Dr. Han's publications include:

  • Ge Han, Xuezhang Hou and Xiaoning Li, The well-posedness of singular second-order dynamic system with Dirichlet boundary value problems, International Journal of Pure and Applied Mathematics (to appear).
  • Ge Han, Analysis of American options on multi-assets, International Journal of Pure and Applied Mathematics (to appear).
  • Ge Han and Jay Zimmerman, Predicting demand for the Carroll Area Transit Authority, The UMAP (Undergraduate Mathematics Applications) Journal 27 (No. 1, 2006).


Dr. Xuezhang (John) Hou's current research interests are in the fields of system control theory, semigroup of linear operators and differential equations.

Some of Dr. Hou's recent publications include:

  • Xuezhang Hou, Spectral analysis and variable structural control of an elastic beam, Journal of Applied Mathematics and Physics (to appear).
  • Xuezhang Hou, Coupled linear feedback and sliding model control for a serially connected Euler-Bernoulli beam, General Mathematics Notes 16 (No. 2, 2013), 1–13.
  • Xuezhang Hou, An optimal energy control of a flexible plate with viscoelastic boundary conditions, International Journal of Differential Equations and Applications 11 (No. 2, 2012), 109–120 .
  • Xuezhang Hou, J. Fu and R. Chen, An optimal distributed control for age-dependent population diffusion system, General Mathematics Notes 6 (No. 1, 2011), 73–85.
  • Xuezhang Hou, Ge Han and Xiaoning Li, The well-posedness of singular second-order dynamic system with Dirichlet boundary value problems, International Journal of Pure and Applied Mathematics 66 (No. 2, 2011), 221–228.
  • Xuezhang Hou, Spectral analysis and semigroup generation for an elastic beam system, Acta Analysis Functionalis Applicata 13 (No. 3, 2011), 319–331.
  • Xuezhang Hou, H. Gao, S. Weng and D. Jiang, Existence principle of solutions to non-resonant singular boundary value problems, Journal of Mathematical Sciences 177 (No. 3, 2011),
    466–473.
  • Xuezhang Hou, Mostafa Aminzadeh and S. Ren, Nonparametric bootstrapping for hierarchical data, Journal of Applied Statistics 37 (No. 9, 2010), 1487–1498.
  • Xeuzhang Hou, An optimal control for a flexible Euler-Bernoulli beam, Journal of System Science and Information 11 (No. 2, 2009),159–165.

Some of Dr. Hou's recent presentations at National and International conferences include:

  • “A Variable Structure Control for a Flexible Euler-Bernoulli Beam”, research presentation at IEEE International Conference on Automation and Logistics, Hong Kong and Macau, China, 2010.
  • “An Optimal Control for a Flexible Robot Arm”, research presentation at the IEEE International Conference on Automation and Logistics, Shenyang, China, 2009.
  • “Sliding Model Control for a Flexible Robot Arm”, research presentation at the IEEE International Conference on Industrial Technology, Chengdu, China, 2008.
  • “Control and Simulation of a Flexible Robot Systems Formulated by Partial Differential Equations”, research presentation at the International Conference on Partial Differential equations and Numerical Analysis, Guangshou, China, 2007.
  • “Upper and lower solutions for nonresonant singular dirichlet boundary vale problems”, lecture at the 2006 Hawaii International Conference on Statistics, Mathematics and Related Fields, Hawaii, 2006.


Dr. Ohoe Kim's current research interests are in the fields of stochastic processes and mathematical finance.

Some of Dr. Kim's publications include:

  • Ohoe Kim, Xuezhang Hou and Ge Han, An operator approach in birth-death process, International Journal of Pure and Applied Mathematics 15 (No. 4, 2004).
  • Ohoe Kim, Computer laboratories for mathematical finance using Mathematica and Excel, Proceedings of International conference on Technology in Collegiate Mathematics, Addison Wesley (2002).
  • R. Boules, G.R. Goodson, O. Kim and M. O'Leary, Laboratory Manuals for Single Variable and Multivariable Calculus,  Harcourt Publishing Company, 2000.


Dr. Michael O'Leary's current research interests are primarily in the fields of applied mathematics, including partial differential equations, fluid dynamics and computer security.

Some of Dr. O'Leary's publications include:

  • Michael O'Leary, Multimodel inference and geographic profiling, Crime Mapping: A Journal of Research and Practice 2 (No. 1, 2010).
  • Michael O'Leary, The mathematics of geographic profiling, Journal of Investigative Psychology and Offender Profiling 6 (No. 3, October 2009), 253–265.

Some of Dr. O'Leary's recent presentations at conferences include:

  • “Implementing a Bayesian approach to criminal geographic profiling”, First International Conference on Computing for Geospatial Research and Application, Washington DC, June 2010.
  • “A cross-institutional faculty research mentorship program in information security and assurance”, Proceedings of the 14th Colloquium for Information Systems Security Education, Baltimore, MD, June 2010 [with Claude Turner and Jidé Odibuyi].
  • “Cooperative information assurance capacity building”, Proceedings of the 13th Colloquium for Information Systems Security Education, Seattle, WA, June 2009 [with Claude Turner, Harry Hochheiser, Jinjuan Feng, Blair Taylor, Jonathan Lazar, Azene Zenebe and Shiva Azadegan].
  • “Cross-site security integration: preliminary experiences across curricula and institutions”, Proceedings of the 13th Colloquium for Information Systems Security Education, Seattle, WA, June 2009 [with Blair Taylor, Harry Hochheiser and Shiva Azadegan].

Dr. O'Leary has received the following grants:

  • Michael O’Leary (PI), Scott Hilberg and Suranjan Chakraborty (co-PIs), Expanding the Reach of IT Programs, Maryland Higher Education Commission BRAC Higher Education Fund, $73,844, January – December 2011.
  • Michael O’Leary (PI), The Mathematics of Geographic Profiling, National Institute of Justice (2009-SQ-B9-K014), $95,465, August 2009 – July 2011.
  • Michael O’Leary (PI), Siddharth Kaza and Subrata Acharya (co-PIs), Expanding an Applied Information Technology Masters Program, Maryland Higher Education Commission BRAC Higher Education Fund, $90,990, January – December 2009.
  • Harry Hochheiser (PI), Blair Taylor, Shiva Azadegan, Claude Turner and Michael O’Leary (co-PIs), Building Security In: Injecting Security throughout the Undergraduate Computing Curriculum, National Science Foundation, Course Curriculum and Laboratory Improvement: Phase 2 (Expansion Projects) (DUE 0817267), $399,506 , September 2008 –August 2011.


Dr. Moustapha Pemy's current research interests are in stochastic analysis, control theory, financial mathematics, Markov switching, free boundary problems and nonlinear functional analysis.

Some of Dr. Pemy's publications include:

  • Moustapha Pemy, Optimal stopping of  Markov switching L’evy processes, Stochastics (to appear).
  • Moustapha Pemy, Control of regime switching L’evy processes and application to optimal trading strategies, Journal Applied Mathematics (to appear).
  • Moustapha Pemy, Tao Pang and Houshiung Chang, Viscosity solution of optimal stopping problem for stochastic systems with bounded memory, Journal of Stochastic Analysis and Applications 30 (No. 6, 2012), 1102–1135.
  • Moustapha Pemy, Optimal algorithms for trading large positions, Automatica 46 (No.7, July 2012) 1353–1358.
  • Moustapha Pemy, Optimal selling rule in a regime switching lévy market, International Journal of Mathematics and Mathematical Sciences 2011, Article ID 264603, 28 pages, doi:10.1155/2011/264603.
  • Moustapha Pemy, Mou-Hsiung Chang and Tao Pang, An approximation scheme for Black-Scholes equations with delays, Journal of Systems Science and Complexity, 23 (No. 3, 2010), 438–455.
  • Moustapha Pemy, Mou-Hsiung Chang and Tao Pang, Finite difference approximations for stochastic control system with delay, Journal of Stochastic Analysis and Applications 26 (No. 3, 2008), 451–470.

Dr. Pemy has received the following grant:

  • Henry C. Welcome Fellowship grant from the Maryland Higher Education Commission.


Dr. Tatyana Sorokina's current research interests are primarily in the fields of approximation theory (splines), computer aided geometric design and numerical analysis.

Some of Dr. Sorokina's publications include:

  • Tatyana Sorokina and Alexei Kolesnikov, Multivariate C1- continuous splines on the Alfeld split of a simplex, Approximation Theory XIV: San Antonio 2013, Springer Proceedings in Mathematics (to appear).
  • Tatyana Sorokina, Redundancy of smoothness conditions and supersmoothness of bivariate splines, IMA Journal of Numerical Analysis (to appear).
  • Tatyana Sorokina and Sergiy Borodachov, An optimal multivariate spline method of recovery of twice differentiable functions, BIT Numerical Mathematics 51 (No. 3, 2011), 497–511.
  • Tatyana Sorokina, Intrinsic super-smoothness of multivariate splines, Numerische Mathematik 116 (No. 3, 2010), 421–434.
  • Tatyana Sorokina, Peter Alfeld and Larry Shumaker, Two condensed macro-elements with full approximation power, Advances in Computational Mathematics 32 (2010), 381–391.
  • Tatyana Sorokina, Larry Shumaker and Andrew Worsey, A C1 quadratic trivariate macro-element space defined over arbitrary tetrahedral partitions, Journal of Approximation Theory 158 (No. 1, 2009), 126–142.
  • Tatyana Sorokina and Peter Alfeld, Two tetrahedral C1 cubic macro elements, Journal of Approximation Theory 157 (No. 1, 2009), 53–69.
  • Tatyana Sorokina, A C1 multivariate Clough-Tocher interpolant, Constructive Approximation 29 (No. 1, 2009). 41–59.
  • T. Sorokina and F. Zeilfelder, An explicit quasi-interpolation scheme based on C1 quartic splines on type-1 triangulations, Journal of Computer Aided Geometric Design 25 (2008), 1–13.
  • Tatyana Sorokina and Andrew Worsey, A multivariate Powell-Sabin interpolant, Advances in Computational Mathematics 29 (No. 1, July 2008), 71–89.


Dr. Mircea Voisei's current research interests are in the fields of nonlinear analysis, optimization, and ordinary partial differential equations.

Some of Dr. Voisei's publications include:

  • Mircea Voisei and C. Zălinescu, Counterexamples to a triality theorem for quadratic-exponential minimization problems, Mathematical Methods of Operations Research (to appear)
  • Mircea Voisei, Characterizations and continuity properties for maximal monotone operators with non-empty domain interior, Journal of Mathematical Analysis and Applications, 391 (2012), 119–138.
  • M.D. Voisei and C. Zălinescu, Counter-xxamples in bi-duality, triality and tri-duality, Discrete and Continuous Dynamical Systems 31 (No. 4, 2011) 1453–1468.
  • M.D. Voisei and C. Zălinescu, Some remarks concerning Gao–Strang’s complementary gap function, Applicable Analysis 90 (No. 6, 2011), 1111–1121.
  • M.D. Voisei and C. Zălinescu, Counterexamples to a triality theorem in "Canonical dual least square method", Computational Optimization and Applications 49 (No. 1, 2011) 173–183.
  • M.D. Voisei and C. Zălinescu, A counter-example to “Minimal distance between two non-convex surfaces”, Optimization 60 (No. 5, 2011), 593–602.
  • M.D. Voisei and C. Zălinescu, Counterexamples to some triality and tri-duality result, Journal of Global Optimization 49 (No. 1, 2011), 173–183.
  • M.D. Voisei and C. Zălinescu, Linear monotone subspaces of locally convex spaces, Set-Valued and Variational Analysis, 18 (No. 1, 2010), 29–55.
  • M.D. Voisei and C. Zălinescu, Maximal monotonicity criteria for the composition and the sum under weak interiority conditions, Mathematical Programming, 123 (No. 1, 2010), 265–283.

 

Department of Mathematics
7800 York Road, Room 316 (campus map)
Hours: Monday - Friday, 8:30 a.m. – 5 p.m.

Phone: 410-704-3091
Fax: 410-704-4149
E-mail: math@towson.edu


 

 

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