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ALLAART
Probability, ranges of vector measures, fair division theory

ANGHEL
 Analysis on manifolds, differential geometry, mathematical physics, several complex variables

BATOR
Functional analysis, geometry of Banach space

BRAND
Graph theory and combinatorics

BRITTENHAM
Geometric topology, low-dimensional topology, knot theory, foliations and laminations in 3-manifolds

BROZOVIC
Classical groups, finite groups of Lie type, permutation groups, subgroup chains in finite groups

CHERRY
Spherical derivatives, Landau-Schottky type theorems, extremal conformal mapping problems, Nevanlinna theory, p-adic analytic geometry, and function theory

CLARK
Dynamical systems with special interest in the topological structure of limit sets and in the topological classification of flows

CONLEY
Representations of real Lie groups and infinite dimensional Lie algebras

DELATTE
Dynamical systems and ergodic theory with special interest in Anosov systems and normal forms

DOUGLASS
Representation theory of Lie groups, Lie algebras, and related structures

IAIA
Elliptic partial differential equations and their application to problems in differential geometry

JACKSON
Logic, set theory, descriptive set theory, especially the influence of the axiom of determinancy

KALLMAN
Optimization, parallel computing, & engineering design, especially directed to the optimal design of optical information processing systems; topological groups, operator algebras, & unitary representations of locally compact groups

KUNG
Discrete mathematics, combinatorics, discrete and computational geometry, lattice theory, computational aspects of geometric configurations

LEWIS
Operators on continuous function spaces, vector measures, and the structure of certain Banach spaces

LIU
Optimization, numerical methods, applied mathematics

MAULDIN
Analysis, probability, descriptive set theory, chaos and dynamical systems

MICHLER
Cyclic homology, algebraic geometry

MONTICINO
Probability modeling, statistical analysis, stochastic optimal control, operations research, and random generation of geometric objects

MORTON
Graph theory

NEUBERGER
Numerical analysis, ordinary and partial differential equations, real variables, functional analysis

QUINTANILLA
Applied probability, stochastic geometry, and random heterogeneous materials

URBANSKI
Dynamical systems, ergodic theory, fractal sets, conformal dynamical systems, topology

VIENS
Probability, stochastic analysis, and applications

WARCHALL
Mathematical physics and nonlinear partial differential equations, investigation of multidimensional solitary waves and scattering theory for nonlinear wave equations

ZAMBONI
Symbolic dynamics, combinatorial number theory

Free University Amsterdam, 1998
Areas of Interest: Probability, ranges of vector measures, fair division theory.

1. An invariant-sum characterization of Benford's law. J. Appl. Prob. 34, 288-291 (1997).
2. Minimax risk inequalities for the location-parameter classification problem.   J. Multivariate Anal. 66, no.2, 255-269 (1998).
3. Bounds on the non-convexity of certain ranges of vector measures with atoms.  (to appear in Contemp. Math.)
4. A sharp non-convexity bound for partition ranges of vector measures with atoms.  (to appear in J. Math. Anal. Appl.)
5. Inequalities relating maximal moments to other measures of dispersion (in preparation).

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NICOLAE ANGHEL, PH.D.
Ohio State University, 1989
Areas of Interest:  Analysis on manifolds, differential geometry, mathematical physics, several complex variables.

1. "A Generalization of Problem 0.59," (Rumanian), Gaz. Mat. 85, No. 5(1980), 200-201.
2. "A Direct Proof of the Fact that $L^1(x,B,\mu)$ Satisfies the Strong Maximum Modulus Principle," (Rumanian), Bull. Inst. Politehn. Bucuresti, Ser. Electroteh. 42, No. 1 (1980), 15-19.
3. "Mixed Grassmann Manifolds," (Rumanian), Stud. Cerc. Mat. 34, No. 5 (1982), 401-415.
4. "The Levi Problem on Mixed Manifolds," Rend. Mat. (7)4, No. 2 (1984), 301-312.
5. "Remark on Callias' Index Theorem," Rep. Math. Phys. 28, No. 3 (1989), 1-6.
6. "$L^2$ -Index Formulae for Perturbed Dirac Operators," Commun. Math. Phys. 128, No. 1 (1990), 77-97.
7. "The Two-Dimensional Magnetic Field Problem Revisited," J. Math. Phys. 31, (9) (1990), 2091-2093.
8. "Extrinsic Upper Bounds for Eigenvalues of Dirac-Type Operators," Proc. Amer. Math. Soc. 117, No. 2 (1993), 501-509.
9. "An Abstract Index Theorem on Non-Compact Riemannian manifolds," Houston J. Math. 19, No. 2 (1993), 223-237.
10. "On the Index of Callias-Type Operators," Geom. Funct. Anal. 3, No. 5 (1993), 431-438.
11. "Index Theory for Short Ranged Fields in Higher Dimensions," J. Funct. Anal. 119 (1994), 19-36.
12. "A Note on a Local Chern Character on the Circle," Manuscripta Math. 85 (1994), 25-31.
13. "Generic Vanishing for Harmonic Spinors of Twisted Dirac Operators," Proc. Amer. Math. Soc. 124, No. 11, 3555-3561, 1996.
14. "A Multiple Sum--Proposed Problem No. 10522," Amer. Math. Monthly 103, No. 5, (1996) 426; "An Iterated Sum--Solution to Problem No. 10522," Amer. Math. Monthly 105, No. 7 (1998), 676.
15. "On the Constructibility with Ruler and Compass of a Minimum Chord in a Parabola," Libertas Math. XVII (1997), 9-12.
16. "SL₂ - Polynomial Invariance," Revue Roumaine Math. Pures Appl. 43, No 1-2 (1998), 17-46.
17. "Geometric Loci Associated to Certain Minimal Chords in Convex Regions," J. Geometry (1999) (to appear).
18. "On The First Vafa-Witten Constant for Two-Dimensional Tori," submitted to J. Math Phys. (1998).
19. "The Vafa-Witten Constant for Noncommutative Tori," in preparation.
20. "Harmonic Morphisms between Spheres," in preparation.
21. "Remark on the Hurwitz- Radon Theorem," in preparation.

ELIZABETH M. BATOR, PH.D.
The Pennsylvania State Univ., l983
Areas of Interest: Functional analysis, Geometry of Banach spaces.

1. "Pettis integrability and the equality of the norms of the weak* integral and the Dunford integral," Proc. Amer. Math. Soc., 95(1985), 265-270.
2. "A decomposition of bounded scalarly measurable functions taking their range in the dual of a Banach space," Proc. Amer. Math. Soc. 102(1988), 850-854.
3. "Some connections between Pettis integration and operator theory," (with P. Lewis and D. Race) Rocky Mountain J. of Math., 17(1987), 683-695.
4. "Pettis decomposition in dual Banach spaces," Proc. Amer. Math. Soc. 104(1988), 795-800.
5. "On weak analytic subsets of  subsets of  $\ell^\infty$" (with R. Huff) Rocky Mountain J. of  Math., 19(1989), 545-547.
6. "Remarks on completely continuous operators," Bull. Acad. Polon. Sci., 37(1989), 409-413.
7. "Weak precompactness and the weak RNP," (with P.W. Lewis) Bull. Acad. Polon Sci., 37(1989), 443-452.
8. "Weak precompactness, strong boundedness, and weak complete continuity," (with C. A. Abbott, R.G. Bilyeu, and P.W. Lewis), Math. Proc. Camb. Phil. Soc., 108(1990), 325-335.
9. "The Vitali integral convergence theorem and uniform absolute continuity," (with R. Bilyeu and P.W. Lewis), Canadian Math. J., 43(1991), 939-947.
10. "Strictly singular and strictly cosingular operators on spaces of continuous functions," (with C. Abbott and P.W. Lewis), Math. Proc. Cam. Phil. Soc., 110(1991), 505-521.
11. "A basic construction in the dual of a separable Banach space," Rocky Mountain J. of  Math., 22(1992), 81-92.
12. "Unconditionally converging and compact operators on c₀," Rocky Mountain J. of  Math., 22 (1992) 417-422.
13. "Operators having weakly precompact adjoints," (with P.W. Lewis) Math. Nachr., 157 (1992), 99-103.
14. "Properties (V) and (wV) on C(omega,X)," (with P. Lewis), Math. Proc. Camb. Phil. Soc., 117(1995), 469-477.
15. "Subspaces determining Pettis integrable functions," (preprint).
16. "Evaluation maps, restriction maps, and compactness (with P. Lewis and J. Ochoa), Colloquium Mathematicum, 78(1998), 1-17.
17. "Representing measures and (sb) operators" (with D. Slavens), submitted.
18. "Applications of a Decomposition in $X\otimes _\lambdaY$, Annali di matematica pura ed Applicata, (to appear)

NEAL BRAND, PH.D.
Stanford University, 1978
Areas of Interest: Graph theory and combinatorics.

1. Necessary conditions for the existence of branched coverings; Inventiones Mathematicae, 54; 1979, 1-10.
2. Classifying spaces for branched coverings; Indiana University Journal of Mathematics, Vol. 29, No. 2, 1980, 229-248.
3. Periodicity phenomena for concordance classes of branched coverings; Topology, Vol. 19; 1980, 255-263. Co-authored with G. Brumfiel.
4. Topological invariants of 2-designs arising from difference families; Journal of Combinatorial Theory, Series A, 36(1984), 253-278. Co-authored with W.C. Huffman.
5. Isomorphic designs that are not multiplier equivalent; Discrete Math., 57(1985), 159-165.
6. Some combinatorial isomorphism theorems; Congressus Numberantium, 50(1986), 155-164.
7. Design invariants; Geometriae Dedicata, 21(1986) 169-179.
8. Constructions and topological invariants of 2-(v,3,l) designs with group actions; European Journal of Combinatorics, 8(1987) 5-26. Co-authored with W.C. Huffman.
9. Invariants and constructions of Mendelsohn designs; Geometriae Dedicata, 22(1987) 173-196. Co-authored with W.C. Huffman.
10. Mendelsohn designs admitting the affine group; Graphs and Combinatorics 3(1987), 313-324. Co-authored with W. C. Huffman.
11. Quadratic isomorphisms of Z_p x Z_p -objects; Congressus Numerantium 58(1987), 157-163.
12. Design isomorphisms and group isomorphisms; Geometriae Dedicata, 27(1988), 281-294.
13. On the Bays-Lambossy Theorem; Discrete Math. 78(1989), 217-222.
14. Isomorphisms of cyclic combinatorial objects; Discrete Math. 78(1989), 73-81.
15. The number of non-zero entries in recursively defined tables modulo primes; Congressus Numerantium 78(1990), 47-59. Co-authored with T. Jacob and S. Das.
16. Design isomorphisms; Congressus Numerantium 70 (1990), 137-144 co-authored with S. Sutinuntopas.
17. Polynomial isomorphisms of combinatorial objects; Graphs and Combinatorics 7(1991), 7-17.
18. Isomorphisms of objects admitting elementary abelian p-group actions; Congressus Numerantium 84(1991), 129-133.
19. Almost all Steinhaus graphs have diameter two; Journal of Graph Theory, Vol. 16, No. 2(1992), 213-219.
20. One-Factors and the existence of affine designs; Discrete Math. 120(1993), 25-35, co-authored with S. Sutinuntopas.
21. Probability of diameter two for Steinhaus graphs; Discrete Applied Math. 41(1993) 165-171. Co-authored with S. Curran, S. Das and T. Jacob.
22. Properties of classes of random graphs; Combinatorics, Probability, and Computing 3(1994) 1-20. Co-authored with S.Jackson.
23. Generalized Steinhaus graphs; Journal of Graph Theory, Vol. 20, No. 1, 47-58 (1995). Co-authored with Margaret Morton.
24. Construction of universal branched coverings; Topology and Its Applications, 76 (1997), 79-93. Co-authored with Debora Tejada.
25. Uniform generalized Steinhaus graphs; Australasian J. of Combinatorics, Vol. 13 (1996), 295-303. Co-authored with Margaret Morton.
26. Necklace connections in the shuffle-exchange graph; preprint.
27. A note on the growth of planar graphs; Proceedings of Discrete Mathematics and Theoretical Computer Science Conference (DMTCS'96), 147-157, 1996. Co-authored with Margaret Morton.
28. Growth of infinite planar graphs; pre-print, co-authored with Margaret Morton and Dirk Vertigan.
29. Properties of linear subspaces of graphs; preprint, co-authored with Daekeun Lim and D.C. Simmons.
30. Planar universal graphs; preprint, co-authored with Margaret Morton.

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MARK BRITTENHAM, PH.D.
Cornell University, 1990
Areas of Interest: Geometric topology, low-dimensional topology, knot theory, foliations and laminations in 3-manifolds.

1. Essential laminations in Seifert-fibered spaces, Topology 32 no. 1 (1993), 61-85.
2. Essential laminations in non-Haken 3-manifolds, Topology and its Applications 53 (1993) 317-324.
3. Essential laminations and deformations of homotopy equivalences: From essential pullback to homeomorphism, Topology and Its Applications 60 (1994) 249-265.
4. Essential laminations and Haken normal form, Pacific J. Math 168 (1995), 217-234.
5. Essential laminations and Haken normal form: Laminations with no holonomy, Comm. Anal. Geom. 3 (1995) 465-477.
6. Essential laminations in I-bundles, Trans. AMS 349 no. 4 (April 1997) 1463-1485.
7. (with R. Naimi and R. Roberts) Graph manifolds and taut foliations, J.  Diff. Geom. 45 (1997) 446-470.
8. Exceptional Seifert-fibered spaces and Dehn surgery on 2-bridge knots, Topology 37 (1998) 665-672.
9. Essential laminations, exceptional Seifert-fibered spaces, and Dehn filling, J. Knot Thy. Ram. 7 (1998) 425-432.
10. Essential laminations in Seifert-fibered spaces: Boundary behavior, to appear in Topology and its Applications.
11. (with R. Roberts) When incompresible tori meet essential laminations, to appear in Pacific Journal of Mathematics.
12. (with Y.-Q. Wu) The classification of Dehn surgeries on 2-bridge knots, submitted for publication.
13. Persistently laminar tangles, submitted for publication.
14. Persistent laminations from Seifert spaces, submitted for publication.
15. Bounding canonical genus bounds volume, submitted for publication.
16. Free genus one knots with large volume, submitted for publication.
17. à₁-injective, proper maps of open surfaces, preprint (1989).
18. Essential laminations and Haken normal form: Regular cell decompositions, preprint (1992).
19. Essential laminations and deformations of homotopy equivalences: The structure of pullbacks, preprint (1994).
20. Incompressible tori and the space of leaves of a foliation, preprint (1996).
21. Essential laminations in I-bundles: laminations with boundary, in preparation.
22. Persistent laminations for knots: non-orientable spanning surfaces, in preparation.
23. Free Seifert surfaces and disk decompositions, in preparation.
24. Foliations and the topology of 3-manifolds, draft of a manuscript based on lectures at the University of  Texas at Austin, Spring 1993.

DOUGLAS BROZOVIC, PH.D.
Ohio State University, 1991
Areas of Interest: Classical groups, finite groups of Lie type, permutation groups, subgroup chains in finite groups.

1. "A Survey on Chains of Subgroups," co-authored with Ronald Solomon. Coding Theory, Design Theory and Graph Theory: Proceedings of the Marshall Hall conference, D. Jungnickel, S.A. Vanstone, editors. John Wiley & Sons, Inc., 1993.
2. "Subgroup Chains in Finite Groups," pages 70-81 of Group Theory: Proceedings of the Biennial Ohio State-Denison Conference, S. Sehgal and R. Solomon, editors, World Scientific Publishing Co. Pte Ltd., 1993.
3. "Groups of Hyperbolic Length in Odd Characteristic Groups of Lie type," J. Algebra 164 (1) (1994), 210-243.
4. "A Reduction Theorem for the Chain Length of an Odd Characteristic Lie Type Group," J. Algebra 163 (3) (1994), 739-756.
5. "Almost Simple p-obstructions in Odd Characteristic Lie Type Groups," Comm. Algebra 22 (4) (1994), 1219-1227.
6. "The Length of Chains in Odd Characteristic Lie Type Groups," J. Algebra 170 (2), (1994), 440-469.
7. "On Primitive Sharp Permutation Groups," Comm. Algebra24 (12), (1996), 3979-3994.
8. "On Groups of Hyperbolic Length," Israel Journal of Mathematics 98 (1997), 61-99.
9. "One point stabilizers in almost simple sharp permutation groups," submitted to Communications in Algebra, Jan. 1999 (26 pages).

WILLIAM CHERRY, PH.D.
Yale University, 1993
Areas of Interest: Spherical derivatives, Landau-Schottky type theorems, extremal conformal mapping problems, Nevanlinna theory, p-adic analytic geometry, and function theory.

Publications List located on home page

Revised January 12, 1999

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ALEX CLARK, PH.D.
Auburn University, 1998
Areas of Interest:   Dynamical systems with special interest in the topological structure of limit sets and in the topological classification of  flows.

1. Flows on solenoids are generically not almost periodic, to appear in Geometry and Topology in Dynamics, Contemporary Mathematics (AMS).
2. Linear flows on k-solenoids, Topology and its Applications, 94 (1999), pp. 27-49.
3. Exponents and almost periodic flows, submitted for publication.
4. Solenoidalization and denjoids, submitted for publication.
5. Linear flows on solenoids, exponents and denjoids, Ph. D. dissertation, Auburn University, 1998.

CHARLES CONLEY, PH.D.
UCLA, 1991
Areas of Interest: Representations of real Lie groups and infinite dimensional Lie algebras.

1. Representations of Finite Length of Semidirect Product Lie Groups, J. Funct. Anal. 114 (1993), 421-457.
2. Extensions of the Mass 0 Helicity 0 Representation of the Poincare Group, in Non-compact Lie Groups and Some of Their Applications, eds. E. Tanner and R. Wilson, Kluwer, 1994, 315-324.
3. Little Group Method for Smooth Representations of Finite Length, Duke Math. J. 79 (1995), No. 3, 619-666.
4. Geometric Realizations of Representations of Finite Length, Reviews Math. Phys., 9 (1997),  No. 7, 821-851.
5. Geometric Realizations of Representations of Finite Length II, Pacific J. Math. 183 (1998), No. 2, 201-213.
6. Super Multiplicative Integrals, Lett. Math. Phys. 47 (1999), No. 2, 63-74.
7. A New Family of Irreducible Representations of  the Witt Lie Algebra, with Christiane Martin, submitted.
8. Generic Bounded Representations of  the Witt Lie Algebra of Length 3, in final preparation.

DAVID ALLEN DELATTE, PH.D.
California Institute of Technology, 1991
Areas of Interest: Dynamical systems and ergodic theory with special interest in Anosov systems and normal forms.

1. "Nonstationary normal forms for Anosov diffeomorphisms and hyperbolic skew products," Thesis, California Institute of Technology (1991).
2. "Nonstationary normal forms and cocycle invariants," Journal of Random and Computational Dynamics, Vol. 1, No. 2, (1992-93).
3. "On normal forms in Hamiltonian dynamics; a new approach to some convergence questions," Ergodic Theory and Dynamical Systems, Vol. 15, No. 1 (1995), p. 49-66.
4. "On the obstructions to smooth equivalence for hyperbolic dynamical systems," preprint.
5. "Simultaneous linearization of commuting analytic maps," UNT Technical Report No. 221, 1996;  American Mathematical Society Abstracts, Vol. 17.4, 1996.
6. "Mathematical Modeling and Dynamical Systems," Consortium for Mathematics and Its Applications, to appear in 1997.
7. "Diophantine Conditions for the Linearization of  Commuting Holomorphic Functions," Journal of Discrete and Continuous Dynamical Systems, Vol. 3, No. 3, 1997.
8. "Diophantine Conditions for the Linearization of  Commuting Holomorphic Functions," Abstracts of the AMS, Vol. 19, No. 1, Jan. 1999.
9. "Normal Forms of Maps with Linear Parts having Jordan Blocks" (with Todor Gramchev), preprint , Fall 1998.

MATTHEW DOUGLASS, PH.D.
University of Oregon, 1988
Areas of Interest: Representation theory of Lie groups, Lie algebras, and related structures.

1. On matrix coefficients of the reflection representation, Proc. Amer. Math. Soc. 105 no. 1 (1989), 62-65 (with B. Shelton) .
2. Cells and the reflection representation of Weyl groups and Hecke algebras, Trans. Amer. Math. Soc. 318 no. 1 (1990), 373-399.
3. An inversion formula for relative Kazhdah-Lusztig polynomials, Comm. in Algebra 18 no. 2 (1990), 371-387.
4. On the cohomology of an arrangement of type B₁, J. Algebra 146 no. 2 (1992) 265-282.
5. A formula for the number of F-stable Levi factors in a reductive algebraic group, Communications in Algebra 22 no. 13 (1994), 5447-5455.
6. An involution of the variety of flags fixed by a unipotent linear transformation, Adv. Appl. Math 17 (1996), 357-379.
7. Irreducible components of fixed point subvarieties of flag varieties, Math. Nach. 189  (1998), 107-120.
8. Toral arrangements and hyperplane arrangements, Rocky Mountain J. Math. 28 (1998), 939-956.
9. The adjoint representation of a semisimple group and exponents of hyperplane arrangements, submitted to Represent. Theory.
10. The G-module structure of the cotangent bundle of a generalized flag variety," in preparation.

JOSEPH A. IAIA, PH.D.
University of Pennsylvania, 1991
Areas of Interest: Elliptic partial differential equations and their application to problems in differential geometry.

1. Isometric Embeddings of Surface of Nonnegative Curvature in R³, Duke Mathematical Journal, Vol. 67, No. 2, August, 1992, 423-459.
2. The Weyl Problem for Surfaces of Nonnegative Curvature, Lecture Notes in Pure and Applied Mathematics, Vol 144: Geometric Analysis and Nonlinear Partial Differential Equations, ed. I. Bakelman, 1993, 213-220.
3. A Priori Estimates and Uniqueness of Inflection Points for Positive Solutions of Semipositone Problems, Journal of Differential and Integral Equations, Vol. 8, No. 2, February, 1995, 393-403.
4. Nonradial Solutions of a Semilinear Elliptic Equation in Two Dimensions, with Henry Warchall, Journal of Differential Equations, Vol. 119, No. 2, July, 1995, pp. 533-558.
5. A Priori Estimates of a Semilinear Elliptic PDE, Nonlinear Analysis, Theory, Methods, and Applications, Vol. 24, No. 7, 1995, pp. 1039-1048.
6. Radial Solutions to a p-Laplacian Dirichlet Problem, Applicable Analysis, Vol. 58, 1995, pp. 335-350.
7. Localized Solutions of Sublinear, Elliptic Equations: Loitering at the Hilltop, with Henry Warchall,  Rocky Mountain Journal of Mathematics, Vol. 27, No. 4, Fall 1997, pp. 1131-1157.
8. Localized Radial Solutions to a Semilinear Elliptic Equation on R^N,  Dynamical Systems and Differential Equations - Proceedings of the International Conference on Dynamical Systems and Differential Equations,  Springfield, Missouri 1996, Vol. I, 1998, pp. 314-326.
9. Encapsulated Vortex Solutions to Equivariant Wave Equations: Existence, with Henry Warchall. To appear in the SIAM Journal of Mathematical Analysis.
10. Positive Solution Curves in Semipositone Problems with Concave-Convex Type Nonlinearities, with Sudhasree Gadam. Submitted for publication to Nonlinear Analysis, July 1998.

STEPHEN JACKSON, PH.D.
University of California, Los Angeles, 1983
Areas of Interest: Logic, set theory, descriptive set theory, especially the influence of the axiom of determinancy.

1. Pointclasses and Well-Ordered Unions (with D.A. Martin), Cabal Seminar 79-81, Lecture Notes in Mathematics, v. 1019, Springer-Verlag, 1983, 56-66.
2. AD and the Projective Ordinals, Cabal Seminar 81-85, Lecture Notes in Mathematics, v. 1333, Springer-Verlag, 1988, 117-220.
3. A New Proof of the Strong Partition Relation on W₁, Transactions of the American Mathematical Society, v. 320, number 2, 1990, 737-745.
4. An Unboundedness Property For Norms of Length ₂," Proceedings of the American Mathematical Society, v. 109, 1990, 487-491.
5. Bulletin Announcement: AD and the Projective Ordinals, Bulletin of the American Mathematical Society, v. 21, number 1, 1989, 77-81.
6. Partition Properties and Well-Ordered Sequences, Annals of Pure and Applied Logic, 48 (1), 1990, 81-101.
7. Admissible Suslin Cardinals in L(R ), The Journal of Symbolic Logic, v. 56, number 1, 1991, p. 260-275.
8. A Computation of, submitted to the Journal of American Mathematical Society.
9. Non-Uniformization Results in the Projective Hierarchy (with R.D. Mauldin). The Journal of Symbolic Logic, v. 56, number 2, 1991, 742-748.
10. Admissibility and Mahloness in L(R). In Set Theory of the Continuum, Mathematical Sciences Research Institute publications, v. 26, 1992, 63-74.
11. Some Complexity Results in Analysis and Topology (with R.D. Mauldin), Fundamenta Mathematicae, v. 141, 1992, 75-83.
12. The Structure of Hyperfinite Borel Equivalence Relations (with R. Dougherty and A.S. Kechris), Transactions of the AMS, v. 341, no. 1 (1994) 193-225.
13. Properties of Classes of Random Graphs (with N. Brand), Combinatorics, Probability, and Computing, v. 3, 1994, 435-454.
14. On Partitions of Lines and Space (with R.D. Mauldin and P. Erdos), Fundamenta Mathematicae, v. 145 (1994), 101-119.
15. Borel Measurable Selections of Paretian Utility Functions (with R.D. Mauldin), Journal of Mathematical Economics, v. 23 (1994), 361-378.
16. A Note on a Theorem of Chriswell (with L. Zamboni), Proceedings of the American Mathematical Society, v. 123, number 9, 1995, 2629-2631.
17. On Infinite Partitions of Lines and Space (with R. D. Mauldin and P. Erdos), Fundamenta Mathematica, 152 (1997), 75-95.
18. Descriptions and Cardinals Below (with F. Khafizov), accepted to appear in the Journal of Symbolic Logic.
19. Structural Consequences of AD, accepted to appear in the Handbook of Set Theory.
20. Supercompactness Within the Projective Hierarchy (with H. Becker), submitted.
21. The Weak Square Property, accepted to appear in the Journal of Symbolic Logic.
22. The sigma-class generated by balls (with R. D. Mauldin), accepted to appear in the Proceedings of the Cambridge Philosophical Society.
23. The Calculus of Partition Sequences, Changing cofinalities, and a Question of Woodin (with A. Apter and J. Henley), accepted to appear in the Transactions of the A.M.S.

ROBERT R. KALLMAN, PH.D.
Massachusetts Institute of Technology, 1968
Areas of Interest: Optimization, parallel computing, and engineering design, especially directed to the optimal design of optical information processing systems; topological groups, operator algebras, and unitary representations of locally compact groups.

1. Uniform continuity, unitary groups, and compact operators, Journal of Functional Analysis, volume 1, number 2, 1967, pp. 245 - 253.
2. A characterization of uniformly continuous unitary representations of connected locally compact groups, Michigan Mathematical Journal, volume 16, 1969, pp. 257 - 263.
3. Unitary groups and automorphisms of operator algebras, American Journal of Mathematics, volume 91, number 3, 1969, pp. 785 - 806.
4. A generalization of free action, Duke Mathematical Journal, volume 36, number 4, 1969, pp. 781 - 789.
5. A remark on a paper of J.F. Aarnes, Communications in Mathematical Physics, volume 14, 1969, pp. 13 - 14.
6. The strong-bounded topology on groups of automorphisms of a von Neumann algebra, Proceedings of the American Mathematical Society, volume 23, 1969, pp. 367 - 372.
7. A problem of Gelfand on rings of operators and dynamical systems, Canadian Journal of Mathematics, volume 22, number 3, 1970, pp. 514 - 517.
8. A theorem on discrete groups and some consequences of Kazdan's thesis, Journal of Functional Analysis, volume 6, number 2, 1970, pp. 203 - 207.
9. On the inequality f 2ó4 f f , pp. 187-192, Inequalities, Volume 2, Academic Press, New York, 1970 (with G.-C. Rota).
10. A decomposition theorem for automorphisms of von Neumann algebras, pp 33 - 35, Functional Analysis - Proceedings of a Symposium, Academic Press, New York, 1970.
11. On spectral mappings, higher order circle criteria, and periodically varying systems, IEEE Transactions on Automatic Control, volume AC-15, number 6, December 1970, pp. 649-652 (with G. Zames).
12. A generalization of a theorem of Berger and Coburn, Journal of Mathematics and Mechanics, volume 19, number 11, l970, pp. 1005 - 1010.
13. One-parameter groups of *-automorphisms of II1 von Neumann algebras, Proceedings of the American Mathematical Society, volume 24, number 2, 1970, pp. 336-340.
14. Certain topological groups are type I, Bulletin of the American Mathematical Society, volume 76, number 2, 1970, pp. 404 - 406.
15. Groups of inner automorphisms of von Neumann algebras, Journal of Functional Analysis, volume 7, number 1, 1971, pp. 43-60.
16. Spatially induced groups of automorphisms of certain von Neumann algebras, Transactions of the American Mathematical Society, volume 156, 1971, pp. 505-515.
17. A conjecture of Gilbert and Pollak on minimal trees, Studies in Applied Mathematics, volume 52, number 2, 1973, pp. 141-151.
18. Certain topological groups are type I, Part II, Advances in Mathematics, volume 10, number 2, 1973, pp. 221-255.
19. A theorem on the restriction of type I representations of a group to certain of its subgroups, Proceedings of the American Mathematical Society, volume 40, number 1, 1973, pp. 291-296.
20. A theorem on finite-dimensional spaces of real-valued functions on the line, Los Alamos Scientific Laboratory, Unclassified Report 1973-1607, pp. 1-10.
21. The existence of invariant measures on certain quotient spaces, Advances in Mathematics, volume 11, number 3, 1973, pp. 387-391.
22. The topology of compact simple groups is essentially unique, Advances in Mathematics, volume 12, number 4, 1974, pp. 416-417.
23. A sufficient condition for a graph to be universal, Los Alamos Scientific Laboratory, Unclassified Report 1974-1044, pp. 1-15.
24. A theorem in the representation theory of totally disconnected groups, Proceedings of the American Mathematical Society, volume 45, number 3, 1974, pp. 457-460.
25. Certain quotient spaces are countably separated, Illinois Journal of Mathematics, volume 19, 1975, pp. 378-388.
26. Editor, Einar Hille: Classical Analysis and Functional Analysis, Selected Papers, M.I.T. Press, Cambridge, Massachusetts, 1975.
27. Certain quotient spaces are countably separated, Part II, Journal of Functional Analysis, volume 21, number 1, l976, pp. 52-62.
28. A uniqueness result for topological groups, Proceedings of the American Mathematical Society, volume 54, 1976, pp. 439-440.
29. Certain quotient spaces are countably separated, Part III, Journal of Functional Analysis, volume 22, number 3, 1976, pp. 225-241.
30. A cross section theorem and an application to C*-algebras, Proceedings of the American Mathematical Society, volume 69, 1978, pp. 57-61 (with R.D. Mauldin).
31. Only trivial Borel measures on Sì are quasi-invariant under automorphisms, Pacific Journal of Mathematics, volume 76, number 2, 1978, pp. 453-461.
32. A uniqueness result for the infinite symmetric group, pp. 32l-322, Studies in Analysis, Advances in Mathematics, Supplementary Studies, volume 4, edited by G.-C. Rota, Academic Press, New York, 1978.
33. The left regular representation of a p-adic algebraic group is type I, pp. 373-384, Studies in Algebra and Number Theory, Advances in Mathematics Supplementary Studies, volume 6, edited by G.-C. Rota, Academic Press, New York, 1979 (with E.C. Gootman).
34. A uniqueness result for a class of compact connected groups, 207-212, Conference on Modern Analysis and Probability, edited by R. Beals, A. Beck, A. Bellow, and A. Hajian, Contemporary Mathematics, vol. 26, American Mathematical Society, Providence, Rhode Island, 1984.
35. Uniqueness results for the ax + b group and related algebraic objects, Fundamenta Mathematicae, volume 12, 1984, pp. 255-262.
36. The optimal construction of synthetic discriminant functions for optical matched filters, Report #73, pp. 1-28, United States Air Force Summer Faculty Research Program, 1984 Technical Reports, Volume II, The SCEEE Press, Orlando, Florida, 1985.
37. A theorem on planar continua and an application to automorphisms of the field of complex numbers, Topology and its Applications, volume 20, 1985, pp. 251-255 (with W.F. Simmons).
38. Uniqueness results for groups of measure preserving transformations, Proceedings of the American Mathematical Society, volume 20, number 1, 1985, pp. 87-90.
39. Rearrangements and category, Pacific Journal of Mathematics, volume 121, number 1, 1986, pp. 41-46 (with R.G. Bilyeu and P.W. Lewis).
40. The construction of low noise optical correlation filters, Applied Optics, volume 25, number 7, 1 April 1986, pp. 1032-1033.
41. The Optimal Construction of Synthetic Discriminant Functions (SDF's), U.S. Air Force Armament Laboratory Technical Report AFATL-TR-86-19, April 1986, pp. i-vi + 1-24.
42. Uniqueness results for homeomorphism groups, Transactions of American Mathematical Society, vol. 295, no. 1, May 1986, 389-396.
43. The Construction of Low Noise Optical Correlation Filters and Their Application to Target Identification Problems, U.S. Air Force Armament Laboratory Technical Report AFATL-TR-86-20, July 1986, i-vi + 1-41.
44. Construction of low noise correlation filters, Proceedings of SPIE-The International Society for Optical Engineering, volume 638, Hybrid Image Processing, pp. 214-217. Proceedings of conference held 1-2 April 1986 in Orlando, Florida. David P. Casasent/Andrew Tescher, Chairmen/Editors.
45. Optimal low noise phase-only and binary phase-only optical correlation filters for threshold detectors, Applied Optics, volume 25, number 23, 1 December 1986, pp. 4216-4217.
46. Editor, Shizuo Kakutani: Selected Papers, Volumes I and II, Birkh„user-Boston, 1986.
47. Direct construction of phase-only correlation filters, Proceedings of SPIE-The International Society for Optical Engineering, volume 827, Real Time Signal Processing X, pp. 184-190. Proceedings of conference held 20-21 August 1987 in San Diego, California. J. P. Letellier, Chairman/Editor.
48. Direct construction of phase-only filters, Applied Optics, volume 26, number 24, 15 December 1987, pp. 5200-5201.
49. Subsequences and category, Journal of Mathematical Analysis and Applications, volume 132, number 1, 15 May 1988, pp. 234-237.
50. Two variants of the optical correlation process, Proceedings of SPIE-The International Society for Optical Engineering, volume 938, Digital and Optical Shape Representation and Pattern Recognition, pp. 40-47.Proceedings of conference held 4-8 April 1988, Orlando, Florida. Richard D. Juday, Chairman/Editor.
51. The Design of Phase-Only Filters for Optical Correlators, AFATL-TR-90-63, Air Force Armament Laboratory, Elgin Air Force Base, Florida, pp. i-xii + 1-104.
52. Invariant Phase-Only Filters for Phase-Encoded Inputs, Proceedings of SPIE-The International Society for Optical Engineering, volume 1564, Optical Information Processing Systems and Architectures III, pp. 330-347. Proceedings of conference held 20-25 July 1991, San Diego, California. Bahram Javidi, Chairman/Editor. (with Dennis H. Goldstein).
53. The Construction of a General Spatial Filter as a Constrained Optimization Question, Proceedings of SPIE-The International Society for Optical Engineering, volume 1959, Optical Pattern Recognition, pp. 104-118. Proceedings of conference held 12-16 April 1993, Orlando, Florida. David P. Casasent, Chairman/Editor.
54. Correlation Results Using Invariant Spatial Filters with TOPS and Model-Based Training Sets , Constrained Optimization Question, Proceedings of SPIE-The International Society for Optical Engineering, volume 1959, Optical Pattern Recognition, pp. 119-132. Proceedings of conference held 12-16 April 1993, Orlando, Florida. David P. Casasent, Chairman/Editor. (with Dennis H. Goldstein and Eric P. Augustus).
55. Invariant Phase-Only Filters for TABILS24 Millimeter Wavelength Radar Data, Proceedings of SPIE-The International Society for Optical Engineering, volume 1960, Automatic Object Recognition III, pp. 74-90. Proceedings of conference held 12-16 April 1993, Orlando, Florida. Firooz A. Sadjadi, Chairman/Editor.
56. An Algorithm to Choose Which Pixels to Zero Out in a Zero and Phase Filter, Proceedings of SPIE-The International Society for Optical Engineering, volume 2026, Photonics for Processors, Neural Networks, and Memories-Optical Implementation of Information Processing, pp. 167-176. Proceedings of conference held 11-16 July 1993, San Diego, California. Joseph L. Horner et al., Chairmen/Editors.
57. The Design of Phase-Only Filters for Millimeter Wavelength Radar Imagery, WL-TR-93-7082, Wright Laboratory, Eglin Air Force Base, Florida, pp. i-xxii + 1-180.
58. Phase-encoding input images for optical pattern recognition, Optical Engineering, volume 332, number 6, June 1994, pp. 1806-1812 (with Dennis H. Goldstein).  To be reprinted in SPIE's Milestone Series of Selected Reprints in the volume Optical Pattern Recognition, edited by Francis T. S. Yu and Shizhuo Yin.
59. Correlation results using invariant filters in an acoustooptic correlator, Proceedings of SPIE-The International Society for Optical Engineering, Optical Pattern Recognition V, pp. 62-73. Proceedings of Conference held 4-8 April 1994, Orlando, Florida. David P. Casasent, Chairman/Editor. (with Eric P. Augustus, Dennis H. Goldstein, Pat Roth, and Terry Turpin).
60. Invariance Properties of Spatial Filters Designed for Zero Mean Inputs, Proceedings of SPIE - The International Society for Optical Engineering, volume 2297, Photonics for Processors, Neural Networks, and Memories II, pp. 40-51. Proceedings of Conference held 24-29 July 1994, San Diego, California. Joseph L. Horner et al., Chairmen/Editors.
61. An optimization algorithm to choose the region of support in a filter whose entries are zero or continuous phase, Proceedings of SPIE-The International Society for Optical Engineering, volume 2565, Optical Implementation of Information Processing, pp. 240-251. Proceedings of Conference held 10-11 July 1995, San Diego, California. Joseph L. Horner et al., Chairmen/Editors.
62. Optical spatial filter development, WL-TR-95-7034, June 1995, Wright Laboratory, Eglin Air Force Base, Florida, pp. i-vi + 1-149.
63. Another formulation of general spatial filter design, to appear in Proceedings of SPIE-The International Society for Optical Engineering, volume 2752, Optical Pattern Recognition VII, paper #2, pp. 1-9. Proceedings of Conference held 9-10 April 1996, Orlando, Florida. David P. Casasent and Tien-Hsin Chao, Chairmen/Editors.
64. Complex-valued Image Correlations using the ImSyn Processor, Proceedings of SPIE-The International Society for Optical Engineering, volume 2754, Advances in Optical Pattern Recognition VII, pp. 1-10.  Proceedings of Conference held 10-11 April 1996, Orlando, Florida. Dennis R. Pape, Chairman/Editor.  (with William R. Franklin, Patrick J. Roth, and Dennis H. Goldstein).
65. A General Optimization Algorithm Useful in Spatial Filter Design, Proceedings of SPIE-The International Society for Optical Engineering, volume 2846, Advanced Signal Processing Algorithms, Architectures, and Implementations VI, pp. 376-382.  Proceedings of conference held 7-8 August 1996, Denver, Colorado. Franklin T. Luk, Chairman/Editor.
66. Optoelectronic Signal Processor for SAR Image Formation and Correlation, Applications of Photonic Technology 2, Communications, Sensing, Materials, and Signal Processing, pp. 591-597.  Proceedings of the International Conference on Applications of Photonic Technology (ICAPT '96), held 29 July-1 August, 1996, in Montreal, Canada.  George A. Lampropoulos/Roger A. Lessard, Editors. Plenum Press, New York, 1997.  ISBN 0-306-45808-X.  (with William R. Franklin).
67. Subseries and Category, accepted for publication in the International Journal of Mathematics and Mathematical Sciences.
68. Every Reasonably Sized Matrix Group is a Subgroup of  S₀₀, accepted for publication in Fandamenta Mathematicae.
69. Square integrable representations are direct summands of the left regular representation, pp. 1-5 (written in 1969, circulated among mathematicians, and referenced in the literature).
70. Certain topological representations are type 1, Part III, pp. 1-18, preprint.
71. The reduced dual determines countable separability, pp. 1-126, preprint.
72. Measure,  category, and rearrangements, preprint.
73. The nonexistence of an algebraically universal second countable locally compact group, in preparation.
74. Synthesis of 2-d images from the Wigner distribution with applications to mammography, in preparation (with Elaine J. Pettit).

JOSEPH P. S. KUNG, PH.D.
Massachusetts Institute of Technology, 1978
Areas of Interest: Discrete mathematics, combinatorics, discrete and computational geometry, lattice theory, computational aspects of geometric configurations.

BOOKS

[Bl] (editor) Young tableaux in Combinatorics, Invariant Theory, and Algebra, Academic Press, New York and London, l982, 334 pp. [ISBN 0-12-428780-8].

[B2] (editor) A Source Book in Matroid Theory, Birkhauser, Basel and Boston, l986, 409 pp. [ISBN 3-7643-3173-9 (Basel), 0-8176-3173-9 (Boston)].

[B3] (editor, with K. B. Bogart and R. Freese) The Dilworth Theorems, Selected Papers of Robert P. Dilworth, Birkhauser, Basel and Boston, 1990, 465 pp. [ISBN 3-7643-3434-7 (Basel), 0-8176-3434-7 (Boston)].

[B4) (editor) Combinatorics: Papers of Gian-Carlo Rota, Birkhauser, Basel and Boston, 1995, 624 pp. [ISBN 3-7643-3713-7 (Basel), 0-8176-3713-7, (Boston)].

RESEARCH PAPERS

1. The core extraction axiom for combinatorial geometries, Discrete Math. 19(l977), 167-175.
2. The Radon transforms of a combinatorial geometry. I., J. Combin. Theory, Ser. A 26(l979), 97-102.
3. (with J. Desarmenien and G.-C. Rota) Invariant theory, Young bitableaux, and combinatorics, Adv. Math. 27(l978), 63-92.
4. The alpha function of a matroid-I. Transversal matroids, Stud. Appl. Math. 58(l978), 263-275.
5. Alternating basis exchanges in matroids, Proc. Amer. Math. Soc. 71(l978), 355-358.
6. Bimatroids and invariants, Adv. Math.  30(l978), 238-249.
7. On specializations of matroids, Stud. Appl. Math. 62(l980), 287-296.
8. (with M. R. Murty and G.-C. Rota) On the Redei zeta function, J. Number Theory 12(l980), 421-436.
9. The Redei function of a relation, J. Combin. Theory, Ser. A 29(l980), 287-296.
10. The cycle structure of a linear transformation over a finite field, Linear Algebra Appl. 36(l981), 141-155.
11. Some algebraic structures associated with the Poisson process, Algebra Universalis 12(1981), 137-147.
12. A probabilistic interpretation of the Goncarov and related polynomials, J. Math. Anal. Appl. 70(l981), 349-351.
13. (with O. D'Antona) Coherent orientations and series-parallel networks, Discrete Math. 34(1980), 95-98.
14. (with J. Kahn) Varieties of combinatorial geometries, Trans. Amer. Math. Soc. 271(1982),485-499.
15. a. (with J. Kahn) Varieties and universal models in theory of combinatorial geometries, Bull. Amer. Math. Soc. (New Series) 3(l980), 857-858.
16. (with G.-C. Rota) On the differential invariants of a linear ordinary differential equation, Proc. Roy. Soc. Edin. A89(l98l), 111-125.
17. Jacobi's identity and the Konig-Egervary theorem, Discrete Math. 49(l984), 75-77.
18. A factorization theorem for comaps of geometric lattices, J. Combin. Theory, Ser. B 34(l983), 40-47.
19. A characterization of orthogonal duality in matroid theory, Geometriae Dedicata 15(l983), 69-72.
20. (with G.-C. Rota) The invariant theory of binary forms, Bull. Amer. Math. Soc. (New Series) 10(1984), 27-85.
21. (with J. Kahn) A classification of modularly complemented geometric lattices, European J. Combin. 7(1986), 243-248.
22. Numerically regular hereditary classes of combinatorial geometries, Geometriae Dedicata 21(1986), 85-105.
23. Growth rates and critical exponents of classes of binary combinatorial geometries, Trans. Amer. Math. Soc., 293(1986), 837-859.
24. Matchings and Radon transforms in lattices. I. Consistent lattices, Order 2(1985), 105-112.
25. Excluding the cycle geometries of the Kuratowski graphs from binary geometries, Proc. London Math. Soc. (3) 55(1987), 209-242.
26. Matchings and Radon transforms in lattices. II. Concordant sets, Math. Proc. Cambridge Philosophical Society 101(1987), 221-231.
27. Gundelfinger's theorem on binary forms, Stud. Appl. Math. 75(1986), 163-170.
28. (with D. Sutherland) The automorphism group of the strong order of the symmetric group, J. London Math. Soc. (2) 37(1988), 193-202.
29. Combinatorial geometries representable over GF(3) and GF(q). I. The number of points, Discrete and Computational Geometry, 5(1990), 83-95.
30. The long-line graph of a combinatorial geometry. I. Excluding M(K₄) and the (q+2)-point line as minors, Quarterly J. Math. (Oxford) (2) 39(1988), 223-234.
31. (with J. G. Oxley) Combinatorial geometries representable over GF(3) and GF(q). II. Dowling geometries, Graphs and combinatorics 4(1988), 323-332.
32. The long-line graph of a combinatorial geometry. II. Geometries representable over two fields of different characteristics, J. Combin. Theory, Ser. B 50(1990), 41-53.
33. (with K. M. Gragg) Consistent dually semimodular lattices, J. Combin. Theory, Ser. A, 60(1992), 246-263.
34. The Radon transforms of a combinatorial geometry. II. Partition lattices, Adv. Math., 101 (1993), 114-132.
35. Extremal matroid theory, in N. Robertson and P. D. Seymour, eds., Graph Structure Theory, Contemporary Mathematics, Volume 147, Amer. Math. Soc., Providence, R. I., 1993, pp. 21-62.
36. Flags and Whitney numbers of matroids, J. Combin. Theory, Ser. B, 59(1993), 85-88.
37. Sign-coherent identities for characteristic polynomials of matroids, Combinatorics, Probability and Computing, 2(1993), 33-51.
38. (with J. Bonin) Every group is the automorphism group of a planar matroid, Geometriae Dedicata, 50(1994), 243-246.
39. Critical problems, in Matroid Theory, J. E. Bonin, J. G. Oxley and B. Servatius, eds., American Math. Soc., Providence, RI, 1996, pp. 1-127.
40. (with J. Bonin) The number of points in a combinatorial geometry with no 7-point line minor, in Mathematical Essays in Honor of Gian-Carlo Rota, B. E. Sagan and R. P. Stanley, eds., Birkhauser, Boston, 1998, pp. 271-284.
41. Pfaffian structures and critical problems in symplectic spaces, Annals of Combinatorics, 1(1997), 159-172.
42. A geometric condition for an arrangement to be free, Adv. Math., 135 (1998), 303-329.
43. Differential symmetry functions, submitted.
44. Critical exponents, colines, and projective geometries, submitted.

[E1] (with G.-C. Rota) Probabilita, in Enciclopedia del Novecento, Vol. 5, pp. 552-571, Istituto dell'Enciclopedia Italiana, Rome, l981 (in Italian).
[E2] Basis-Exchange properties, in N. L. White (ed.), Theory of Matroids, Vol. I, Cambridge University Press, Cambridge, l986, pp. 62-75.
[E3] Strong maps, ibid., pp. 224-253.
[E4] (with H. Q. Nyugen) Weak maps, ibid., pp. 254-271.
[E5] Radon transforms in combinatorics and lattice theory, in I. Rival, ed., Combinatorics and Ordered Sets (Proceedings of the American Mathematical Society Summer Research Conference, Arcata, California, 1985), Contemporary Mathematics, Vol. 57, Amer. Math. Soc., Providence, Rhode Island, 1986, pp. 33-74.
[E6] Canonical forms for binary forms of even degree, in Invariant theory, S. S. Koh, ed., Lecture Notes in Mathematics 1278, Springer-Verlag, Berlin and New York, 1988, pp. 52-61.
[E7] Commentary, in Selected works of S. Kakutani, vol. 2, Birkhauser, Boston, 1987, pp. 443-444.
[E8] Reconstructing finite Radon transforms, in Statistical Mechanics (Proceedings of the Third University of California Conference on Statistical Mechanics), C. Garrod, ed., North-Holland, Amsterdam, 1988, pp. 44-49.
[E9] Canonical forms for binary forms: Variations on a theme of Sylvester, in Invariant theory and tableaux, D. Stanton, ed., Springer-Verlag, Berlin and New York, 1989, pp. 46-58.
[E10] Matroids, in Handbook of Algebra, Vol. 1, M. Hazewinkel, ed., North-Holland, Amsterdam and New York, 1995, pp. 157-184.
[E11] Review of David Hilbert, "Theory of algebraic invariants," Adv. Math. 116 (1995), 389-393.
[E12] Combinatorics and nonparametric mathematics, Annals of Combinatorics 1 (1997), 105-106.
[E13] The number of points in a combinatorial geometry with no 8-point-line minor, in Mathematical Essays in honor of Gian-Carlo Rota (B. E. Sagan and R. P. Stanley, eds.), Birkhauser Boston, 1998, pp. 271-284.
Revised March 9, 1999
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PAUL W. LEWIS, PH.D.
University of Utah (1970)
Areas of Interest: Operators on continuous function spaces, vector measures, and the structure of certain Banach spaces.

1. "Extension of Operator Valued Set Functions With Finite Semi-variation," Proc. Amer. Math. Soc. 22(1969), 563-569.
2. "Some Regularity Conditions on Vector Measures With Finite Semi-Variation," Rev. Roumaine Math. 15(1970), 375-384.
3. "Regularity Conditions and Absolute Continuity," J. Reine Und Angew. Math. 247(1971), 80-86.
4. "Regularity of Baire Measures," Proc. Amer. Math. Soc. 26(1970), 92-94 (With N. Dinculeanu).
5. "Vector Measures and Topology," Rev. Roumaine Math. 16 (1971), 1201-1209.
6. "Addendum to: `Vector Measures and Topology'," Rev. Roumaine Math. 16(1971), 1211-1213.
7. "Operators on Function Spaces," Bull. Amer. Math. Soc. 78(1972), 697-701 (With J. Brooks).
8. "Variational Semiregularity and Norm Convergence," J. Reine Und. Angew. Math. 260(1973), 21-30.
9. "Permanence Properties of Absolute Continuity Conditions," Vector and Operator Measures and Applications, Academic Press, New York, 1973, 197-206.
10. "Linear Operators and Vector Measures," Trans. Amer. Math. Soc. 192(1974), 139-162 (with J. Brooks).
11. "Strongly Bounded Operators," Pac. J. Math. 53(1974), 207-209.
12. "Linear Operators and Vector Measures II," Math Zeitschrift 144(1975), 45-53 (with J. Brooks).
13. "Some Mapping Properties of Representing Measures," Ann. Mat. Pura Appl. CIX(1976), 273-286 (with R. G. Bilyeu).
14. "Orthogonality and the Hewitt-Yosida Theorem in Spaces of Measures," Rocky Mountain J. Math. 7(1977), 629-638 (with R. G. Bilyeu).
15. "Operators on Continuous Function Spaces and Convergence in the Space of Operators," Advances in Math. 29(1978), 157-177 (with J. Brooks).
16. "Compact Operators, Weakly Compact Operators and Smooth Points," Rocky Mountain J. Math. 9(1979) 587-591(with R. G. Bilyeu).
17. "Uniform Differentiability, Uniform Absolute Continuity, and the Vitali-Hahn-Saks Theorem," Rocky Mountain J Math. 10(1980), 533-557 (with R. G. Bilyeu).
18. "Operators on Spaces of Continuous Functions," Bull. Polon. Acad. Sci. (Polska) XXVII (No. 5), (1979), 355-358 (with J. Brooks).
19. "Vector Measures and Weakly Compact Operators on Continuous Function Spaces: A Survey," Measure Theory and Appl., Proc. 1980 Conf., Northern Illinois University, (1981), pp. 165-172, (with R. G. Bilyeu).
20. "Unconditionally Converging Operators on Continuous Function Spaces," Bull. Polon. Acad. Sci., 30(1982), pp. 157-160 (With R.G. Bilyeu).
21. "Norm Attaining Operators and Norming Functionals," Proc. Amer. Math Soc., 85(1982), 245-250 (with R. G. Bilyeu).
22. "Differentiability of Convex Functions and Rybakov's Theorem," Proc. Am. Math. Soc., 80(1982), 186-187 (with R. G. Bilyeu).
23. "Applications of Geometry of Infinite Dimensional Spaces to Vector Measures." Contemporary Math., 52(1986), 96-101, (with R.G. Bilyeu).
24. "Rearrangement and Category," Pacific J. Math., 121(1986), 41-46 (with Robert Kallman and R.G. Bilyeu).
25. "Uniform differentiability, compactness, and l¹," Proc. Amer. Math. Soc., 97(1986), 87-92 (with R.G. Bilyeu).
26. "Uniform Exhaustivity and Banach Lattices," Annali di Mat. Pura Appl., (IV) CXLIV(1986), 57-74 (with W. Bell and R.G. Bilyeu).
27. "Differentiability of Convex Functions, Pettis Integrability, and Rybakov's Theorem," Bull. Polish Acad. Sci., Ser. Math., 33(1985), 581-585 (with R.G. Bilyeu).
28. "Some connections between Pettis integration and operator theory," Rocky Mtn. J. Math., 17(1987), 683-695 (with E. Bator and D. Race).
29. "Weak precompactness and the weak RNP," Bull. Polish Acad. Sci. Math., 37(1989), 443-452 (with E. Bator).
30. "Weak precompactness, strong boundedness, and weak complete continuity," Math. Proc. Cambridge Phil. Soc., 108(1990), 325-335 (with C. Abbott, E. Bator, and R. Bilyeu).
31. "The Vitali integral convergence theorem and uniform absolute continuity," Canadian Journal of Mathematics, 43(1991), 939-947 (with E. Bator and R. Bilyeu).
32. "Strictly singular and strictly cosingular operators on spaces of continuous functions," Math. Proc. Cambridge Phil. Soc., 10(1991), 505-521 (with E. Bator and Catherine Abbott).
33. "Operators having weakly precompact adjoints," Mathematischen Nachrichten, 157(1992), 99-103 (with E. Bator).
34. "Properties (V) and (wV) on C("omega",X), Math. Proc. Camb. Phil. Soc., 117(1995), 469-477 (with E. Bator).
35. "The Range of a Representing Measure," Mathematical Proceeding of the Cambridge Philosophical Society, 124(1998), 365-369 (with J. Ochoa).
36. "Evaluation Maps, Restriction Maps, and Compactness," Colloquium Mathematicum 78 (1998), 1-17  (with E. Bator and J. Ochoa).
37. "Dunford-Pettis Sets," submitted.
38. "Mapping Properties of c₀," submitted.

JIANGUO LIU, PH.D.
Cornell University (1994)
Areas of Interest: Optimization, numerical methods, applied mathematics.

1. "An interior trust region algorithm for linearly constrained minimization," Optimization: Techniques and Applications, L. Caccetta et al., editors, ICOTA '98, Perth, Australia, 1998, 487-494.
2. "A new affine scaling algorithm for linear feasibility," Proceedings of the Fifth Annual Conference on Applied Mathematics, Edmond, Oklahoma, 1999, pp. 144-149..
3. "A fast hierarchical algorithm for 3-D capacitance extraction," Proceedings of the 35th Design Automation Conference, San Francisco, 1998, pp. 212-217 (co-authored wtih W. Shi, N. Kakani, and T. Yu).
4. "Superconvergence of gradient of triangular linear element in general domain," Natural Sciences Journal, Xiangtan University, 1 (1987), pp. 114-127. {Mathematical Reviews 88f:65193}, (co-authored with C. Chen).
5. "An interior Newton Method for quadratic programming," Mathematical Programming (co-authored with T. Coleman), to appear.
6. "An exterior Newton method for large-scale convex quadratic programming," Computational Optimization and Applications (co-authored with T. Coleman), to appear.
7. "A quasi-Newton quadratic penalty method for minimization subject to nonlinear equality constraints, " Computational Optimization and Applications (co-authored with T. Coleman and Y. Yuan), to appear.
8. "An interior trust region algorithm for nonlinear minimization with linear constraints," Journal of Computational Mathematics, to appear.
9. "A new trust region algorithm for equality constrained optimization," submitted.
10. "On the superlinear convergence of a quasi-Newton method for nonlinear optimization," in preparation.
11. "A note on optimality conditions for general quadratic programming," in preparation.
12. "Accuracy Enhancement in 3-D Capacitance Extraction," in preparation.

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RUTH MICHLER, PH.D.
University of California at Berkeley, 1993
Areas of Interest: Cyclic homology, algebraic geometry.

1. Hodge-components of cyclic homology of quasi-homogeneous hypersurfaces, Asterisque, 226, 1994, 321-333.
2. Torsion of K„hler differentials for affine quasi-homogeneous hypersurfaces, Rocky Mountain Journal of Mathematics, Vol. 26:1, 1996.
3. Torsion of differentials of hypersurfaces with an isolated singularity, Journal of Pure and Applied Algebra, 104, No. 1, 1995, 81-88.
4. Cyclic homology of hypersurfaces with isolated singularities, Journal of Pure and Applied Algebra, 120, No. 3, 1997, 291-299.
5. Invariants of isolated singularities, Proceedings of the International Conference on Syzygies and Geometry, Boston, 1995, 76-80.
6. On the number of generators of the torsion modules of differentials of affine hypersurfaces with isolated singularities (submitted to Proceedings of Summer School on Commutative Algebra, Barcelona, July 16-26, 1996).
7. The number of generators of torsion modules of differentials of isolated hypersurface singularities (Proceedings of Summer School on Commutative Algebra, Barcelona, July 16-26, 1996, volume 2, pp. 224-225).
8. The dual of the torsion module of differentials (accepted by Communications in Algebra, November 1998).
9. Invariants of singular plane curves (in preparation).
10. A comparison of de-Rham and crystalline cohomology for singular plane curves (in preparation).
11. Isolated hypersurface singularities with "large" Hochschild homology (preprint).
12. A mathematical model for an exhaust oxygen (joint with P. Worfolk, T. Leise, B. v.Dohlen, X. Chen, S. Othman, G. Barrick, D. Calhoun, X. Huang, H. Lomeli, D. Baker), IMA preprint 1422, 1996, pp. F1-F30.
13. Mathematical modeling of electronic rectifiers (joint with G. Kriegsmann, D. Alterman, M. Bond, X. Huang, H. Lomeli, K. Matthews, K. Zangara, B. v.Dohlen), IMA preprint 1422, 1996, pp. C1-C28.

PAPERS

1. "Utility functions which ensure the adequacy of stationary strategies," Transactions of the American Mathematical Society, Vol. 325, No. 1, 1991, pp. 187-204.
2. "The adequacy of universal strategies in analytic gambling problems," Mathematics of Operations Research, Vol. 16, No. 1, 1991, pp. 21-41.
3. "A survey of the search theory literature," Naval Research Logistics, Vol. 38, 1992, pp. 469-491 (with S.J. Benkoski and J.R. Weisinger).
4. "Randomly generated distributions," Israel Journal of Mathematics, Vol. 91, 1995, 215-237 (with R.D. Mauldin).
5. "Optimal cut-off strategies in capacity expansion problems, Naval Research Logistics, Vol. 42, 1995, pp. 1021-1039 (with James Weisinger). Work supported by an NSF Small Business Innovative Research Grant.
6. "Directionally reinforced random walks," Advances in Mathematics, Vol. 117, No. 2, 1996, 239-252 (with Heinrich v. Weizsacker and R. D. Mauldin). Work supported by an Office of Naval Research grant.
7. "Constructing prior distributions with trees of exchangeable processes," Journal of Statistical Planning and Inference--Bose Memorial Volume, 1998.
8. "Constructions of random distributions via sequential barycenters," Annals of Statistics , Vol. 26, No. 4, 1998, pp. 1242-1253 (with T. Hill).
9. "Web-Analysis, Stripping away the hype," invited article, IEEE Computer, December 1998.
10. "Using decision analysis in check risk analysis," invited article DPL News (Price-Waterhouse-Coopers industry newsletter), Winter 1999.
11. "Analyzing web site usage," invited, featured article on Netscape Netcenter - Computing and Internet Channel (Netscape's Internet content site).  To appear March 1999.
12. "Random probability measures," submitted to The American Mathematical Monthly, January 1999.
13. "Randomly distributions of mass in space," in preparation (with T. Hill).
14. "Statistical models for environmental gradient inference," in preparation (with Harry Williams).

1. "The effects on non-homogeneous environment on passive sonobuoy search for a submerged target," Daniel H. Wagner Associates Technical Report to Naval Oceanographic Research and Development Activity, December 1988 (with S.J. Benkoski).
2. "Optimal layered searches," Daniel H. Wagner Associates Technical Report, June 1989.
3. "The feasibility of applying search theory to the Korean tunnel problem," Daniel H. Wagner Associates Technical Report to Commander Belvoir Research, Development and Engineering Center, U.S. Army, July 1989 (with J.R. Weisinger).
4. "Strategic planning for capacity expansion under uncertainty," Final Report NSF Small Business Innovative Research Grant, Award Number 151-9160 155, 38 pages.
5. "Exchangeable tree priors and random distributions," UNT Department of Mathematics Technical Report 1991.
6. "Controlling a process which leaps to a goal," UNT Department of Mathematics Technical Report 1992.
7. "Optimal capacity expansion under uncertainty," Final Project Report--NSF Small Business Innovative Research Grant, 1993 (with J. R. Weisinger). Award number ISI-9160155.
8. "Moments of the distribution of the mean for a Dubins-Freedman prior," UNT Department of Mathematics Technical Report 1994.

See Morton's home page.

Revised September 20, 1999
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1. "Continuous Products and Nonlinear Integral Equations," Pac. J. of Math., 8 (1958), 529-549.
2. "Concerning Boundary Value Problems," Pac. J. of Math., 10 (1960), 1385-1392.
3. "An Analyticity Condition," J. London Math. Soc., 38 (1963), 91-98.
4. "A Quasi-Analyticity Condition in Terms of Finite Differences," Proc. London Math. Soc., XIV (1964), 245-259.
5. "A Generator For A Set of Functions," Ill. J. Math., 9 (1965), 31-39.
6. "The Lack of Self-Adjointness in Three-Point Boundary Value Problems," Pac. J. Math., 28 (1966), 165-168.
7. "An Exponential Formula for One-Parameter Semigroups of Non-linear Transformations," J. Math. Soc. Japan, 19 (1966), 1954-1957.
8. "Symmetry in Non-Self-Adjoint Sturm-Liouville Systems," Bull. Amer. Math. Soc., 73 (1967), 701-703.
9. "Toward a Characterization of the Identity Component in Rings and Nearrings of Continuous Transformations," J. fur die Reine und Angewandte Mathematik, 238 (1969), 100-104.
10. "Quasi-Analytic Collections Containing Fourier Series Which Are Not Infinitely Differentiable," J. London Math. Soc., 43 (1968), 612-616.
11. "Tensor Products and Successive Approximations for Partial Differential Equations," Isr. J. Math., 6 (1968), 121-132.
12. "Existence of a Spectrum for Nonlinear Transformations," Pac. J. Math., 31 (1969), 157-159.
13. "Product Integral Formulae for Nonlinear Expansive Semigroups and Nonexpansive Evolution Systems," J. of Math. and Mech., 19 (1969), 403-409.
14. "Analyticity and Quasi-Analyticity for One-Parameter Semigroups," Proc. Amer. Math. Soc., 25 (1970), 488-494.
15. "Quasi-Analyticity and Semigroups of Bounded Linear Transformations," Bull. Amer. Math. Soc., 78 (1972), 85-87.
16. "Lie Generators for Strongly Continuous Equi-Uniformly Continuous One Parameter Semigroups on a Metric Space," Ind. Univ Math J., 21 (1971), 961-971.
17. "Lie Generators for One Parameter Semigroups of Transformations," J. Reine Ang. Math., 258 (1973), 133-136.
18. "Differentiable Semigroups With a Neighborhood of the Identity Homeomorphic to a Banach Space," Proc. Amer. Math Soc., 34 (1972), 595-600.
19. "Quasi-Analyticity and Semigroups," Bull. Amer. Math. Soc., 78 (1972), 909-922.
20. "Quasi-Analytic Semigroups," J. London Math. Soc., (2), 7 (1973), 259-264.
21. "Norm of Symmetric Product Compared with Norm of Tensor Product," J. Linear Multi-Linear Algebra, 2 (1974), 115-121.
22. "An Iterative Method for Solving Nonlinear Partial Differential Equations," Advances in Math., 19 (1976), 245-265.
23. "Differentiability of the Exponential of a Member of a Nearring," Proc. Amer. Math. Soc., 48 (1975), 98-100.
24. "A Resolvent for an Iteration Method for Nonlinear Partial Differential Equations," Trans. Amer. Math. Soc., 226 (1977), 231-343.
25. "Projection Methods for Linear and Nonlinear Systems of Partial Differential Equations," Proceedings 1976 Dundee Conference on Differential Equations, Springer-Verlag Lecture Notes, 564, 341-349.
26. "Square Integrable Solutions to Linear Inhomogenous Systems, J. Differential Equations, 27 (1978), 144-152.
27. "Boundary Value Problems for Systems of Nonlinear Partial Differential Equations," Functional Analysis and Numerical Analysis, Springer-Verlag Lecture Notes #701, 196-208.
28. "Iteration for Systems of Nonlinear Partial Differential Equations," Nonlinear Equations in Abstract Spaces, Academic Press (1977), 253-263.
29. "An Iterative Method for Approximating Solutions to Nonlinear Partial Differential Equations," Applied Nonlinear Analysis, Academic Press, (1979), 287-297.
30. "Boundary Value Problems for Linear Systems," Proc. Royal Soc., Edinburgh, 83A (1979), 297-302.
31. "Finite Dimensional Potential Theory Applied to Numerical Analysis," Linear Alg. Appl., 35 (1981), 193-202.
32. "A Type-Independent Iterative Method for Systems of Non-Linear Partial Differential Equations: Application to the Problem of Transonic Flow," Computers and Mathematics With Applications, 7 (1980), 67-78.
33. "A Solvability Condition for Systems of Functional Differential Equations," Proceedings Conf. Functional and Integral Equations, Marcel Dekker, Inc., (1981).
34. "A Type-Independent Numerical Method for Solving Systems of Non-Linear Partial Differential Equations," Proceedings Second International Conf. on Innovative Numerical Analysis, Univ. of Montreal, (1980).
35. "A Type-Independent Iterative Method Using Finite Elements," Proceedings Third International Conf. on Finite Elements and Flow Theory, University of Calgary, (1980).
36. "An Iterative Method Based Upon Residual Averaging," Proc. Symposium on Computational Methods in Nonlinear Structural and Solid Mechanics, NASA (1980).
37. "A Type-Independent Numerical Method with Applications to Navier-Stokes Equations," Proc. Ninth Conference on Numerical Simulation of Plasmas, Northwestern University, (1980).
38. (With R. J. Renka) "A Portable Software Package for Non-Linear Partial Differential Equations," Oak Ridge National Laboratory, CSD-102 (1982).
39. "Steepest Descent for Systems of Non-Linear Partial Differential Equations," Oak Ridge National Laboratory, CSD/TM-161 (1981).
40. "Steepest Descent for General Systems of Linear Differential Equations in Hilbert Space," Springer Lecture Notes 1032 (1983), 390-406.
41. "Some Global Steepest Descent Results for Nonlinear Systems," Trends Theory Applications Diff. Eq., Marcel Dekker (1984), 413-418.
42. "Use of Steepest Descent for Systems of Conservation Equations," Proc. Special Year in Partial Differential Equations, Univ. of Houston (1983).
43. (with D.W. Noid) "Numerical Solution of Eigenvalues for Schroedinger Equation, Chemical Physics Letters, 104 (1984), 1-3.
44. "Gradient Inequalities and Steepest Descent for Systems of Partial Differential Equations," Proc. Conf. on Numerical Analysis, Texas Tech. University, 1983.
45. "Steepest Descent and Time-Stepping for the Numerical Solution of Conservation Equations," Proc. Conf. on Physical Math and Nonlinear Differential Equations, Marcel Dekker (1984).
46. (With D.W. Noid) "Numerical Solution of Eigenvalues for Schroedinger Equation II, Chemical Physics Letters, 112 (1984), 393-395.
47. "Steepest Descent and Differential Equations," J. Math. Soc. Japan , 37 (1985), 187-195.
48. "Chaos and Higher Order Differences," Proc. Amer. Math. Soc., 101 (1987), 45-50.
49. "Numerical Solutions of Eigenvalues for Schrodinger Equation III," J. Computational Chemistry, 8 (1987), 459-461.
50. "Semigroups of Steepest Descent," Semesterberich Funktional Analysis, Tubingen University, Funktional Analysis 12 (1987), 57-62.
51. "A Constructive Lemma for the Deficiency Index Problem, Proceedings Focused Research Program on Spectral Theory, Argonne National Laboratory, 2 (1987).
52. "Constructive Variational Methods for Differential Equations, J. Nonlinear Analysis 13 (1988), 413-428.
53. "Quasi-analytic Collections of Square Integrable Functions," Bulletin London Math. Soc., 20 (1988), 321-326.
54. Editor: Collected works of Arne Beurling (with L. Carleson, P. Malliavin, J. Wermer), Birkhauser (1989).
55. "Generation of Nonlinear Semigroups by a Partial Differential Equation," Semigroup Forum 40 (1990), 93-99.
56. "Calculation of Sharp Shocks Using Sobolev Gradients," Contemporary Mathematics, American Mathematical Society 108 (1990), 111-118.
57. "Beurling's Analyticity Theorem," Mathematics Intelligencer,15 (1993), 34-38.
58. "Predictability in the Absence of Chaos," J. Math. Anal. Appl., 175 (1993), 321-332.
59. "Nonlinear Semigroups," Matematisk Institut Aarhus Universitet (1992), 283-305.
60. "Continuation for Quasiholomorphic Semigroups," Semigroups of Operators, G.R. and J.A. Goldstein, eds., (1993) Kluwer, 241-249.
61. "A Feasibility Study of Nuclear Superfluorescence" (with B. Balko and I. Kay), Lasers '92, Proceedings of International Conference, C. P. Wong editor (1993), 89-93.
62. "Lie Generators for Semigroups of Transformations on a Polish Space," (with J. R. Dorroh), Elec. J. Differential Equations (1993), 1-7.
63. "Minimal Surfaces and Sobolev Gradients" (with R. J. Renka), Siam J. Sci. Comp. (1995), 1412-1427.
64. "A Theory of Strongly Continuous Semigroups in Terms of Lie Generators" (with J. R. Dorroh), J. Functional Analysis, 136 (1996), 114-126.
65. "Prevalance of Chaotic Differences for Unpredictable Functions," Acta Scientiarum Math., 61 (1995), 181-196.
66. "Nuclear Superfluorescence: A Feasibility Study based on the Generalized Haake-Reibold Theory," Physical Rev. B(1995), 858-869 (with B. Balko, I. Kay).
67. "An Investigation of the Possible Enhancement of Nuclear SF Through Crystalline and Hyperfine Interaction Effects," Proc. Int. Conf., Laser 95 V.I. Corcoran and T.A. Goldman, eds., STS Press (1996) (with B. Balko, I. Kay, R. Vuduc).
68. "Superfluorescence in the Presence of Inhomogeneous Broadening and Relaxation," Hyperfine Interactions 107 (1997), 369-379.  (with B. Balko, I. Kay, J. Silk, R. Vaduc).
69. "Sobolev Gradients and Boundary Conditions for Partial Differential Equations," Contemporary Mathematics 204 (1997), 171-181.
70. "Snowflake Harmonics and Computer Graphics: Numerical Computation of Spectra on Fractal Drums," Int. J. Bifurcation and Chaos 6 (1996), 1185-1210    (with M. Lapidus, R. Renka, C. Griffith).
71. "Continuous Steepest Descent in Higher Order Sobolev Spaces," Nonlinear Analysis 30 (1997), 3517-3520.
72. "Laplacians and Sobolev Gradients," Proc. Am. Math. Soc.  126 (1998), 2053-2060.
73. "Sobolev Gradients and the Ginzburg-Landau Equations," Siam J. Sci. Comp. 20 (1998), 582-590.   (with R. Renka).
74. "Recovery of Superfluorescence in Inhomogeneously Broadened Systems through Rapid Relaxation," Physical Rev. B. 55 (1997), 171-181. (with B. Balko, I. W. Kay, R. Vuduc).
75. Sobolev Gradients and Differential Equations, Lecture Notes in Mathematics 1670, Springer-Verlag .
76. "Numerical Calculation of Singularities for Ginzburg-Landau Functionals," Elec. J. Differential Equations (1997), No. 10, 1-4. (with R. J. Renka).
77. "An Inverse Function Theorem," Contemporary Mathematics, 221 (1998), 127-132  (with A. Castro).
78. "Approximation of Eigenvalues on the Dirichlet Laplacian on a Fractal Drum," Proceedings of the Third IMACS International Symposium on Iterative Methods in Scientific Computation, July 9-12, 1997, Jackson Hole, Wyoming (with R. J. Renka).
79. "Spectral Characterization of Solutions to Systems of Linear Differential Equations," Proc. Am. Math. Soc. (to appear).
80. "Numerical Calculation of the Essential Spectrum of a Laplacian," Experimental Mathematics, to appear (with R. J. Renka).
81. "Continuous Newton's Method for Polynomials," Mathematical Intelligencer (to appear ).

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JOHN QUINTANILLA, PH.D.
Princeton University, 1997
Areas of Interest: Applied probability, stochastic geometry, and random heterogeneous materials.

1. (With S. Torquato), "New Bounds on the Elastic Moduli of Suspensions of Spheres," Journal of Applied Physics 77, pp. 4361-4372 (1995).
2. (With S. Torquato), "Microstructure and Conductivity of Hierarchical Laminate Composites," Physical Review E 53, pp. 4368-4378 (1996).
3. (With S. Torquato), "Lineal Measures of Clustering in Overlapping Particle Systems," Physical Review E 54, pp. 4027-4036 (1996).
4. (With S. Torquato), "Clustering Properties of d-dimensional Overlapping Spheres," Physical Review E 54, pp. 5331-5339 (1996).
5. (With S. Torquato), "Microstructure Functions for a Model of Statistically Inhomogeneous Random Media,"Physical Review E 55, pp. 1558-1565 (1997).
6. With S. Torquato), "Local Volume Fraction Fluctuations in Random Media," Journal of Chemical Physics 106, pp 2741-2751 (1997).
7. (With S. Torquato), "Clustering in a Continuum Percolation Model," Advances in Applied Probability29, pp. 327-336 (1997).
8. "Microstructure and Properties of Random Heterogeneous Materials: A Review of Theoretical Results," Polymer Engineering and Science, 39, pp. 327-336 (1999).
9. (With S. Torquato), "Exact Expressions for Local Volume Fraction Fluctuations in Periodic Media,"Journal of Chemical Physics, 110, pp. 3215-3219 (1999).
10. (With S. Torquato), "Percolation in a Model of Statistically Inhomogeneous Random Media," Journal of Chemical Physics, to appear.
11. "Microstructure Functions for Random Media with Impenetrable Particles," in preparation.

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1. Sharp Upper Bound on Exponential Behavior of a Stochastic Partial Differential Equation. Random Operators and Stochastic Equations  4 (1) (1996) 43-49.  With R. Carmona, S. Molchanov.
2. Almost-sure Exponential Behavior of a Stochastic Anderson Model with Continuous Space Parameter. Stochastics and Stochastic Reports 64 (1998) 251-273. With R. Carmona.
3. Robustness of Zakai's equation via Feynman-Kac representations. Stochastic analysis, control, optimization and applications. Eds: W. M. McEneaney, G. Yin, Q. Zhang. Birkhauser.  339-352 (1999).  With R. Atar, O. Zeitouni.
4. Evolution Equation of a Stochastic Semigroup with White-noise Drift.  Accepted, Annals of Probability.  1999.  With D. Nualart.
5. Stochastic heat equation with white noise drift and space-time white noise potential. Accepted, Annales de l'IHP.  1999.  With E. Alos, D. Nualart.
6. On space-time regularity for the stochastic heat equations on Lie groups. Submitted to Journal of Functional Analysis, June 1999.  With S. Tindel.
7. Almost-Sure Exponential Behavior of a Linear System of Stochastic Partial Differential Equations.  In preparation.
8. Simulation of the non-linear filter via particle methods. In preparation.  With John W. Neuberger.
9. The connection between the Dorroh-Neuberger semigroup and weak solutions to stochastic differential equations.  In preparation.  With John W. Neuberger.
10. Fast random magnetic dynamo via particle and Feynman-Kac methods.  To appear in Fields Institute Communications (2000).  AMS.  With S.B. Hazra.
11. Lyapunov exponents for the stochastic heat equation on Lie groups.  In preparation.  With S. Tindel.
12. Necessary and sufficient conditions for continuity of function-valued stochastic heat equations.  In preparation.
13. Filtering the stochastic volatility from the history of stock prices.  In preparation.  With J.-P. Fouque.

HENRY WARCHALL, PH.D.
University of California, Berkeley, 1983
Areas of Interest: Mathematical physics and nonlinear partial differential equations, investigation of multidimensional solitary waves and scattering theory for nonlinear wave equations.

1. Implementation of automorphism groups in certain representations of the canonical commutation relations. J. Math. Phys. 23 (1983) 2221-2228.
2. C*-algebraic scattering theory and explicitly solvable quantum field theories. J. Math. Phys. 26 (1985) 1264-1279.
3. Simple physical models entailing inequivalent representations of the canonical commutation relations. J. Math. Phys. 26 (1985) 1280-1297.
4. Wave operators for the scattering of solitary waves in multiple spatial dimensions. Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Nicolaenko, Holm, and Hyman, eds., AMS Lect. Appl. Math. 23 (1986) 31-54.
5. Scattering of solitary waves in multiple spatial dimensions. Physica 18D (1986) 315-317.
6. Explicit multidimensional solitary wave solutions to nonlinear evolution equations. The Physics of Phase Space, Kim and Zachary, eds., Springer Lecture Notes in Physics 278 (1987) 429-431.
7. Multidimensional solitary waves: explicit examples and scattering theory. Nonlinear Analysis and Applications, Lakshmikantham, ed., Lecture Notes in Pure and Applied Mathematics 109 (1987) 583-592.
8. Explicit construction of all spherically symmetric solitary waves for a nonlinear wave equation in multiple dimensions (with E. Deumens). Nonlin. Anal., Th., Meth., & Appl. 12 (1988) 419-447.
9. Wave propagation at computational domain boundaries. Commun. in Partial Diff. Eq. 16 (1991) 31-41.
10. Induced lacunas in multiple-time initial value problems and unbounded domain simulation. Partial Differential Equations, Wiener & Hale, eds., Pittman Research Notes in Mathematics 273 (1992) 258-264.
11. Purely nonlinear norm spectra and multidimensional solitary waves. Differential Equations with Applications to Mathematical Physics, Ames, Herod & Harrell, eds., Mathematics in Science and Engineering 192 (1993), 313-323.
12. Nonradial solutions of a semilinear elliptic equation in two dimensions (with J. Iaia). J. Differential Equations 119 (1995) 533-558.
13. Reflectionless boundary propagation formulas for partial wave solutions to the wave equation (with J. Navarro). Electronic Journal of Differential Equations (1995) #17 (10 pages).
14. Localized solutions of sublinear elliptic equations: Loitering at the Hilltop (with J. Iaia and F. Weissler).  Rocky Mountain J. Math. 27 (1997) 1131-1157.
15. Encapsulated-vortex solutions to equivariant wave equations: Existence (with J. Iaia).  SIAM J. Math. Anal.  30 (1998) 118-139.
16. Hidden ground states (with F. Weissler).  To appear in Communications in Applied Analysis.

LUCA ZAMBONI, PH.D.
Brown University, 1989
Areas of Interest: Symbolic dynamics, combinatorial number theory.

1. (with S. Ferenczi, C. Holton),  The structure of 3-interval exchange transformations I:  Simultaneous approximation, Farey quadrilaterals, and a Lagrange type theorem, preprint (1999).
2. (with S. Ferenczi, C. Holton), The structure of 3-interval exchange transformations II:  Ergodic and spectral properties, preprint (1999).
3. (with J.-P. Allouche, J.L. Davison, M. Queffelec), Transcendence of sturmian or morphic continued fractions, preprint (1999).
4. (with J. Cassaigne), Unbalanced sequences of complexity 2n+1, preprint (1999).
5. (with N. Wozny), Frequencies of factors in Arnoux-Rauzy sequences, preprint (1999).
6. (with C. Holton), Overlaps in sturmian words, preprint (1999).
7. (with R. Parsons), Some combinatorial properties of Arnoux-Rauzy sequences (1998), preprint.
8. (with R. Risley), A generalization of Sturmian flows; combinatorial structure and transcendence (1998), Acta Arithm., in press.
9. (with C. Holton), Directed graphs and substitutions,From Cristals to Chaos (eds. P. Hubert, R. Lima, and S. Vaienti), World Scientific, New York, 1999.
10. Une generalisation du theoreme de Lagrange sur le developpement en fraction continue, C.R. Acad. Sci. Paris, Serie I  t. 327 (1998), p. 527-530.
11. (with P. Ketkar), Primitive substitutive numbers are closed under rational multiplication, J. Theor. Nombr. Bordeaux10 (1998), p. 315-320.
12. (with C. Holton), Iterations of maps by primitive substitutive sequences, Discrete Math (1998), in press.
13. (with C. Holton), Substitutions, partial isometries of R and actions on trees, Bull. Belgian Math. Soc. (1998), in press.
14. (with C. Holton), Descendants of primitive substitutions, Theory Comput. Systems  32 (1999), p. 133-157.
15. (with J.-P. Allouche), Algebraic irrational binary numbers cannot be fixed points of non-trivial constant length or primitive morphisms, J. Number Theory 69  (1998), p. 119-124.
16. (with C. Holton), Geometric realizations of substitutions, Bull. Soc. Math. France 126 (1998), p. 149-179.
17. Geodesic Laminations on Compact Surfaces and Homeomorphisms of the Cantor Set, Rocky Mount. J. Math. (1998), in press.
18. (with C. Holton), Exotic Actions on Trees, Bull. Lond. Math. Soc. 29 (1997) p.  309-313.
19. On Splittings of Groups Acting Freely on -Trees, Conference Proceedings in Combinatorial Group Theory (1995).
20. On the Growth Rate of Alternating Walks Along a Finite Set of Graphs, Houst. Jour. Math. 21 (1995), p. 291-295.
21. Tree Fibrations, Houst. Jour. Math. 20 (1994), p. 53-74.
22. (with S. Jackson), On a Theorem of Chiswell, Proceedings of the AMS 123 9 (1995), p. 2629-2639.
23. (With M. Urbanski), Circle Maps, Measured Laminations, and Free Actions on -Trees, Math. Nachr. 170 (1994), p. 277-285.
24. (With M. Urbanski), On free actions on -trees, Math. Proc. Cam. Phil. Soc. 113 (1993), p. 535-542.
25. On the Invariance of Conjugation in Cyclic Homology, Riv. Mat. Univ. Par. 1 (1992), p. 295-304.
26. A Chern Character in Cyclic Homology, Transactions of the A.M.S. 31 1 (1992), p. 157-173.
27. Cyclic Homology of a Differential Graded Algebra, Ph.D. Thesis, Brown University, (1989).