We show that the jump set of the solution of the minimizing Total Variation ow decreases with time for any initial condition in BV (Ω)∩L (Ω). We prove that the size of the jump also decreases with time.

The Heider theory of cognitive dissonance in social groups, formulated recently in terms of differential equations, is generalized here for the case of asymmetric interpersonal ties. The space of initial states is penetrated by starting the time evolution several times with random initial conditions. Numerical results show the fat-tailed distribution of the time when the dissonance is removed. ...

In this article we focus our attention on the relation between consistent and non-consistent initial conditions of a class of singular linear discrete time systems. First we analyze how both types of initial conditions are connected to the column vector space of the finite and the infinite eigenvalues of the related to the singular system matrix pencil and after we prove that a non-consistent i...

Reaching a target while remaining in a given set for impulse dynamics can be characterized by a non deterministic controlled differential equation and a controlled instantaneous reset equation. The set of initial conditions from which a given objective can be reached is calculated using the Hybrid Guaranteed Capture Basin Algorithm. This algorithm was developed in finance to evaluate options in...

We present a model of slow-roll inflation in the context of effective Supergravities arising from string theories. The uplifting of the potential (to generate dS or Minkowski vacua) is provided by the D-term associated to an anomalous U(1), in a fully consistent and gauge invariant formulation. We develop a minimal working model which incorporates eternal topological inflation and complies with...

We point out that for a class of ‘new inflation’ models in supergravity the required initial value of the inflaton field is dynamically set if there is another inflation (‘pre-inflation’) before the ‘new inflation’. We study the dynamics of both inflatons by taking a hybrid inflation model for the ‘pre-inflation’ as an example. We find out that our ‘new inflation’ model provides reheating tempe...

In this paper, the control problem of the forced Burgers equation: ∂u ∂t = ν ∂2u ∂x2 − u ∂u ∂x +mu+ f(x), 0 < x < 2π, t > 0 subject to Neumann boundary conditions: ∂u ∂x (0, t) = ũ1(t), ∂u ∂x (2π, t) = ũ2(t) t > 0. and the initial condition: u(x, 0) = u0(x), x ∈ (0, 2π) t > 0, where ν is a positive constant, the parameter m ∈ IR, and ũ1(t), ũ2(t) are two control inputs is considered. We show th...

This problem models heat propagation in a rod where the left end is kept at constant temperature T1, the right end is kept at temperature T2, the initial temperature is f(x) and at each point x, there is heat radiating at the rate F (x, t) at time t. Note that the PDE, the boundary conditions, and the initial condition, are nonhomogeneous. We can use the principle of superposition to decompose ...

If our universe underwent inflation, its entropy during the inflationary phase was substantially lower than it is today. Because a low-entropy state is less likely to be chosen randomly than a high-entropy one, inflation is unlikely to arise through randomlychosen initial conditions. To resolve this puzzle, we examine the notion of a natural state for the universe, and argue that it is a nearly...

For an endofunctor H on a hyper-extensive category preserving countable coproducts we describe the free corecursive algebra on Y as the coproduct of the final coalgebra for H and the free Halgebra on Y . As a consequence, we derive that H is a cia functor, i.e., its corecursive algebras are precisely the cias (completely iterative algebras). Also all functors H(−) + Y are then cia functors. For...