Note: The information is provided by each faculty member individually.
Catherine Bénéteau, Ph.D., SUNY-Albany, 1999; Assistant Professor. cbeneteau@cas.usf.edu
Research Interests: Complex analysis, interpolation, extremal problems in Hardy and Bergman spaces.
Selected Publications: Jensen-type inequalities and radial null sets (with B. Korenblum), Analysis 21 (2001), 99-105. Some coefficient estimates for HP functions (with B. Korenblum), “Complex Analysis and Dynamical Systems”, Contemporary Mathematics, vol. 364, 2004, pp. 5-14. Remarks on the Bohr phenomenon (with A. Dahlner and D. Khavinson), Computational Methods and Function Theory 4 (2004), no. 1, 1-19. Extremal problems for non-vanishing functions in Bergman spaces (with D. Aharonov, D. Khavinson and H. S. Shapiro), Operator Theory: Advances and Applications 158 (2005), 59-86. The isoperimetric inequality via approximation theory and free boundary problems (with D. Khavinson), Computational Methods and Function Theory 6 (2006), no. 2, 253-274.
W. Edwin Clark, Ph.D., Tulane University, 1964; Professor Emeritus. eclark@math.usf.edu
Research Interests: I am interested in a variety of algebraic, combinatorial and geometric problems. I have secondary interests in semigroups of matrices, associative rings and algebras, homological algebra, and categorical aspects of rings and semigroups.
Selected Publications: On the probability that a t-subset of a finite vector space contains an r-subspace---with applications to short, light codewords in a BCH code, (with Stephen Suen), Congressus Numerantium 137 (1999), 139-159. k-Point separating families of functions (with Gregory McColm and Boris Shekhtman), Journal of the London Mathematical Society (1998), no. 2, 297-310. Tight upperbounds for the domination number of graphs of given order and minimum degree, (with Larry Dunning), Electronic Journal of Combinatorics 4 (1997), no. 1, Research Paper 26, 1-25. Binomial and q-binomial coefficient inequalities related to the hamiltonicity of the Kneser graphs and their q-analogues, (with Mourad Ismail), Journal of Combinatorial Theory, Series A 76 (1996), no. 1, 83-98. Sum-free sets in vector spaces over GF(2) [with John Pedersen], Journal of Combinatorial Theory (Series A) 61 (1992), 222-229.
Brian Curtin, Ph.D., University of Wisconsin-Madison 1996; Associate Professor. bcurtin@chuma1.cas.usf.edu
Research Intersts: The algebraic combinatorics of distance-regular graphs, spin models, Bose-Mesner algebras, and planar algebras.
Selected Publications: Distance-regular graphs related to the quantum enveloping algebra of sl(2). (with K. Nomura), Journal of Algebraic Combinatorics 12 (2000), 25-36. The Terwilliger algebra of a 2-homogeneous bipartite distance-regular graph. Journal of Combinatorial Theory, Series B 81 (2001), 125-141. Spin models and hyper-self-dual Bose-Mesner algebras. (with K. Nomura), Journal of Algebraic Combinatorics 13 (2001), 173-186. Some planar algebras related to graphs, preprint.
Natasha Jonoska, Ph.D., SUNY-Binghamton, 1993; Professor & Graduate Admissions Director. jonoska@math.usf.edu
Research Interests: Interaction between formal language theory and symbolic dynamics, cellular automata and picture languages, computation with splicing languages and connections to splicing DNA. In particular, I am interested in algorithms and mathematical problems rising from DNA-based computations.
Selected publications: Three Dimensional DNA Structures in Computing, BioSystems 52 (1999), 143-153. Bounded Complexity of DNA Computing, (with S. Karl and M. Saito), BioSystems 52 (1999), 63-72. DNA Hybridization, Shifts of Finite Type and Tiling of the Integers, in “Words, Sequences, Languages: Where Computer Science, Biology and Linguistics Meet,” (Carlos Martin-Vide, ed.), Kluwer, (to appear). A Conjugancy Invariant for Reducible Sofic Shifts and its Semigroup Characterizations, (with E. Coven), Israel J. Math. 106 (1998), 221-249.
A.G. Kartsatos, Ph.D., University of Athens, 1969; Professor. akartsat@chuma.cas.usf.edu
Research Interests: Nonlinear functional analysis; evolution equations in Banach spaces; accretive and monotone operator theory.
Selected Publications: On compact perturbations and compact resolvents of nonlinear m-accretive operators in Banach spaces, Proc. Amer. Math. Soc., 119 (1993), 1189-1199. The method of lines and the approximation of zeros of m-accretive operators in general Banach spaces [with K. Shin], J. Diff. Eq., 113 (1994), 128-149. Sets in the ranges of sums for perturbations of nonlinear m-accretive operators in Banach spaces, Proc. Amer. Math. Soc., (1995). A compact evolution operator generated by a nonlinear time-dependent m-accretive operator in a Banach space, Math. Ann., (1995). Ranges of perturbed maximal monotone and m-accretive operators in Banach spaces [with Z. Guan], Trans. Amer. Math. Soc., (1995).
Dmitry Khavinson, Ph.D., Brown University, 1983; Professor. dkhavins@cas.usf.edu
Research Interests: Complex analysis, operator theory, potential theory, partial differential equations, harmonic functions, approximation theory, free boundary problems, gravitational microlensing.
Selected Publications: Symmetry and uniform approximation by analytic functions (with H. S. Shapiro), Proc. Amer. Math. Soc. 101 (1987), no. 3, 475-483. Dirichlet's problem when the data is an entire function, Bull. London Math. Soc. 24 (1992), 458-468. Contractive zero divisors in Bergman spaces (with P. Duren, H. S. Shapiro and C. Sundberg), Pacific J. Math. 157 (1993), no. 1, 37-56. Invariant subspaces in Bergman spaces and the biharmonic equation (with P. Duren, H. S. Shapiro and C. Sundberg), Mich. Math. J. 41 (1994), 247-259. On Dirichlet series with gaps (with J. M. Anderson and H. S. Shapiro), Revista Math. Iber. 2 (1995), no. 2, 453-476. Extending solutions of holomorphic partial differential equations across real hypersurfaces (with P. Ebenfelt and H. S. Shapiro), J. London Math. Soc. 57 (1998), no. 2, 411-432. Point-to-point reflection of harmonic functions across real analytic hypersurfaces in Rn (with P. Ebenfelt), J. d'Analyse 68 (1996), 145-182. Bohr's power series theorem in several variables (with H. P. Boas), Proc. Amer. Math. Soc. 125 (1997), no. 10, 2975-2979. Certain linear extremal problems in Bergman spaces of analytic functions (with M. Stessin), Indiana Univ. Math. J. 46 (1997), 933-974. On a maximal number of zeros of certain harmonic polynomials (with G. Swiatek), Proc. Amer. Math. Soc. 131 (2003), no. 2, 409-414. On the number of zeros of certain rational harmonic functions (with G. Neumann), Proc. Amer. Math. Soc. 134 (2006), no. 4, 1077-1085.
Milé Krajcevski, Ph.D., SUNY-Binghamton, 1994; Instructor. mile@math.usf.edu
Research Interests: Geometric Methods in Group Theory, Combinatorial Group Theory, Hyperbolic Groups.
Selected Publications: Tilings of the plane, hyperbolic groups and small cancellation theory, Memoirs of the AMS (to appear).
Joseph J. Liang, Ph.D., Ohio State University, 1969; Professor Emeritus. liang@math.usf.edu
Research Interests: A unified theory of pattern recognition; coding theory, arithmetic simplification in a finite field; arithmetic invariants in algebraic number fields; fractals.
Selected Publications: Intelligent Systems for Processing Oriental Languages, (Edited by J. Ton & Liang), 1992. Mathematical classifications of evoked potential waveforms [with V. Clauson], IEEE Transactions in Systems, Man and Cybernetics 19 (1989). A new approach to classification of brainwaves, Pattern Recognition (1989). On extended fundamental sets over a finite field [with Y. Abbas], Communications in Algebra 13 (1985). On modular weight and nonajacent forms for arithmetic codes [with W.E. Clark], IEEE Trans. Inf. Theory 20 (1974). On relations between unit of normal algebraic number fields and their subfields, Acta Arithmetica 20 (1972).
Wen-Xiu Ma, Ph.D., Academia Sinica, Beijing, 1990; Associate Professor. mawx@math.usf.edu
Research Interests: Integrable systems, bi-Hamiltonian theory, symmetries and generalized symmetries, symmetry constraints and integrable decompositions, algebraic structures related to Lax pairs and soliton equations, symbolic computation of symmetries and conservation laws.
Selected Publications: Binary symmetry constraints of N-wave interaction equations in 1 + 1 and 2 + 1 dimensions, Journal of Mathematical Physics 42 (2001), 4345-4382 [with Z.X. Zhou]. Master symmetries from Lax operators for certain lattice soliton hierarchies, Journal of the Physical Society of Japan 69 (2000), 351-361 [with K. M. Tamizhmani]. Separation of variables for soliton equations via their binary constrained flows, Journal of Mathematical Physics 40 (1999), 6526-6557 [with Y.B. Zeng]. Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations, Journal of Mathematical Physics 40 (1999), 2400-2418 [with B. Fuchssteiner]. Extending Hamiltonian operators to get bi-Hamiltonian coupled KdV systems, Physics Letters A 246 (1998), 511-522 [with M. Pavlov]. Time-dependent symmetries of variable-coefficient evolution equations and graded Lie algebras, Journal of Physics A: Mathematical and General 30 (1997), 5141-5149 [with R. K. Bullough, P. J. Caudrey and W. I. Fushchych].
M.N. Manougian, Ph.D., University of Texas, 1968; Professor. manoug@math.usf.edu
Research Interests: Solutions of nonlinear ordinary and partial differential equations.
Selected Publications: The Perron integral and existence and uniqueness theorem for a first order nonlinear differential equation, Proc. Amer. Math. Soc. An existence theorem for a nonlinear differential equation, J. Diff. Eq. Oscillations of functional-differential equations, [with A.G. Kartsatos], J. Math. Anal. Appl.
Gregory L. McColm, Ph.D., UCLA, 1986; Associate Professor. mccolm@math.usf.edu
Research Interests: My primary interest is in mathematical logic and theoretical computer science, especially in logical expressibility, finite model theory, and descriptive and computational complexity. I am also interested in finite and infinite combinatorics, especially in Ramsey theory, random and extremal graph theory, and combinatorial games. I am also interested in random processes, category theory, and miscellaneous analysis. Additionally, I am interested in pedagogy and related fields of applied psychology, and in theoretical biology.
Selected Publications: When is arithmetic possible?, Ann. Pure Appl. Logic 50 (1990), no. 1, 29-51. A Ramseyian theorem for products of trees, J. Combinatorial Theory-A 57 (1991), no. 1, 68-75. Pebble games and subroutines in least fixed point logic, Inform. and Comp. 122 (1995), no. 2, 201-220. A splitting inequality, Ramanujan Journal 2 (1998), no. 4, 511-519.
Arunava Mukherjea, Ph.D., Wayne State University, 1967; Professor. arun@math.usf.edu
Research Interests: Probability on Algebraic Structures. Random walks and random matrices. Multivariate Analysis: Problems on Identification of Parameters.
Selected Publications: “Probability Measures on Semigroups: Convolution Products, Random Walks and Random Matrices,” (with G. Högnäs), The University Series in Mathematics, Plenum Press, New York, 1995, 400 pp. “Topics in Products of Random Matrices,” A publication of the Tata Institute of Fundamental Research, 2000, 121 pp. “Probability on Algebraic Structures,” (A. Mukherjea, G. Budzban and P. Feinsilver, eds.), American Mathematical Society, 2000, 238 pp.
Kenneth L. Pothoven, Ph.D., Western Michigan University, 1969; Associate Professor Emeritus. pothoven@chuma.cas.usf.edu
Research Interests: Measure theory, functional analysis, and nonlinear differential equations: e.g. boundary value problems involving nonlinearities dependent on derivatives and in investigating methods of nonlinear analysis to generate existence results.
Selected Publications: Real Analysis [Real and Functional Analysis], Part A, [with A. Mukherjea] (Plenum, New York, 1984). Functional Analysis [Real and Functional Analysis], Part B, [with A. Mukherjea] (Plenum, New York, 1986). Nonlinear elliptic equations at resonance where the non-linearity depends essentially on the derivative [with Nagle & Singhofer], J. Diff. Equations 38 (1980) 210-225.
Evgueni A. Rakhmanov, Sc.D., Steklov Mathematics Institute, Moscow, 1983; Professor. rakhmano@math.usf.edu
Research Interests: Analysis, theory of analytic functions, approximation theory (Padé and rational approximation), potential theory, orthogonal polynomials.
Selected Publications: On the convergence of diagonal Pade approximants, Math. USSR Sb. 33 (1977). On the convergence of simultaneous Pade approximants for systems of functions of Markov type, [with A.A. Gonchar] Proc. Steklov Inst. N3 (157). On the equilibrium problem for vector potentials, [with A.A. Gonchar], Russian Math. Surveys 40 (1985). Rational approximations, orthogonal polynomials, and equilibrium distributions [with G. Lopez], Lecture Notes in Math. 1329 (1988). Equilibrium distributions and degree of rational approximations of analytic functions [with A.A. Gonchar], Math. USSR Sb. 62 (1989), 305-348. Strong asymptotics for orthogonal polynomials associated with exponential weights, in Methods of Approximation Theory in Complex Analysis and Mathematical Physics, (Moscow, 1992), NAUKA, pp. 71-97. Electrons on the sphere [with E.B. Saff and Y.M. Zhou], ICM Report 94-012, Dept. of Mathematics, USF.
Kandethody M. Ramachandran, Ph.D., Brown University, 1987; Professor, ram@chuma.cas.usf.edu
Research Interests: Stochastic control problems; approximate solutions using weak convergence or Martingale techniques; computational techniques to obtain optimal controls; learning algorithms, which may arise in the context of artificial intelligence, via stochastic approximation techniques; applied problems involving stochastic calculus and distributed parameter systems; Software reliability, Digital communications, Applications of Wavelet analysis in Statistics and Signal Processing.
Selected Publications: Optimal and approximately optimal control policies or queues in heavy traffic, (with H.J. Kushner), SIAM J. Opt. and Control 27 (1989), 1293-1318. Asymptotic behavior of a hierarchical system of learning automata, (with M.A.L. Thathachar), Information Sciences 35 (1985), 91-110. Nearly optimal state feedback controls for delay differential equations with a small parameter, (with G. Yin), J. Math. Anal.Appl. 172 (1993), no. 2, 480-499. Stochastic differential games with a small parameter, Stochastics and Stochastics Reports 43 (1993), 73-91. Convergence problems for an impulsively and singularly controlled system, Nonlinear Analysis, Theory, Methods & Applications 30 (1997), no.1, 223-232. Wavelet Framework for joint Filtering and Compression based on Moments, (with R. Chandramouli and S. Gomatam), submitted to Signal Processing, 1999. Stochastic differential games and applications, book chapter, to appear in “Handbook of Stochastic Analysis and Applications,” (D. Kannan and V. Lakshmikantham, eds.), Marcel Dekker, Inc., 2000.
J.S. Ratti, Ph.D., Wayne State University, 1966; Professor. ratti@math.usf.edu
Research Interests: Real Analysis (summability and functional equations); Complex Analysis (polynomials and univalent functions); Graph Theory (algebraic aspects).
Selected Publications: The radius of convexity of certain analytic functions, Int. J. Math. (1980), 483-489. On a functional equation involving iterates of a bijection, Nonlinear Analysis (1983), 899-908. On anti-commutative semirings, Int. J. Math. (1989), 205-207. Dirichlet product of summable series (to appear).
Masahiko Saito, Ph.D., University of Texas at Austin, 1990; Professor & Graduate Program Director. saito@math.usf.edu
Research Interests: Knot theory, low dimensional topology, and related areas. Specifically, diagrammatic and geometric methods for the study of knotted surfaces in 4-dimensional space, invariants of knots and manifolds, algebraic structures in relation to knots and triangulated manifolds.
Selected Publications: Quandle homology groups, their Betti numbers, and virtual knots [with J.S. Carter, D. Jelsovsky, S. Kamada], J. Pure Appl. Algebra 157 (2001), 135-155. “Knotted Surfaces and Their Diagrams,” [with J.S. Carter], Mathematical Surveys and Monographs, volume 55, American Mathematical Society, 1998. “Classical and quantum 6j symbols,” [with J.S. Carter and D.E. Flath], Mathematical Notes, vol. 43, Princeton University Press, 1993. A note on cobordism of surface links in S4, Proc. AMS 111 (1991), 883-887.
Boris Shekhtman, Ph.D., Kent State University, 1980; Professor. boris@chuma.cas.usf.edu
Research Interests: Mathematics in general (Classical and Abstract Analysis, Approximation Theory, Discrete Mathematics, Linear Algebra in particular). Meaning of life, Psychology, Creative Writing and a bunch of other stuff. Anything that's fun.
Selected Publications: On the Divergence of Polynomial Interpolation, Constr. Approx. 17 (2001). On Interpolation by and Banach Spaces of Polynomials, Erdös Memorial Volume (2001). On Density Principle for Rational Functions, Numerical Algorithms 25 (2000). A Two-Dimensional Hahn-Banach Theorem, Proc. of AMS 129 (2000), (with B.L. Chalmers). Linear Discrete Operators on the Disk Algebra, Proc. AMS 129 (2000), (with I. Ivanov). On Archimidian Ordered Vector Spaces and a Characterization of Simplices, Proc. AMS 116 (1992), (with G.Gierz). Science Fiction of Distance Learning, preprint.
W. Richard Stark, Ph.D., University of Wisconsin, 1975; Professor. wrstark@yahoo.com
Research Interests: Algebraic foundations for parallel and distributed computation. There is reason to believe that the mathematical foundations for serial computing (e.g., recursion theories) are not applicable or extendable to the problems of parallel and distributed computing. This new mode of computing is for me exciting and important. I believe that parallel and distributed computing may relate to serial computing as quantum mechanics relates to Newtonian mechanics. Thus, it may also represent the future of computer science.
Selected Publications: A measure of subgroup diversity, J. of Algebra 61 (1979), 308. A glimpse into the paradise of combinatory algebra, Int. J. of Computer and Information Sciences 13 (1984), 219. A logic for distributed processes, Zeit. Math. Logik (1989). The social metaphor for distributed processing, J. Par. Dist. Comp. 7 (1989), 125. LISP, Lore, and Logic, (Series in Theoretical Computer Science) Springer-Verlag (1990). Tissue models with programming problems from God's notebooks, ACM SIGBio (June 1992). On the complexity of deadlock-free programs on a ring of processors [with W.E. Clark & G.L. McColm], J. Par. Dist. Comp. 16 (1992), 1.
Stephen Suen, Ph.D., University of Bristol, 1985; Associate Professor. ssuen@math.usf.edu
Research Interests: My main interests are in combinatorics and are often related to theoretical computer science. Current focus is on probabilistic aspects, in particular the study of random graph properties and the analysis of randomized algorithms. I am also interested in approximation schemes for hard counting problems such as finding the number of Hamilton cycles in graphs. Recent work includes a study of the depth first search algorithm on random graphs; analysis of randomized algorithms for finding large matchings in graphs and satisfiable assignments for boolean formulas in conjunctive normal form.
Selected Publications: A correlation inequality and a Poisson limit theorem for nonoverlapping balanced subgraphs of a random graph, Random Structures and Algorithms 1 (1990), 231-242. On the largest strong components in m-out digraphs, Discrete Mathematics 94 (1991), 45-52. Counting the number of Hamilton cycles in random digraphs [with A.M. Frieze], Random Structures and Algorithms 3 (1992), 235-241. On depth first search trees in m-out digraphs, Combinatorica (1993).
V. Totik, Sc.D., Hungarian Acad. Sci., 1986; Professor. totik@math.usf.edu
Research Interests: Approximation by polynomials and positive operators, potential theory, general orthogonal polynomials and their asymptotics, harmonic analysis, and interpolation of operators.
Selected Publications: "Moduli of smoothness" [with Z. Ditzian], Springer Series in Computational Mathematics (1987). "General Orthogonal Polynomials" [monograph with H. Stahl], to appear. Sharp converse theorem of Lp-polynomial approximation, Constructive Approximation 4 (1988), 419-433. Behaviour of polynomials of best uniform approximation [with E.B. Saff], Trans. Amer. Math. Soc. 316 (1989), 567-593.
Chris P. Tsokos, Ph.D., University of Connecticut, 1968; Distinguished Research Professor. profcpt@math.usf.edu
Research Interests: Linear and nonlinear statistical models for health sciences, operations research problems, and economic systems; frequentist and Bayesian reliability analysis and sensitivity modeling; forecasting models for stationary and nonstationary time series analysis; and differential stochastic control systems.
Selected Publications: Forecasting models -- Parts I & II, Stochastic Anal. and Applications 3, 247-284, 285-313. Methods for estimating time series models for forecasting, Applied Math. and Computation 16, 265-275. Random integral equations with applications to life science and engineering [with Padgett], (Academic Press, 1974). The theory and applications of reliability with emphasis on Bayesian and nonparametric methods, Vols. I and II (Academic Press, 1978).
Carol A. Williams, Ph.D., Yale University, 1967; Professor. cw@math.usf.edu
Research Interests: Dynamical systems of astronomical interest such as galactic systems, planetary and satellite orbits, and space flight dynamics; algorithms for the simplification and/or normalization of Hamiltonian systems; recursive algorithms to generate literal solutions to dynamical systems with algebraic processors; the nature of resonances in dynamical systems.
Selected Publications: Simplifications toward integrability of perturbed Keplerian systems [with S. Ferrer], Anal. N.Y. Acad. Sci. 536, 127 (1988). Gylden Systems: Rotation of Pericenters [with A. Deprit and B. Miller], Astrophysics and Space Science 159, 239 (1989). The Lissajous Transformation Part IV. Delaunay and Lissajous Variables, Celestial Mechanics and Dynamical Astronomy 51 (1991) 271-280. A planetary theory with elliptic functions and elliptic integrals exhibiting no small divisors (to appear).
George P. Yanev, Ph.D., University of Sofia, 1991; Ph.D., University of South Florida, 2001; Assistant Professor, gyanev@cas.usf.edu
Research Interests: Branching Processes: controlled branching processes, varying environment, extremes, branching trees, statistics of branching processes. Statistical modeling in biology and ecology.
Selected Publications: Borel-Tanner distribution: empirical Bayes modification of the MLE under LINEX loss, J. Applied Statistical Science, in press. A critical branching process with stationary-limiting distribution [with N. Yanev], Stochastic Analysis and Applications 22 (2004), 3:721-738. Extremes of geometric variables with applications to branching processes, [with K. Mitov and A. Pakes], Statistics and Probability Letters 65 (2003), 4:379-388. Decision-theoretic estimation of the offspring mean in mortal branching processes, [with C.P. Tsokos], Commun. Statistics: Stochastic Models 15 (1999), 5:889-902. On the maximum family size in branching processes, [with I. Rahimov], J. Applied Probability 36 (1999), 3:632-643.
Yuncheng You, Ph.D., University of Minnesota, 1988; Professor. you@math.usf.edu
Research Interests. Infinite dimensional dynamical systems in physics; control theory of distributed parameter systems; partial differential equations; functional differential equations, especially global dynamics of semilinear parabolic and hyperbolic evolution equations; optimal control, controllability and stabilization; invariant manifold and inertial manifolds.
Selected Publications: A nonquadratic Bolza problem and a quasi-Riccati equation for distributed parameter systems, SIAM J. Control and Optimization 25 (1987), 904-920. Optimal syntheses for infinite semicausality approach [with E.B. Lee], Appl. Math and Optimization 19 (1989), 113-136. Pointwise boundary stabilizability of hyperbolic equations, J. Math. Anal. Appl. 165 (1992), 239-265. Inertial manifolds: the non-self adjoint case [with G.R. Sell], J. Diff. Eqns. 96 (1992), 203-255.
Please direct questions to mthmaster@nosferatu.cas.usf.edu.
Last updated: 14-Jun-2007.
Copyright © 1996, USF Department of Mathematics.