Seminars, 2018

  • April 17, 2018
    How we can partition the integers into arithmetic progressions and related questions
    Dr. Ofir Schnabel, Haifa University

    The evens and odds form a partition of the integers into arithmetic progressions. It is natural to try to describe in general how the integers can be partitioned into arithmetic progressions. For example, a classic result from the 1950's shows that if a set of arithmetic progressions partitions the integers, there must be two arithmetic progressions with the same difference. Another direction is to try to determine when such a partition is a proper refinements of another non-trivial partition.
    In my talk I will give some of the more interesting results on this subject, report some (relatively) new results and present two generalizations of partitioning the integers by arithmetic progressions, namely:
    1. Partitions of the integers by Beatty sequences (will be defined).
    2. Coset partition of a group.
    The main conjecture in the first topic is due to A. Fraenkel and describes all the partitions having distinct moduli.
    The main conjecture in the second topic, due to M. Herzog and J. Schonheim, claims that in every coset partition of a group there must be two cosets of the same index.
    Again, we will briefly discuss the history of these conjectures, recall some of the main results and report some new results.
  • March 27, 2018
    A probabilistic model of thermal explosion in polydisperese fuel spray
    Dr. Ophir Nave and Dr. Vladimir Gol’dshtein, Ben-Gurion University

    Our research concerned with an analysis of polydisperse spray droplets distribution on the thermal explosion processes. In many engineering applications it is usual to relate to the practical polydisperse spray as a monodisperse spray. The Sauter Mean Diameter (SMD) and its variations are frequently used for this purpose Lefebvere (1989). The SMD and its modifications depend only on``integral'' characterization of polydisperse sprays and can be the same for very different types of polydisperse spray distributions.
    We presents a new, simplified model of the thermal explosion in a combustible gaseous mixture containing vaporizing fuel droplets of different radii (polydisperse). The polydispersity is modeled using a Probability Density Function (PDF) that corresponds to the initial distribution of fuel droplets size. This approximation of polydisperse spray is more accurate than the traditional 'parcel' approximation and permits an analytical treatment of the simplified model. Since the system of the governing equations represents a multi-scale problem, the method of invariant (integral) manifolds is applied.
    An explicit expression of the critical condition for thermal explosion limit is derived analytically. Numerical simulations demonstrate an essential dependence of these thermal explosion conditions on the PDF type and represent a natural generalization of the thermal explosion conditions of the classical Semenov theory.
  • March 20, 2018
    On the Eisenbud-Green-Harris Conjecture
    Dr. Abed Abedelfatah, Haifa University