For a random walk with both downward and upward jumps (increments), the joint distribution of the exit time across a given level and the undershoot or overshoot at crossing is determined through its generating function, when assuming that the distribution of the jump in the direction making the exit possible has a Laplace transform which is a rational function. The expected exit time is also de...

Keywords: Fractional calculus Anomalous diffusion Continuous time random walk Central limit theory Operator stable law a b s t r a c t In a continuous time random walk (CTRW), a random waiting time precedes each random jump. The CTRW is coupled if the waiting time and the subsequent jump are dependent random variables. The CTRW is used in physics to model diffusing particles. Its scaling limit ...

We detail the Gibbs phenomenon and its resolution for the family of orthogonal expansions consisting of eigenfunctions of univariate polyharmonic operators equipped with homogeneous Dirichlet boundary conditions. As we establish, it is possible to completely describe this phenomenon, including determining exact values for the size of the overshoot near both the domain boundary and the interior ...

It is now possible to detect small variations with time of the characteristics of the transition at the bottom of the solar convection zone, as determined from the periodic signal in the frequencies. Such measurements may allow us to establish whether and in what manner the deeper convection zone changes with the solar magnetic cycle. This is important for understanding the dynamics at the base...

The human enterprise is in overshoot, depleting essential ecosystems faster than they can regenerate and polluting the ecosphere beyond nature’s assimilative capacity. Overshoot a meta-problem that cause of most symptoms eco-crisis, including climate change, landscape degradation biodiversity loss. proximate driver overshoot excessive energy material ‘throughput’ to serve global economy. Both r...

In this paper, a new theoretical approach to submicrometer MOSFET subthreshold current modeling is presented. The diffusion and drift currents are calculated, respectively. The effect of velocity overshoot on subthreshold current is investigated. Comparison with MEDICI simulation results verifies the model.