Publications: J. C. Alexander

Publications arranged more or less by topic (although of course some topics overlap), in reverse chronological order. In the fox-hedgehog dichotomy, I find myself an extreme fox. Postscript and PDF files and abstracts (linked titles). Coauthors. Back to home page

Topics

• Medical
• Fluid mechanics/interface phenomena
• Continuum mechanics
• Travelling waves
• Nonlinear optics
• Sliding modes
• Riddling
• Bifurcation of systems with structure
• Robotics, wheeled mobile robots
• ICBMs (infinitely convolved Bernoulli measures), fat bakers transformations, etc.
• Chemical reactor simulation
• Bursting systems
• Power system analysis
• Precision guided munitions
• Global bifurcation and continuation, theory
• Global bifurcation and continuation, numerics
• Geodesy
• Cobordism
• Other geometry and topology
• Other
• Expository articles and editorships
• Facts on File Math Library

• Chronic ethanol and triglyceride turnover in white adipose tissue in rats: inhibition of the anti-lipolytic action of insulin after chronic ethanol contributes to increased triglyceride degradation ( with Li Kang, Xiaocong Chen, Becky M. Sebastian, Brian T. Pratt, Ilya R. Bederman, Stephen F. Previs, Laura E. Nagy), J Biol Chem. 282(39) (Sep 28, 2007), 28465-73.
• Novel application of the "doubly-labeled" water method: measuring CO₂ production and the tissue-specific dynamics of lipid and protein in vivo, (with Ilya R. Bederman, Danielle A. Dufner, and Stephen Previs), Am. J. Physiol. Endocrin. Metab. 290 (May 2006), E1048-E1056.
• Quantitation of rates of protein synthesis in humans using deuterated water: measurements in chronically dialyzed patients with end stage renal disease, (with Stephen F. Previs, Richard Fatica, Visvanathan Chandramouli, Henri Brunengraber, and Bernard R. Landau), Am. J. Physiol. Endocrin. Metab. 286 (April 2004), E665-E672.
• Influence of diet on modeling of adipose tissue triglycerides during growth, (with Daniel Z. Brunengraber, Brendan J. McCabe, Tahir Kasumov, Visvanathan Chandramouli and Stephen F. Previs) Am. J. Physiol. Endocrin. Metab. 285 (October 2003), E917-E926.

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• Determination of interphase line tension in Langmuir films, (with Jacob R. Wintersmith, Lu Zou, Andrew J. Bernoff, J. Adin Mann Jr., Edgar E. Kooijman, Elizabeth K. Mann), Phys. Rev. E, 75(6), June, 2007.
• Domain relaxation in Langmuir layers (with Andrew Bernoff, Elizabeth K. Mann, J. Adin Mann, Jr., Jacob Wintersmith and Lu Zou), J. Fluid Mech, 571 (January 25, 2007), 191-219.
• Hole dynamics of polymer Langmuir films (with Andrew Bernoff, Elizabeth K. Mann, J. Adin Mann, Jr. and Lu Zou), Physics of Fluids, 18(6), 062103 (June 2006).

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• Finite-energy solutions of mixed 3d div-curl systems (with G. Auchmuty) Quart. Appl. Math. 64(2) (2006), 335-357.
• L² well-posedness of 3-d div-curl boundary-value problems (with G. Auchmuty), Quart. Appl. Math., 63(3) (2005), 479-508.
• L²-well-posedness of planar div-curl problems (with G. Auchmuty), Arch. Rat. Mech. Anal., 160(2) (2001), 91-134.
• On the topological structure of the set of generalized solutions of the catenary problem (with M. Reeken), Proc. Roy. Soc. Edinburgh Sect. A 98 (1984), 339-348.
• Global behavior of solutions of nonlinear equations depending on infinite-dimensional parameters (with S. Antman), Indiana Univ. Math. J. 32 (1982), 39-62.
• Nonlinear eigenvalue problems for the whirling of heavy elastic strings II: New methods in global bifurcation theory (with S. Antman), Proc. Roy. Soc. Edinburgh Sect. A 93 (1982), 197-227.
• The ambiguous twist of Love (with S. Antman), Quart. Appl. Math. 40(1) (1982/83), 83-92.
• Global and local behavior of bifurcating multidimensional continua of solutions for multiparameter nonlinear eigenvalue problems (with S. Antman), Arch. Rat. Mech. Anal. 76 (1981), 339-354.
• Global bifurcation of waves (with G. Auchmuty), Manuscripta Math. 27 (1979), 159-166.

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• On the transverse instability of solitary waves in the Kadamstev-Petviashvili equation (with R. Pego and R. Sachs), Phys. Lett. A 226 (3,4) (1997), 187-192.
• Linear instability of solitary waves of a Boussinesq-type equation: A computer assisted computation (with R. Sachs), Nonlinear World ) 2 (1995), 471-507.
• Existence and stability of asymptotically oscillatory double pulses (with C. Jones), J. Reine Angew. Math. 446 (1994), 49-79.
• Existence and stability of asymptotically oscillatory triple pulses (with C. Jones), Z. Angew. Math. Phys. 44 (1993), 189-200.
• A topological invariant arising in the stability analysis of travelling waves (with C. Jones and R. Gardner), J. Reine Angew. Math. 410 (1990), 167-212.

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• Stability of multiple pulses in optical fibers with phase-sensitive amplification and noise (with R. Moore, W. L. Kath, B. Sandstede and C. K. R. T. Jones), Optics Comm. 195 (2001) 127-139.
• Existence and stability of N-pulses on optical fibers with phase-sensitive amplifiers (with C. Jones and B. Sandstede), Physica D 106 (1-2) (1997), 167-206.
• Stability of pulses on optical fibers with phase-sensitive amplifiers (with M. Grillakis, C. Jones and B. Sandstede), Z. Angew. Math. Phys. 48 (2) (1997), 175-192.

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• PowerPoint slides of colloquium lecture on sliding. Physikzentrum Bad Honnef, Germany, May, 1998

• Sliding modes in intersecting switching surfaces, II: Hysteresis (with T. Seidman), Houston J. Math. 25(1) (1999), 185-211.
• Sliding modes in intersecting switching surfaces, I: Blending (with T. Seidman), Houston J. Math. 24(3) (1998), 545-569.

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• Intermingled basins for the triangle map (with B. Hunt, I. Kan and J. Yorke), Erg. Th. Dyn. Sys. 16 (1996), 651-662.
• The transition to chaotic attractors with riddled basins (with E. Ott, J. Sommerer, I. Kan and J. Yorke), Physica D 76(4) (1994), 384-410.
• Scaling behavior of chaotic systems with riddled basins (with E. Ott, J. Sommerer, I. Kan and J. Yorke), Phys. Rev. Lett. 71(25) (1993), 4134-4137.
• Riddled basins (with I. Kan, J. Yorke and Z-P. You), Int. J. Bif. & Chaos 2 (1992), 795-813.

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• Generic Hopf bifurcation from lines of equilibria without parameters: III. Binary Oscillations (with B. Fiedler and S. Liebscher) Int. J. Bifurcation and Chaos in Appl. Sciences and Eng. 10(9) (2000), 1613-1622.
• Generic Hopf bifurcation from lines of equilibria without parameters: I. Theory (with B. Fiedler and S. Liebscher) J. Diff. Eq.167(1) (2000), 16-35.
• Global decoupling of coupled symmetric oscillators (with B. Fiedler), in "Differential Equations: Proceedings of the EQUADIFF Conference," C. Dafermos, G. Ladas, G. Papanicolaou, eds., Dekker, (1989), 7-16.
• Bifurcation analysis of reaction-diffusion equations VI: Multiply periodic travelling waves (with G. Auchmuty), SIAM J. Math. Anal. 19 (1988), 100-109.
• Patterns at primary Hopf bifurcations of a plexus of identical oscillators, SIAM J. Appl. Math. 46 (1986), 199-221.
• Global bifurcations of phase-locked oscillators (with G. Auchmuty), Arch. Rational Mech. Anal. 93 (1986), 253-270.

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• Shortest paths for wheeled mobile robots (with J. Maddocks and B. Michalowski), IEEE Trans. on Robotics and Automation 14(5) (Oct., 1998), 657-662.
• Bounds on the friction dominated motion of a pushed object (with J. Maddocks), Int. J. Robot. Res. 12(4) (1993), 231-248.
• On the kinematics of wheeled mobile robots (with J. Maddocks), Int. J. Robot. Res. 8(5) (1989), 15-27.
• Reprinted in: "Autonomous Robot Vehicles," I. J. Cox & G. T. Wilfong, eds., Springer-Verlag, (1990), 5-24.
• On the maneuvering of vehicles (with J. Maddocks), SIAM J. Appl. Math. 48 (1988), 38-51.

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• The entropy of a certain infinitely convolved Bernoulli measure (with D. Zagier), J. London Math. Soc. 44 (1991), 121-134.
• The entropy of the Fibonacci code (21 pages), (1989).
• Discerning fat baker's transformations (with W. Parry), Dynamical Systems: Proceedings, University of Maryland 1986-87, J. Alexander, ed., Lecture Notes in Mathematics 1342, Springer-Verlag. (1988), 1-6.
• Fat baker's transformations (with J. Yorke), Erg. Th. Dyn. Sys. 4 (1984), 1-23.

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• Dynamics of a CSTR for styrene polymerization initiated by a binary initiator mixture---II. Effect of viscosity dependent heat transfer coefficient (with K-J. Kim and K-Y. Choi), Polym. Engng. Sci. 32(7) (1992), 494-505.
• Dynamics of a cascade of two continuous stirred tank polymerization reactors with a binary initiator mixture (with K-J. Kim and K-Y. Choi), Polym. Engng. Sci. 31(5) (1991), 333-351.
• Dynamics of a CSTR for styrene polymerization initiated by a binary initiator system (with K-J. Kim and K-Y. Choi), Polym. Engng. Sci. 30(5) (1990), 279-290.

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• On the dynamics of bursting systems (with D-Y. Cai), J. Math. Biol. 29(5) (1991), 405-423.
• On the resonance structure in a forced excitable system (with E. Doedel and H. Othmer), SIAM J. Appl. Math. 50(5) (1990), 1373-1418.
• Resonance and phase-locking in excitable systems (with E. Doedel and H. Othmer), in "Some Mathematical Questions in Biology: The Dynamics of Excitable Media," H. G. Othmer, ed., Lectures on Mathematics in the Life Sciences, 21, American Mathematical Society (1989), 1-37.
• A period doubling bubble in the dynamics of coupled oscillators, in "Nonlinear Oscillations in Biology and Chemistry," H. G. Othmer, ed., Lecture Notes in Math. Biology, vol. 66, Springer-Verlag, (1986), 208-220.
• Spontaneous oscillations in 2 two-component cells coupled by diffusion, J. Math. Biol. 23 (1986), 205-219.

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• Dynamic bifurcations in a power system model exhibiting voltage collapse (with E. Abed, H. Wang, A. Hamdan and H-C. Lee), Int. J. Bif. Chaos 3(5) (1993), 1169-1176.
• Conference presentation in: "Proc. 1992 IEEE Int. Symp. Circuits and Systems, San Diego, May 1992," IEEE (1992).
• Approximation of faulted power system trajectories via averaging (with E. Abed), in "Proc. 26th Conf. on Decision and Control," IEEE (1987), 863-865.
• Oscillatory solutions of a model nonlinear swing equation, Int. J. Elec. Pow. & Ener. Syst. 8 (1986), 130-136.

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• Analysis of guidance laws for precision guided munitions (10 pages), technical report (1985).
• On hitting a stopping vehicle with a precision guided munition (4 pages), technical report (1985).

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• A note on the regularity of solutions obtained by global topological methods. in "Nonlinear Functional Analysis and its Applications," F. Browder, ed., AMS Proc. Symp. Pure Math. 45, American Mathematical Society (1986), 1-6.
• Constrained multiparameter global bifurcation, J. Func. Anal. 59(3) (1984), 490-497.
• On the continuability of periodic orbits of parametrized three-dimensional differential equations (with J. Yorke), J. Diff. Eq. 49 (1983), 171-184.
• On the connectivity properties of the solution sets of infinitely parametrized families of vector fields (with I. Massabó and J. Pejsachowicz), Boll. Un. Mat. Ital. A 6 (1982), 309-312.
• Global bifurcation for solutions of equations involving several parameter multivalued condensing mappings (with P. Fitzpatrick), in "Fixed Point Theory," E. Fadell & G. Fornier, eds, Lecture Notes in Mathematics 886, Springer-Verlag, (1981), 1-19.
• Galerkin approximations in several parameter bifurcation problems (with P. Fitzpatrick), Math. Proc. Cambridge Philos. Soc. 87 (1980), 489-500.
• Calculating bifurcation invariants as elements in the homotopy of the general linear group, II, J. Pure Appl. Algebra 17 (1980), 117-125.
• The homotopy of certain spaces of nonlinear operators and its relation to global bifurcation of the fixed points of parametrized condensing operators (with P. Fitzpatrick), J. Func. Anal. 34(1) (1979), 87-106.
• Bifurcation of zeroes of parametrized functions, J. Func. Anal. 29(1) (1978), 37-53.
• Calculating bifurcation invariants as elements in the homotopy of the general linear group, J. Pure Appl. Algebra 13 (1978), 1-8.
• Global bifurcation of periodic orbits (with J. Yorke), Am. J. Math. 100 (1978), 263-292.
• Parametrized functions, bifurcation, and vector fields on spheres, in "Problems of the Asymptotic Theory of Nonlinear Equations" (with J. Yorke), V. Korolyuk, ed., Academy of Sciences of the Ukrainian SSR (1977), 15-17.
• The implicit function theorem and the global methods of cohomology (with J. Yorke), J. Func. Anal. 21 (1976), 330-339.

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• Average intersection and pivoting densities, SIAM J. Num. Anal. 24(1) (1987), 129-145.
• Piecewise smooth homotopies (with T-Y. Li and J. Yorke), in "Homotopy Methods and Global Convergence," B. C. Eaves, F. J. Gould, H-O. Peitgen, M. J. Todd, eds. (1983), 1-14.
• Global convergence rates of piecewise-linear continuation methods: a probabilistic approach (with E. Slud), in "Homotopy Methods and Global Convergence," B. C. Eaves, F. J. Gould, H-O. Peitgen, M. J. Todd, eds. (1983), Plenum Press, 15-30.
• Numerical continuation methods and bifurcation, in "Functional Differential Equations and Approximation of Fixed Points," H-O. Peitgen & H-O. Walther, eds., Lecture Notes in Mathematics 730, Springer-Verlag, (1979), 455-483.
• The topological foundations of an embedding method, in "Continuation Methods," H-J. Wacker, ed., Academic Press (1978), 1-15.
• The homotopy continuation method: numerically implementable topological procedures (with J. Yorke), Trans. Amer. Math. Soc. 242 (1978), 271-284.

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• On the numerics of computing geodetic ellipsoids, SIAM Review 27(2) (1985), 241-248.
• Reprinted in ""Mathematical Modelling: Classroom Notes in Applied Mathematics," M. S. Klamkin, ed., SIAM (1987).
• Higher harmonic effects of the earth's gravitational field from post-glacial rebound as observed by Lageos, Geophys. Res. Lett. 10 (1983), 1085-1087.

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• On the deRham invariant of a fibered (4r-1)-dimensional orientable manifold, Math. Ann. 256 (1981), 429-437.
• Characteristic number obstructions to fibering oriented and complex manifolds over surfaces (with S. Kahn), Topology 19 (1980), 265-282.
• Unitary approximations to framed bordism, Bol. Soc. Mat. Mexicana 20 (1975), 1-5.
• On (U,Sp) cobordism, Am. J. Math. 99 (1975), 617-625.
• A family of indecomposable symplectic manifolds, Am. J. Math. 94 (1972), 699-710, correction and addendum, 99 (1977), 1361-1364.
• On Liulevicius' and Hazewinkel's generators for BP_*, University of Maryland Technical Report TR 72-14 (1972).
• The bordism ring of manifolds with involution, Proc. Am. Math. Soc. 31 (1972), 536-542.
• Cobordism Massey products, Trans. Amer. Math. Soc. 166 (1972), 197-214.

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• Closed geodesics on certain surfaces of revolution, J. of Geom. and Symm. in Physics 8 (2006), 1-16.
• First integrals for singular holomorphic foliations with leaves of bounded volume (with A. Verjovsky), in "Holomorphic Dynamics, Proceedings, Mexico, 1986," X. Gomez-Mont, J. Seade, A. Verjovsky, eds., Lecture Notes in Mathematics 1345, Springer-Verlag, 1-10.
• The additive inverse eigenvalue problem and topological degree, Proc. Amer. Math. Soc. 70 (1978), 5-7.
• Morse functions on Grassmannians, Ill. J. Math. 15 (1971), 672-681.
• On mod p connected K-theory, Topology 10 (1971), 337-371.

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• Blending in mathematics (2008) (54 pages).
• Comparable and extensive rates of triglyceride turnover in white adipose tissue of mice consuming a low-fat high-carbohydrate or very-high fat carbohydrate-free diet: Evidence in support of glyceroneogenesis? (with Ilya R. Bederman and Stephen F. Previs) FASEB J., 20 #530.7 (2006) A861 (abstract of presentation).
• Risk neutrality and ordered vector spaces (with M. Sobel), 2006, submitted.
• Dimensions of attractors of chaotic systems (with J. Yorke), in "Proceedings of 17th Annual Conference on Information Science and Systems," Dept. of Electrical Engineering and Computer Science, Johns Hopkins University, Baltimore, MD (1983), 88-92.
• Calculations of direct energy losses from ceiling mounted radiant heating panels to fenestrated areas, Energy Engineering 78 (1981), 35-48.
• A mathematical model for the open dating of perishable grocery products (with R. Stokes), Consumer Research Institute Technical Report (1974).
• The boundary count of digital pictures (with A. Thaler), J. Assoc. Comput. Mach. 18 (1971), 105-112.
• A study of the effect of redundancy on the failure rate of computer components, Westinghouse Technical Report (1963).

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Expository articles and editorships

• Splashing a wall with a garden hose, College Math. J. 36(2) (2005), 149-152.
• Loxodromes: A rhumb way to go, Math. Mag. 77(5) (2004), 349-358.
• The symbolic dynamics of the sequence of pedal triangles, Math. Mag. 66(3) (1993), 147-158.
• A java applet demo of pedal triangles
• Dynamical Systems: Proceedings, University of Maryland 1986-87, editor, Lecture Notes in Math 1342, Springer-Verlag, (1988).
• Geometry and Topology: Proceedings of the Special Year held at the University of Maryland College Park, 1983-1984, editor (coeditor with John Harer), Lecture Notes in Mathematics 1167, Springer-Verlag, (1986).
• Dynamics in Schwarzschild space and the classical tests of general relativity, University of Maryland Technical Report TR 81-33 (1981, revised 1982).
• A primer on connectivity, in "Fixed Point Theory," E. Fadell & G. Fornier, eds., Lecture Notes in Mathematics, vol. 886, Springer-Verlag, (1981), 455-483.
• A simplicial Hopf map, University of Maryland Technical Report TR 78-18 (1978).
• Matrices, eigenvalues and complex projective space, Am. Math. Monthly 85 (1978), 727-733.
• On the connected sum of projective planes, tori, and Klein bottles, Am. Math. Monthly 78 (1971), 185-187.

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Facts on File Math Library

Material for high-school classes. (Lead author with teams consisting of Ross Cirincione, Brendan Foreman, Michael Harvey, Catherine Hollway, Earl Johnson, Scott Kersey, Melissa Rogers, Mary Pattison, David Singer, Ellen Stenson)

• Math on File: Algebra, 2002
• Math on File: Geometry, 2003
• Math on File: Calculus, 2003

Math on File: Geometry is an invaluable curriculum-based and curriculum-enhancing resource. The problems are clearly and logically presented and will give your students a more concrete way of looking at geometry with real-world applications. This work is recommended as a required supplement for all high school geometry instructors. American Reference Books Annual 2004, entry 1542

Math on File: Calculus, part of a three-volume series that includes volumes on Algebra and Geometry, addresses five geometric categories: "Functions, Graphs, and Limits": "Differentiation and Applications": "Integration and Applications": and "Advanced Applications." ... Math on File: Calculus is an invaluable curriculum-based and curriculum enhancing resource. The problems are clearly and logically presented. I recommend this book to be a required supplement for all hight school calculus instruction. American Reference Books Annual 2005, entry 1535

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List of coauthors

Number of collaborations in parenthesis

• Eyad Abed, University of Maryland (Electrical Engineering) (2)
• Stuart Antman, University of Maryland (4)
• Giles Auchmuty, University of Houston (6)
• Ilya R. Bederman, Case Western Reserve University (Physiology and Biophysics) (4)
• Andrew J. Bernoff, Harvey Mudd College (3)
• Daniel Z. Brunengraber, Case Western Reserve University (Medical Scientist Program) (1)
• Henri Brunegraber, Case Western Reserve University (Nutrition) (1)
• Dayong Cai, Tsinghua University, Bejing (1)
• Visvanathan Chandramouli, University Hospitals (Endocrinology) (2)
• Xiaocong Chen, Case Western Reserve University (Nutrition), Cleveland Clinic (Pathobiology) (1)
• Kyu-Yong Choi, University of Maryland (Chemical Engineering) (3)
• Eusebius Doedel, Concordia University (2)
• Danielle A. Dufner, Case Western Reserve University (Nutrition) (1)
• Richard Fatica, Cleveland Clinic Foundation (Nephrology and Hypertension) (1)
• Bernold Fiedler, Freie Universität Berlin (3)
• Patrick Fitzpatrick, University of Maryland (3)
• Robert Gardner, University of Massachusetts, Amherst (1)
• Manoussos Grillakis, University of Maryland (1)
• Anan M. A. Hamdan, Jordan University of Science and Technology, Irbid, Jordan (1)
• John Harer, Duke University (coeditor)
• Brian Hunt, University of Maryland (1)
• Chris Jones, University of North Carolina (6)
• Steven Kahn, Wayne State University (1)
• Ittai Kan, Finetre Corporation (4)
• Tahir Kasumov, Case Western Reserve University, (Nutrition) (1)
• Li Kang, Case Western Reserve University, (Biochemistry) (1)
• William Kath, Northwestern University (1)
• Kee-Jeong Kim, University of Maryland (Chemical Engineering) (3)
• Edgar E. Kooijman, Kent State University (Physics) (1)
• Bernard R. Landau, Case Western Reserve University (Clinical and Molecular Endocrinology) (deceased) (1)
• Hsien-Chairn Lee, Chung Shan Institute of Science and Technology, Lung-Tan, Taiwan (1)
• Tien-Yien Li, Michigan State University (1)
• Stefan Liebscher, Freie Universität Berlin (2)
• Brendan J. McCabe, Case Western Reserve University (Nutrition) (1)
• John Maddocks, École Polytechnique Fédérale de Lausanne (4)
• Elizabeth Mann, Kent State University (Physics) (3)
• J. Adin Mann, Jr., Case Western Reserve University (Chemical Engineering) (3)
• Ivar Massabó, Università della Calabria (1)
• Brian Michalowski, Volt Technical Resources (1)
• Richard Moore, New Jersey Institute of Technology (1)
• Laura E. Nagy, Case Western Reserve University (Nutrition), Cleveland Clinic (Gastroenterology and Pathobiology) (1)
• Hans Othmer, University of Minnesota (2)
• Ed Ott, University of Maryland (Physics/Electrical Engineering) (2)
• William Parry, University of Warwick (1)
• Robert Pego, Carnegie Mellon University (1)
• Jacobo Pejsachowicz, Politécnico di Torino (1)
• Brian T. Pratt, Case Western Reserve University (Pathobiology) (1)
• Stephen F. Previs, Case Western Reserve (Nutrition) (5)
• Michael Reeken, Universität Wuppertal (1)
• Robert Sachs, George Mason University (2)
• Björn Sandstede, University of Surrey (3)
• Becky M. Sebastian, Cleveland Clinic (Pathobiology) (1)
• Thomas Seidman, University of Maryland, Baltimore County (2)
• Eric Slud, University of Maryland (1)
• Matthew Sobel, Case Western Reserve University (Operations) (1)
• John Sommerer, Johns Hopkins University Applied Physics Lab (2)
• Ray Stokes (1)
• Alvin Thaler, National Science Foundation (1)
• Alberto Verjovsky, Instituto de Matemáticas UNAM--Unidad Cuernavaca (1)
• Hua Wang, Boston University (Aerospace and Mechanical Engineering) (1)
• Jacob R. Wintersmith, Harvey Mudd College (2)
• James Yorke, University of Maryland (13)
• Zhiping You, Argose, Inc. (1)
• Don Zagier, Max-Planck-Institut für Mathematik, Bonn (1)
• Lu Zou, Kent State University (Physics) (3)

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