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Mathematics & Statistics

Faculty Research

Mathematics | Statistics

Mathematics Faculty Research

Catherine Bénéteau, Ph.D., SUNY-Albany, 1999; Associate Professor.

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 \(H^{P}\) 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.

Thomas Bieske, Ph.D., University of Pittsburgh, 1999; Associate Professor.

Research interests: Analysis, nonlinear partial differential equations, and potential theory in sub-Riemannian and general metric spaces.

Selected publications: The parbolic infinite-Laplace equation in Carnot groups (with E. Martin), Mich. Math. J. 63 (2016), no. 3, 489-509. Generalizations of a Laplacian-type equation in the Heisenberg group and a class of Grushin-type spaces (with K. Childers), Proc. Amer. Math. Soc. 142 (2014), no. 3, 989-1003. A sub-Riemannian maximum principle and its application to the \(p\)-Laplacian in Carnot groups, Ann. Acad. Sci. Fenn. 37 (2012), 119-134. The Carnot-Carathéodory distance vis-a-vis the eikonal equation and the infinite Laplacian, Bull. London Math. Soc. 42 (2010), no. 3, 395-404. The Carnot-Carathéodory distance and the infinite Laplacian (with F. Dragoni and J. Manfredi), J. Geo. Anal. 19 (2009), no. 4, 737-754. The \(P\)-Laplace equation on a class of Grushin-type spaces (with J. Gong), Proc. Amer. Math. Soc. 134 (2006), no. 12, 3585-3594. On ∞-harmonic functions on the Heisenberg group, Comm. PDE 27 (2002), nos. 3-4, 727-761. Lipschitz extensions on generalized Grushin spaces, Mich. Math. J. 53 (2005), no. 1, 3-31. The Aronsson-Euler equation for absolutely minimizing Lipschitz extensions with respect to Carnot-Carathéodory metrics (with L. Capogna), Trans. Amer. Math. Soc. 357 (2005), no. 2, 795-823.

W. Edwin Clark, Ph.D., Tulane University, 1964; Professor Emeritus.

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.

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, Pacific J. Math. 209 (2003), no. 2, 231-248.

Arthur Danielyan, Ph.D., Institute of Mathematics of Academy of Sciences of Armenia, 1987; Assistant Professor.

Research Interests: Complex analysis and approximation theory.

Selected Publications: Rubel's problem on bounded analytic functions, Ann. Acad. Sci. Fenn. Math. 41 (2016), no. 2, 813–816. A theorem of Lohwater and Piranian, Proc. Amer. Math. Soc. 144 (2016), no. 9, 3919–3920. A converse to a theorem of Salem and Zygmund (with V. Totik), Bull. Sci. Math. 140 (2016), no. 3, 260–272. On the zero-free polynomial approximation problem, J. Approx. Theory 205 (2016), 60–63. Weak-star convergence and a polynomial approximation problem, Results Math. 69 (2016), no. 1-2, 257–262. On the peak points, Complex Var. Elliptic Equ. 60 (2015), no. 11, 1475–1479. On a polynomial approximation problem, J. Approx. Theory 162 (2010), no. 4, 717–722. On a problem of M. A. Lavrent′ev on the representability of functions by polynomial series in the complex plane, Izv. Math. 63 (1999), no. 2, 245–254

Mohamed Elhamdadi, Ph.D., University of Nice-Sophia Antipolis (France), 1996; Associate Professor.

Research Interests: Low dimensional topology, quantum algebra, and knot theory.

Selected Publications: Cohomology of the adjoint of Hopf Algebras [with J. S. Carter, A. Crans and M. Saito], J. Generalized Lie Theory Appl. 2 (2008), no. 1, 19-34. A Lower bound for the number of Reidemeister moves of type III [with J. S. Carter, M. Saito and S. Satoh], Topology Appl. 153 (2006), 2788-2794. Cocycle Knot Invariants from Quandle Modules and Generalized Quandle Cohomology [with J. S, Carter, M. Grana, and M. Saito], Osaka J. Math. 42 (2005), no. 3, 499-541. Homology Theory for the Set-Theoretic Yang-Baxter Equation and Knot Invariants from Generalizations of Quandles [with J. S. Carter and M. Saito], Fund. Math. 184 (2004), 31-54. Extensions of Quandles and cocycle knot invariants [with J. S. Carter, M. A. Nikiforou, and M. Saito], J. Knot Theory Ramifications 12 (2003), no. 6, 725-738. Twisted Quandle homology theory and cocycle knot invariants [with J. S. Carter and M. Saito], Algbr. Geom. Topol. 2 (2002), 95-135. On \(S^{3}\)-equivariant homology, Int. J. Math. Math. Sci. 26 (2001), no. 4, 193-197. A note on lambda-operations in orthogonal K-theory, Proc. Amer. Math. Soc. 128 (2000), no. 1, 1-4.

Xiang-dong Hou, Ph.D., University of Illinois at Chicago, 1990; Professor.

Research Interests: Algebra: finite fields and finite rings, classical groups over finite fields; Number Theory: number theory of finite fields, exponential sums, function fields over finite fields, p-adic fields; Coding Theory and Cryptography: covering radius, Reed-Muller codes, number of inequivalent codes, group actions on Boolean functions; Combinatorics: bent functions, difference sets, applications of finite fields in combinatorics; Topology: knot invariants.

Selected Publications: Some results on the covering radii of Reed-Muller codes, IEEE Trans. Inform. Theory 39 (1993), 366–378. AGL(m,2) acting on R(r,m)/R(s,m), J. Algebra 171 (1995), 921–938. Results on bent functions (with P. Langevin), J. Combin. Theory A 80 (1997), 232–246. A generalization of an addition theorem of Kneser (with K. H. Leung and Q. Xiang), J. Number Theory 97 (2002), 1–9. Enumeration of isomorphism classes of extensions of p-adic fields (with K. Keating), J. Number Theory 104 (2004), 14–61. Solution to a problem of S. Payne, Proc. Amer. Math. Soc. 132 (2004), 1–8. A note on the proof of a theorem of Katz, Finite Fields Appl. 11 (2005), 316–319. Reversed Dickson permutation polynomials over finite fields (with G. L. Mullen, J. A. Sellers, J. L. Yucas), Finite Fields Appl. 15 (2009), 748–773. Automorphism groups of Alexander quandles, J. Algebra 344 (2011), 373–385. Connected quandles associated with pointed abelian groups (with W. E. Clark, M. Elhamdadi, M. Saito, T. Yeatman), Pacific J. Math. 264 (2013), 31–60. A new approach to permutation polynomials over finite fields, II (with N. Fernando and S. D. Lappano), Finite Fields Appl. 22 (2013), 122–158. Permutation polynomials over finite fields—a survey of recent advances, Finite Fields Appl. 32 (2015), 82–119. Switchings of semifield multiplications (with F. Ozbudak and Y. Zhou), Des. Codes Cryptogr. 80 (2016), 217–239. On global P-forms, J. Number Theory 160 (2016), 307–325. Polynomials meeting Ax's bound, Acta Arith. 176 (2016), 65–80. Proof of a conjecture on monomial graphs (with S. D. Lappano and F. Lazebnik), Finite Fields Appl. 43 (2017), 42–68.

Nataša Jonoska, Ph.D., SUNY-Binghamton, 1993; Professor.

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 “Grammars and automata for string processing”, (Carlos Martin-Vide, ed.), pp. 369-380, Topics in Comput. Math., vol. 9, Taylor & Francis, London, 2003. 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.

Research Interests: Nonlinear functional analysis; evolution equations in Banach spaces; accretive and monotone operator theory.

Selected Publications: A topological degree theory for perturbations of the sum of two maximal monotone operators (with D. R. Adhikari), Nonlinear Analysis 74 (2011), 4622–4641. A Browder degree theory from the Nagumo degree on the Hilbert space of elliptic super-regularization in reflexive separable Banach spaces (with D. Kerr), Nonlinear Analysis 74 (2011), 501–515. A Browder degree theory for pseudo-monotone perturbations of maximal monotone operators (with T. Asfaw), Advances in Mathematical Sciences and Applications 22 (2012), 91-148. Variational inequalities for perturbations of maximal monotone operators in reflexive Banach spaces (with T. Asfaw), Tohoku Mathematical Journal 66 (2014), 171-203. New results for perturbations of locally defined generalized pseudomonotone operators in Banach spaces (with T. Asfaw), Advances in Mathematical Sciences and Applications 24 (2014), 1-10. Invariance of domain and eigenvalues for perturbations of densely defined linear maximal monotone operators (with D. R. Adhikari), Applicable Analysis 94 (2015), 1-19.

Dmitry “Dima” Khavinson, Ph.D., Brown University, 1983; Distinguished University Professor.

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 \(R^{n}\) (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 Krajčevski, Ph.D., SUNY-Binghamton, 1994; Assistant Professor.

Research Interests: Geometric Methods in Group Theory, Combinatorial Group Theory, Hyperbolic Groups.

Selected Publications: Tilings of the plane, hyperbolic groups and small cancellation theory, Mem. Amer. Math. Soc. 154 (2001), no. 733.

Seung-Yeop Lee, Ph.D., University of Chicago, 2007; Assistant Professor.

Research Interests: Complex analysis, integrable systems, mathematical physics, asymptotic analysis, Riemann-Hilbert problems, orthogonal polynomials, various problems related to 2D Coulomb systems

Selected Publications: Topology of quadrature domains (with N. Makarov), J. Amer. Math. Soc. 29 (2016), 333-369. Remarks on Wilmshurst’s theorem (with A. Lerario and E. Lundberg), Indiana Univ. Math. J. 64 (2015), 1153-1167. Strong asymptotics of the orthogonal polynomial with respect to a measure supported on the plane (with F. Balogh, M. Bertola and K. D. T-R McLaughlin), Comm. Pure Appl. Math. 68 (2015), no. 1, 112–172. First colonization of a hard-edge in random matrix theory (with M. Bertola), Const. Approx. 31 (2010), no. 2, 231–257. The boundary correlation function of fixed-to-free boundary-condition-changing operators in a square-lattice Ising model, J. Stat. Mech. (2007), P10011. Bubble break-off in Hele-Shaw flows: Singularities and integrable structures (with E. Bettelheim and P. Wiegmann), Physica D 219 (2006) 22-34.

Joseph J. Liang, Ph.D., Ohio State University, 1969; Professor Emeritus.

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; Professor.

Research Interests: Applied Mathematics (soliton theory, integrability and applications of differential equations, Riemann-Hilbert problems and orthogonal polynomials, bifurcation and chaos); Mathematical Physics (symmetries and conservation laws, variational principles, Lie group method, Hamiltonian and bi-Hamiltonian theories, quantum and super-symmetric integrable systems); Symbolic Computation (symmetries and conservation laws, interactions of solitons and breathers, resonance and web structure of solitons, integrable decompositions, computer-assisted theorem proofs).

Selected Publications: A linear system arising from a polynomial problem and its applications [with B. Shekhtman], Chinese Annals of Mathematics, Series B, 23 (2002), 373-384. Semidirect sums of Lie algebras and discrete integrable couplings [with X. X. Xu and Y. Zhang], Journal of Mathematical Physics 47 (2006), 053501, 16 pp. Solving the Korteweg-de Vries equation by its bilinear form: Wronskian solutions [with Y. You], Transactions of the American Mathematical Society 357 (2005), 1753-1778. Complexiton solutions of the Toda lattice equation [with K. Maruno], Physica A 343 (2004), 219-237. Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems [with M. Blaszak], Journal of Geometry and Physics 47 (2003), 21-42. Binary nonlinearization of spectral problems of the perturbation AKNS systems [with R. G. Zhou], Chaos, Solitons & Fractals 13 (2002), 1451-1463. Binary symmetry constraints of N-wave interaction equations in \(1+1\) and \(2+1\) dimensions [with Z. X. Zhou], Journal of Mathematical Physics 42 (2001), 4345-4382. Master symmetries from Lax operators for certain lattice soliton hierarchies [with K. M. Tamizhmani], Journal of the Physical Society of Japan 69 (2000), 351-361. Separation of variables for soliton equations via their binary constrained flows [with Y. B. Zeng], Journal of Mathematical Physics 40 (1999), 6526-6557. Algebraic structure of discrete zero curvature equations and master symmetries of discrete evolution equations [with B. Fuchssteiner], Journal of Mathematical Physics 40 (1999), 2400-2418.

M. N. Manougian, Ph.D., University of Texas, 1968; Professor.

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.

Research Interests: My original interests were in mathematical logic and theoretical computer science, especially in logical expressibility, finite model theory, and descriptive and computational complexity. In order to deal with issues arising from logic, I applied tools from other areas, and consequently became active in finite and infinite combinatorics, especially in combinatorial games, Ramsey theory, random and extremal graph theory, and stochastic processes. Recently, I became active in applications of geometry to materials science and nanoscale science and technology; this involves mathematics (including Riemannian geometry and tiling theory, discrete and convex and computational geometry, geometric group theory and group representation theory, and category theory) and other natural sciences (including crystallography, molecular geometry, and related fields). Additionally, I am interested in pedagogy and related fields of applied psychology, in philosophy (especially the philosophy of science) and in academic politics (which as an academic field is usually classified as “educational leadership” or “sociology of science”).

Selected Publications: When is arithmetic possible?, Ann. Pure Appl. Logic 50:1 (1990), 29-51. A Ramseyian theorem for products of trees, J. Combinatorial Theory-A 57 (1991), 68-75. Pebble games and subroutines in least fixed point logic, Inform. and Comp. 122:2 (1995), 201-220. A splitting inequality, Ramanujan Journal 2:4 (1998), 511-519. Guarded Quantification in Least Fixed Point Logic, J. Logic, Language and Information 13 (2004), 61–110. A University’s Dilemma in the Age of National Security (with Sherman Dorn), Thought & Action (Fall, 2005), 163–177. A Metaphor for Mathematics Education, Notices of the American Mathematical Society (April, 2007), 499-502. Flexible versus Rigid Tile Assembly (with N. Jonoska; G. McColm presenting), Proceedings LNCS 4135; ed. by Cristian S. Calude et al (2006), pp. 139–151. When is Betweenness Preserved? (with X.-D. Hou), Rocky Mountain J. Mathematics 38:1 (2008), 123–137. Is Logic Necessary? Logica Universalis 4:2 (2010), pp. 241-254.

Marcus McWaters, Ph.D., University of Florida, 1966; Associate Professor.

Research Interests: Topology, Topological Algebra, Algebraic Topology.

Selected Publications: Arcs, Semigroups and Hyperspaces, Canadian Journal of Mathematics, Vol. 20, No. 5 (1968), pp. 1207-1210. A note on Topological Semilattices, The London Mathematical Journal 2, I (1969), pp. 64-66. Retractions and Quasi-Monotone Mappings of Unicoherent Spaces, (with J. H. Reed), Proc. Amer. Math. Soc., Vol. 33, No. 2 (1972), pp. 557-561. Some Continua Admitting Only Trivial Multiplications, (with J. H. Reed), Semigroup Forum, Vol. 3 (1971), pp. 89-91. Semi-locally connected spaces and Unicoherence, (with J. H. Reed), Fundamenta Mathematica, (XX), No. 8 (1972), pp. 657-661. On the triviality of the law \((sy)(zx)=yz\), (with Y. F. Lin), The London Math. Journal, Vol. 5, No. 18 (1972), pp. 276-278. Infinitesimal rotations (with A. D. Snider), American Journal of Physics 48 (3), (1980), pp. 250-251.

Kenneth L. Pothoven, Ph.D., Western Michigan University, 1969; Associate Professor Emeritus.

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.

Evguenii A. Rakhmanov, Sc.D., Steklov Mathematics Institute, Moscow, 1983; Professor.

Research Interests: Analysis, theory of analytic functions, approximation theory (Padé and rational approximation), potential theory, orthogonal polynomials.

Selected Publications: On the convergence of diagonal Padé approximants, Math. USSR Sb. 33 (1977). On the convergence of simultaneous Padé 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.

J. S. Ratti, Ph.D., Wayne State University, 1966; Professor.

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, Indian J. Math. 31 (1989), no. 3, 265-270.

Masahiko Saito, Ph.D., University of Texas at Austin, 1990; Professor.

Research Interests: Knot theory, low dimensional topology, related algebraic structures, and applications to DNA recombination.

Selected Publications: Surfaces in 4-space [with J. S. Carter and S. Kamada], Encyclopedia of Mathematical Sciences, vol. 142, Springer-Verlag, 2004. 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.

Boris Shekhtman, Ph.D., Kent State University, 1980; Professor.

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. Amer. Math. Soc. 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.

Lesław Skrzypek, Ph.D., Jagiellonian University, 2001; Associate Professor.

Research Interests: Approximation Theory and Functional Analysis. In particular I am interested in Minimal Projections and \(L_{p}\) spaces.

Selected Publications: Chalmers-Metcalf Operator and Uniqueness of Minimal projections, J. Approx. Theory 148 (2007), 71-91 (with G. Lewicki). Norming Points and Unique Minimality of Otrhogonal Projections, Abstract and Applied Analysis, 2006, Art. ID 42305, 1-17, (with B. Shekhtman). Uniqueness of Minimal Projections onto Two-Dimensional Subspaces, Studia Mathematica 168 (2005), 273-284 (with B. Shekhtman). The Uniqueness of Norm-One Projection in James-type Spaces, J. Approx. Theory 100 (1999), 73-93.

W. Richard Stark, Ph.D., University of Wisconsin, 1975; Professor.

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. Random Choice in Amorphous Processes, Natural Computing.

Stephen Suen, Ph.D., University of Bristol, 1985; Associate Professor.

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).

Razvan Teodorescu, Ph.D., University of Chicago, 2004; Associate Professor.

Research Interests: Integrable nonlinear differential equations, stochastic processes and harmonic analysis, biorthogonal polynomials and approximation theory, mathematical physics.

Selected Publications: Viscous shocks in Hele-Shaw flow and Stokes phenomena of the Painlevé I transcendent, with S-Y. Lee and P. Wiegmann, Physica D (2011) (doi:10.1016/j.physd.2010.09.017). Lemniscates are destroyed by Laplacian growth, with D. Khavinson, M. Mineev-Weinstein and M. Putinar, Mathematical Research Letters 17 2 (2010), 337. Random matrix theory in 2D, Laplacian growth, and operator theory, with M. Mineev-Weinstein and M. Putinar, J. Phys. A: Math. Theor. 41 (2008), 263001. Normal matrix ensemble as a growth problem, with E. Bettelheim, O. Agam, A. Zabrodin and P. B. Wiegmann, Nucl. Phys. B 704 (2005) 407.

V. Totik, Sc.D., Hungarian Acad. Sci., 1986; Professor.

Research Interests: Approximation theory, potential theory, orthogonal polynomials and polynomial inequalities.

Selected Publications: “Moduli of smoothness” [with Z. Ditzian], Springer Series in Computational Mathematics (1987). “General Orthogonal Polynomials” [monograph with H. Stahl], Cambridge University Press (1992). “Weighted approximation with varying weights”, Lecture Notes in Mathematics, 1569, Springer Verlag, (1994). “Logarithmic Potentials with External Fields” [with E. B. Saff], Grundlehren der mathematischen Wissenschaften, 316, Springer Verlag, (1997). “Metric properties of harmonic measures”, Memoirs of the American Mathematical Society, 867 (2006). “Problems and Theorems in Set Theory” [with P. Komjáth], Problem Books in Mathematics, Springer Verlag (2006). “Polynomial Approximation on Polytopes”, Memoirs of the American Mathematical Society, 212 (2014).

Carol A. Williams, Ph.D., Yale University, 1967; Professor Emeritus.

Research Interests: Infinite dimensional dynamical systems; Nonlinear partial differential equations and applications; Stochastic partial differential equations; Control theory of distributed systems; Functional differential equations; Global and random dynamics of attraction and invariance; Turbulent flows; Dispersive waves; Mathematics of Finance; Mathematical Biology; Interdisciplinary data analysis.

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, Chaos, Resonance, and Collective Dynamical Phenomena in the Solar System: Proceedings of the 152nd Symposium of the International Astronomical Union held in Angra dos Reis, Brazil, 15-19 July, 1991. Edited by Sylvio Ferraz-Mello. International Astronomical Union. Symposium no. 152, Kluwer Academic Publishers, Dordrecht, 1992, p.43.

Yuncheng You, Ph.D., University of Minnesota, 1988; Professor.

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: G. R. Sell and Y. You, “Dynamics of Evolutionary Equations”, Springer, 2002. W.-X. Ma and Y. You, Solving the Korteweg-de Vries equations by its bilinear form: Wronskian solutions, Trans. Amer. Math. Soc. 357 (2005), 1753-1778. Y. You, Multiple-spike ground state solutions of the Gierer-Meinhardt equations for biological activator-inhibitor systems, Dynamics of PDE 2 (2005), 187-260. Y. You, Sharp asymptotic estimates for vorticity solutions of 2D Navier-Stokes equation, Electronic Journal of Differential Equations, vol. 2008, no. 163, 1-25. Y. You, Dynamics of two-compartment Gray-Scott equations, Nonlinear Analysis, Series A, 74 (2011), 1969-1986. J. Qiu, S. Tang and Y. You, 2D backward stochastic Navier-Stokes equations with nonlinear forcing, Stochastic Processes and Their Applications 122 (2012), 334-356. Y. You, C. Chao and S. Zhou, The existence of uniform attractors for 3D Brinkman-Forchheimer equations, Discrete and Continuous Dynamical Systems, Series A, 32 (2012), 3787-3800. Y. You, Random attractors and robustness for stochastic reversible reaction-diffusion systems, Discrete and Continuous Dynamical Systems, Series A, 34 (2014), 301-333. H. Li, Y. You and J. Tu, Random attractors and averaging for non-autonomous stochastic wave equations with nonlinear damping, J. Differential Equations 258 (2015), 148-190. Y. You, Random dynamics of stochastic reaction-diffusion systems with additive noise, J. Dynamics and Differential Equations 29 (2017), 83-112.

Statistics Faculty Research

Gangaram “Gan” S. Ladde, Ph.D., University of Rhode Island, 1971; Professor.

Research Interests: Dynamic Reliability Analysis and Control; Stochastic Modeling of Dynamical Processes in Biological, Chemical, Engineering, Medical, Physical and Social Sciences; Time Series Analysis and Applications; Deterministic and Stochastic Qualitative and Quantitative Properties of Dynamic Systems; Stability Theory; Stochastic Estimation and Filtering; Deterministic and Stochastic Control and Differential Games; Multivariate/Large-Scale Systems Analysis; Hereditary Systems; Stochastic Modeling of Network Dynamics; Multi-Agent and Multi-Market/Finance Systems; Stochastic Approximation and Statistical Analysis; Stochastic Hybrid Dynamical and Extreme Statistical Analysis.

Selected Publications: Collective Behavior of Multi-Agent Network Dynamic Systems under Internal and external Random Perturbations (with J. Chandra), Nonlinear Analysis: Real World Applications, Vol. 11 (2010), pp. 1330-1344. Modeling Hybrid Network Dynamics under Random Perturbations (with Andrzej Korzeniowski), Nonlinear Analysis: Hybrid Systems, Vol. 3 (2009), pp. 143-149. Stochastic Modeling and Statistical Analysis on the Stock price Processes (with Ling Wu), Nonlinear Analysis: Theory and Methods, Vol. 71 (2009), pp. e1203-e1208. Dynamic Modeling of Root Water Uptake Using Soil Moisture Data (with Nirjhar Shah and Mark Ross), Neural, Parallel, and Scientific Computations, Vol. 16 (2008), pp. 105-124. Large-scale stochastic hereditary Systems under Markovian Structural Perturbations I, II & III, Article ID: JAMSA/19871, 67268 & 24643 (2006). Hybrid Dynamical Inequalities, Dynamic Systems Applications, Vol. 14 (2005), pp. 481-514. Qualitative Properties of Stochastic Iterative Processes under Markovian Structural Perturbations (Byron L. Griffin), Math. Comp. in Simulations, Vol. 67 (2004), pp. 181-200. Averaging Principle and Systems of Singularly Perturbed Stochastic Differential Equations (with J. Golec), Journal of Mathematical Physics, Vol. 31 (1990), pp. 1116-1123. Processing of Prefiltered GPS Data (M. S. Smith), IEEE Trans. Of Aerospace and Eng. Syst., Vol. 25 (1989), pp. 711-728. Stochastic Analysis of Compressible Gas Lubrication Slider Bearing Problem, (with Jagdish Chandra and V. Lakshmikantham), SIAM Journal on Applied Mathematics, Vol. 43 (1983), pp. 1174-1186. Multiplex Control Systems: Stochastic Stability and Dynamic Reliability (D. D. Siljak), Int. J. of Contr., Vol. 28 (1983). Stochastic Stability of Short-Run Market Equilibrium: A Comment, (with R. Kulkarni), The Quarterly Journal of Economics, Vol. 93 (1979). Stability and Oscillations in Single-Species Processes with Past Memory, International Journal of Systems Science, Vol. 10 (1979), pp. 621-647. Competitive Processes II: Stability of Random Systems, Journal of Theoretical Biology, Vol. 68 (1977), pp. 331-354. Cellular Systems II: Stability of Compartmental Systems, Mathematical Biosciences, Vol. 30 (1976), pp. 1-21. Systems of Differential Inequalities and Stochastic Differential Equations III, Journal of Mathematical Physics, Vol. 17 (1976), pp. 2113-2120. Competitive Processes and Comparison Differential Systems, Transactions of the American Mathematical Society, Vol. 221 (1976), pp. 391-402. Differential Inequalities and Differential Games III, Journal of Mathematical Analysis and Applications, Vol. 51 (1975), pp. 368-376. Variational Comparison Theorem and Perturbations of Nonlinear Systems, Proc. of Amer. Math. Soc., Vol. 52 (1975), pp. 165-187. Monographs: Stochastic Versus Deterministic Systems of Differential Equations (with M. Sambandham), Marcel Dekker, Inc., New York, 2004. Oscillation Theory of Differential Equations with Deviating Arguments (with V. Lakshmikantham and B. G. Zhang), Marcel Dekker, Inc., New York, 1987. Monotone Iterative Techniques for Nonlinear Differential Equations (with V. Lakshmikantham and A. S. Vatsala), Pitman Publishing, Inc., Marshfield, Massachusetts, 1985. Random Differential Inequalities (with V. Lakshmikantham), Academic Press, New York, 1980.

Lu Lu, Ph.D., Iowa State University, 2009; Assistant Professor.

Research Interests: Reliability analysis, design of experiment, response surface methodology, survey sample design and methodology, multiple objective optimization, statistical engineering.

Selected Publications: Optimization of Designed Experiments based on Multiple Criteria Utilizing Pareto Frontier (with C. M. Anderson-Cook and T. J. Robinson), Technometrics 53 (2011), 353-365. A Case Study on Selecting a Best Allocation of New Data for Improving the Estimation Precision of System and Sub-System Reliability using Pareto Fronts (with J. L. Chapman and C. M. Anderson-Cook), Technometrics 55:4 (2013), 473-487. Optimal Designed Experiments Using a Pareto Front Search for More Focused Desirability Function Weights (with C. M. Anderson-Cook and D. Lin), Computational Statistics and Data Analysis 71 (2014), 1178-1192. Incorporating Response Variability into Pareto Front Optimization (with J. L. Chapman and C.M. Anderson-Cook), Computers and Industrial Engineering 76 (2014), 253-267. Multiple Response Optimization for Higher Dimensions in Factors and Responses (with J. L. Chapman and C. M. Anderson-Cook), Quality Reliability Engineering International, DOI: 10.1002/qre.2051. Multiple Objective Optimization in Reliability Demonstration Test (with M. Li and C. M. Anderson-Cook), Journal of Quality Technology 48:4 (2016), 326-342.

Kandethody M. Ramachandran, Ph.D., Brown University, 1987; Professor.

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.

Christos “Chris” P. Tsokos, Ph.D., University of Connecticut, 1968; Distinguished University Professor.

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).