A topic of recent interest in the retail financial sector has been the growth of credit unions or “pure cooperatives”. Past credit union researchers built mathematical models of credit union operations. These models identified important operating characteristics but were modeled under assumptions of static operating environments. The model presented in this paper departs from the traditional st...

The existence of a weak solution to a McKean-Vlasov type stochastic differential system corresponding to the Enskog equation of the kinetic theory of gases is established under suitable hypotheses. The distribution of any solution to the system at each fixed time is shown to be unique. The existence of a probability density for the time-marginals of the velocity is verified in the case where th...

Since many rotor systems normally operate above their critical speeds, the problem of accelerating the machine through its critical speeds without excessive vibration draws increasing attention. This paper provides an analytical imbalance response of the Jeffcott rotor under constant acceleration. The response consists of three parts: transient vibration due to the initial condition of the roto...

The long-time behavior of the solution of the system θτ−απτ = Ω(θ), πτ−θτ = πξξ is investigated. Such a system is related to the modeling of detonation waves subjected to strong hydraulic resistance. We establish that some initial conditions yield decay (failure of ignition) while for other initial conditions our results strongly suggest convergence to traveling waves (successful ignition).

Sufficient conditions are given so that the initial value problem for the Shabat equation has a unique analytic solution, which, together with its first derivative, converges absolutely for z ∈ C : |z| < T , T > 0. Moreover, a bound of this solution is given. The sufficient conditions involve only the initial condition, the parameters of the equation, and T . Furthermore, from these conditions,...

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 study the large time behavior of the solutions of the Cauchy problem for the Anderson model restricted to the upper half space D = Zd−1 × Z+ and/or D = Rd−1 × R+ when the potential is a homogeneous random field concentrated on the boundary ∂D. In other words we consider the problem: ∂u(t, z) ∂t = κ∆u(t, z) + ξ(x)u(t, z) z = (x, y), with y ≥ 0 and t ≥ 0 with an appropriate initial condition. ...