Leopold Flatto - Publications

  1. Periodic Solutions of Singularly Perturbed Systems, L. Flatto and N. Levinson, J. of Rat. Mech. and An., 4 (1955), pp. 943-950.
  2. A Problem of Random Walk, L. Flatto, Quart. J. of Math., Oxford, 9 (1958), pp. 299-300.
  3. Functions with A Mean Value Property, L. Flatto, J. of Math. & Mech., 10 (1961), pp. 11-18.
  4. The Random Division of an Interval and the Random Covering of a Circle, L. Flatto and A. H. Konheim, SIAM Review, 4 (1962), pp. 211-222.
  5. Functions with a Mean Value Property II, L. Flatto, Amer. J. of Math., 85 (1963), pp. 248-270.
  6. Limit Cycles for Circuits Containing One Esaki Diode, L. Flatto, J. of Math. An. and Appl., 9 (1964), pp. 360-383.
  7. Partial Differential Equations and Difference Equations, L. Flatto, Proc. of A.M.S., 16 (1965), pp. 858-863.
  8. The Converse of Gauss's Theorem for Harmonic Functions, L. Flatto, J. of Diff. Eqs., 1 (1965), pp. 483-490.
  9. On Polynomials Characterized by a Certain Mean Value Property, L. Flatto, Proc. of A.M.S., 3 (1966), pp. 598-601.
  10. The Level Curves of Harmonic Functions, L. Flatto, D. J. Newman and H. S. Shapiro, Trans. of A.M.S., 123 (1966), pp. 425-436.
  11. The Approximation of Certain Functions of Several Variables by Sums of Functions of Fewer Variables, L. Flatto, Am. Math. Monthly, 73 (1966), pp. 131-132.
  12. Infinitely Divisible Distributions on Cyclic Groups, L. Flatto and P. A. Scheinock, Am. Math. Monthly, 74 (1967), pp. 255-261.
  13. On the Group of Linear Transformations which Leave a Polynomial Invariant, L. Flatto and B. Gross, Am. Math. Monthly, 74 (1967), pp. 942-947.
  14. Basic Sets of Invariants for Finite Reflection Group, L. Flatto, Bull. A.M.S., 74 (1968), pp. 730-734.
  15. A Theorem on Level Curves of Harmonic Functions, L. Flatto, J. London Math. Soc., 1 (1969), pp. 470-472.
  16. Invariants of Finite Reflection Groups and Mean Value Problems, L. Flatto and Sister Margaret M. Wiener, Am. J. of Math., 91 (1969), pp. 591-597.
  17. Invariants of Finite Reflection Groups and Mean Value Problems II, L. Flatto, Am. J. of Math., 92 (1970), pp. 552-561.
  18. A New Proof of the Transposition Theorem, L. Flatto, Proc. of A.M.S., 24 (1970), pp. 29-31.
  19. On Groups of Motions Generated by Two Rotations, L. Flatto, Am. M. Monthly, 77 (1970), pp. 733-735.
  20. Regular Polytopes and Harmonic Polynomials, L. Flatto and Sister Margaret M. Wiener, Can. J. Math., 22 (1970), pp. 7-21.
  21. A Quadrature Formula of Degree Three, S. Haber and L. Flatto, J. of Approximation Theory, 9 (1972), pp. 44-52.
  22. A Limit Theorem for Random Coverings of a Circle, L. Flatto, Israel J. of Math., 15 (1973), pp. 167-184.
  23. A Proof of Cauchy's Integral Theorem, O. Shisha and L. Flatto, J. of Approximation Theory, 7 (1973), pp. 386-390.
  24. Recurrence Criteria for Random Walks on Countable Abelian Groups, J. Pitt and L. Flatto, Illinois J. of Math., 18 (1974), pp. 1-19.
  25. Recurrent Random Walks on Courtable Abelian Groups of Rank 2, J. Pitt and L. Flatto, Annals of Probability, 3 (1975), pp. 380-386.
  26. Functions Satisfying the Mean Value Property for Product Measures, D. Jacobson and L. Flatto, Am. J. of Math., 97 (1976), pp. 1049-1059.
  27. Advanced Calculus, L. Flatto, Williams & Wilkins Co., 1976.
  28. The Multiple Range of Two-Dimensional Recurrent Walk, L. Flatto, Annals of Probability, 4 (1976), pp. 229-248.
  29. Uniform Distribution of Kakutani's Interval Splitting Procedure, R. Adler and L. Flatto, Z. Wahrscheinlichkeitstheorie verw. Gebiete, 38 (1977), pp. 253-259.
  30. Random Coverings, D. J. Newman and L. Flatto, Acta Mathematica, 138 (1977), pp. 241-264.
  31. Two Queues in Parallel, H. P. McKean and L. Flatto, Comm. on Pure & Appl. Math., 30 (1977), pp. 255-263.
  32. Invariants of Finite Reflection Groups, L. Flatto, L'Enseignement Mathematique, 24 (1978), pp. 237-292.
  33. Cross Section Maps for Geodesic Flows, I (The Modular Surface), R. Adler and L. Flatto, Ergodic Theory and Dynamical Systems II Processings, Special Year, Maryland, 1980.
  34. Functions Satisfying a Discrete Mean Value Property, D. Jacobson and L. Flatto, Aequationes Mathematicae, 22 (1981), pp. 173-193.
  35. Limit Theorems for Some Random Variables Associated with Urn Models, L. Flatto, Annals of Probability, 10 (1982), pp. 927-934.
  36. A Geometric Problem in Approximation Theory, L. Flatto, J. of Approximation Theory, 36 (1982), pp. 321-327.
  37. Two Parallel Queues Created by Arrivals with Two Demands, L. Flatto and S. Hahn, SIAM J. on Applied Mathematics, 44 (1984), pp. 1041-1053.
  38. Cross Section Map for Geodesic Flow on the Modular Surface, R. Adler and L. Flatto, Contemporary Mathematics, 6 (1984), pp. 9-24.
  39. The Backward Continued Fraction Map and Geodesic Flow, R. Adler and L. Flatto, Ergodic Theory and Dynamical Systems, 4 (1984), pp. 487-492.
  40. Expected Makespans for Largest-First Multiprocessor Scheduling, E. G. Coffman, L. Flatto and G. S. Lueker, Performance '84, Elsevier Science Publishers, 1984, pp. 491-506.
  41. Optimum Head Separation in a Disk System with Two Read/Write Heads, A. R. Calderbank, E. G. Coffman and L. Flatto, Journal of A.C.M., 31 (1984), pp. 826-838.
  42. Sequencing Problems in Two Server Systems, L. Flatto, A. R. Calderbank, E. G. Coffman and Jr., Mathematics of Operation Research, 10 (1985), pp. 585-598.
  43. Random Shuffles and Group Representations, L. Flatto, A. M. Odlyzko and D. B. Wales, Annals of Probability, 13 (1985), pp. 154-178.
  44. Sequencing Two Servers on a Sphere, A. R. Calderbank, E. G. Coffman and L. Flatto, Stochastic Models, 1 (1985), pp. 17-28.
  45. Two Parallel Queues Created by Arrivals with Two Demands II, L. Flatto, SIAM J. on Applied Mathematics, 45 (1985), pp. 861-878.
  46. On Optimal Codes for Binary Asymmetric Channels, L. Flatto, Transactions on Information Theory, IT-32:5 (1986), pp. 695-697.
  47. Minimizing Expected Makespans on Uniform Processor Systems, E. G. Coffman, L. Flatto, M. R. Garey and R. R. Weber, Adv. Appl. Prob., 19 (1987), pp. 177-201.
  48. Optimal Directory Placement on Disk Storage Devices, A. R. Calderbank, E. G. Coffman and L. Flatto, Journal A.C.M., 35 (1988), pp. 433-446.
  49. Stochastic Models of Queue Storage, E. G. Coffman, L. Flatto, C. Knessl, I. Mitrani and L. A. Shepp, Probability in the Engineering and Information Sciences, 2 (1988), pp. 75-93.
  50. Performance Analysis of a Buffer under Locking Protocols, Flatto, L., E. G. Coffman and D. P. Gaver, Proc. 4th Int. Conf. Modelling Tech. & Tools for Comp. Perf. Evaluation, North Holland, Amsterdam, 1988.
  51. A Note Extending the Analysis of Two-Headed Systems to More General Seek-Time Characteristics, A. R. Calderbank, E. G. Coffman and L. Flatto, IEEE Trans. on Comp., 38:11 (1989), pp. 1584-1586.
  52. The Longer Queue Model, L. Flatto, Probability in the Engineering and Information Sciences, 3 (1989), pp. 537-559.
  53. First-fit Allocation of Queue, E. G. Coffman, L. Flatto and F. T. Leighton, Stochastic Processes and Their Applications, 36 (1990), pp. 311-330.
  54. Geodesic Flows, Interval Maps, and Symbolic Dynamics, R. Adler and L. Flatto, Bulletin of the A.M.S., 25:2 (1991), pp. 229-334.
  55. Height Distributions in Data Communication Buffers with Locking Protocols, E. G. Coffman, L. Flatto and D. P. Gaver, Stochastic Models, 7:2 ( 1991), pp. 243-260.
  56. Z-Numbers and $ beta $ -Transformations, L. Flatto, Contemporary Mathematics, Conference in Modern Analysis and Probability, 1992, pp. 181-201.
  57. Stochastic Machine Minimization with Constant Service Times, E. G. Coffman, L. Flatto and P. E. Wright, Math of OR, 18:2 (1993), pp. 300-316.
  58. Optimal Stochastic Allocation of Machines under Waiting Time Constraints, E. G. Coffman, L. Flatto and P. E. Wright, SIAM J. of Computing, 22(2) (1993 ), pp. 332-348.
  59. A Stochastic Checkpoint Optimization Problem, E. G. Coffman, L. Flatto and P. E. Wright, SIAM J. of Computing, 22(3) (1993), pp. 650-659.
  60. Scheduling Saves in Fault-Tolerant Computations, E.G. Coffman, L. Flatto and A. Y. Kreinin, Acta Informatica, 30 (1993), pp. 409-423.
  61. The Processor Minimization Problem with Independent Waiting-Time Constraints, E. G. Coffman, L. Flatto, B. Poonen and P. E. Wright, Theoretical Computer Science, 125 (1994), pp. 3-16.
  62. The Zeta Function of the Beta Transformation, L. Flatto, J. C. Lagarias and B. Poonen, Ergod. Th. & Dynam. Syst., 14 (1994), pp. 237-266.
  63. On the Range of Fractional Parts {$zeta ( p over q ) sup u $}, L. Flatto, J. C. Lagarias and A. D. Pollington, Acta Arithmetica, 52(2) (1995), pp. 125-147.
  64. The Lap-Counting Function for Linear Mod One Transformations, I. Explicit Formulas and Renormalizability, L. Flatto and J. C. Lagarias, Ergod. Th. & Dynam. Syst., to appear.
  65. The Lap-Counting Function for Linear Mod One Transformations, II. Markov Chain for Generalized Lap Numbers, L. Flatto and J. C. Lagarias, Ergod. Th. & Dynam. Systm., to appear .