We consider the continuity equation for open chaotic quantum systems in the semiclassical limit. First we explicitly calculate a semiclassical expansion for the probability current density using an expression based on classical trajectories. The current density is related to the survival probability via the continuity equation, and we show that this relation is satisfied within the semiclassica...

We present a practical framework to prove, in simple way, two-term asymptotic expansions for Fourier integrals $$\begin{aligned} {{\mathcal {I}}}(t) = \int _{{\mathbb {R}}}(\mathrm{e}^{it\phi (x)}-1) \mathop {}\!\mathrm {d}\mu (x), \end{aligned}$$ where $$\mu $$ is probability measure on $${{\mathbb {R}}}$$ and $$\phi measurable. This applies many basic cases, link with Levy’s continuity theore...

CDMA cellular networks support soft handover, which guarantees the continuity of wireless services and enhanced communication quality. Cellular networks support multimedia services under varied propagation environmental conditions. In this paper, we have shown the effect of characteristic parameters of the cellular environments on the soft handover performance. We consider path loss exponent, s...

This paper is on developing stochastic analysis simultaneously under a general family of probability measures that are not dominated by a single probability measure. The interest in this question originates from the probabilistic representations of fully nonlinear partial differential equations and applications to mathematical finance. The existing literature relies either on the capacity theor...

We consider structural topology optimization problems including unilateral constraints arising from, for example, non-penetration conditions in contact mechanics or noncompression conditions for elastic ropes. To construct more realistic models and to hedge off possible failures or inefficient behaviour of optimal structures, we allow parameters (for example, loads) defining the problem to be s...

This paper is concerned with the existence of mild solutions and exact controllability for a class fractional measure evolution systems state-dependent delay nonlocal conditions. We first establish an result problem by applying integral equation which given in terms probability density semigroup theory. Then, are obtained using calculus theory, Kuratowski noncompactness Mönch fixed point theore...