[1] In this study we develop a stochastic model for transient unsaturated-saturated flow in randomly heterogeneous media with the method of moment equations. We first derive partial differential equations governing the statistical moments of the flow quantities by perturbation expansions and then implement these equations under general conditions with the method of finite differences. The stoch...

Abstract. Mean field type models describing the limiting behavior of stochastic differential games as the number of players tends to +∞, have been recently introduced by J-M. Lasry and P-L. Lions. Under suitable assumptions, they lead to a system of two coupled partial differential equations, a forward Bellman equation and a backward Fokker-Planck equations. Finite difference schemes for the ap...

The aim of this paper is to prove that given a linear recurrence sequence U = kb u„ +z = u„ + , + u„, n w 1, u t =1, uz > u l , then the set of positive integers can be partitioned uniquely into two disjoint subsets such that the sum of any two distinct members from any one set can never be in U and study related problems . We prove our main result in Section 2. In Section 3 we give a graph the...

The second author introduced with I. Törmä a two-player word-building game [Playing with Subshifts, Fund. Inform. 132 (2014), 131–152]. The game has a predetermined (possibly finite) choice sequence α1, α2, . . . of integers such that on round n the player A chooses a subset Sn of size αn of some fixed finite alphabet and the player B picks a letter from the set Sn. The outcome is determined by...

We propose a rigorous comparison of two widely known dynamic information flow mechanisms: Secure Multi-Execution (SME) and Multiple Facets (MF). Informally, it is believed that MF simulates SME while providing better performance. Formally, it is well known that SME has stronger soundness guarantees than MF. Surprisingly, we discover that even if we approach them to enforce the same soundness gu...

This paper introduces a simple theoretical model for the response time of thermal flow sensors. Response time is defined here as the time needed by the sensor output signal to reach 63.2% of amplitude due to a change of fluid flow. This model uses the finite-difference method to solve the heat transfer equations, taking into consideration the transient conduction and convection between the sens...

Part 4. K-theory and geometry II 139 20. K∗(CP) and the K-theoretic analog of the degree 139 21. Interlude on the calculus of finite differences 147 22. The Euler class 153 23. Chern classes 165 24. Comparing K-theory and singular cohomology 169 25. The Grothendieck-Riemann-Roch Theorem 176 26. The algebro-geometric GRR theorem 187 27. Formal group laws and complex-oriented cohomology theories 191

The method of multiscale analysis is constructed for dicrete systems of evolution equations for which the problem is that of the far behavior of an input boundary datum. Discrete slow space variables are introduced in a general setting and the related finite differences are constructed. The method is applied to a series of representative examples: the Toda lattice, the nonlinear Klein-Gordon ch...