Partial differential equations (PDEs) are a general starting point for mathematical modeling and computer-based analysis throughout all of science, engineering and applied mathematics. Computer-based methods for the numerical and analytical solution of PDEs are therefore of broad interest. In this chapter, we discuss some of the general approaches to the traveling wave solution of PDEs, includi...

The numerical approximation of the generalized Lienard equation is considered using delay as parameter. First, the delay difference equation obtained by using Euler method is written as a map.According to the theories of bifurcation for discrete dynamical systems,the conditions to guarantee the existence of Hopf bifurcation for numerical approximation are given. The relations of Hopf bifurcatio...

In the main text, we noted that the shape parameters (characteristic length, Λ, and loop radius, Ro) of the patterns only depend weakly on the deployment height. To resolve this height dependence of the pattern length scales, we have performed a series of numerical simulations where we have varied the normalized deployment height, H̄, while keeping the gravito-bending length fixed at Lgb = 3.3 c...

Cardiac fibroblasts, when coupled functionally with myocytes, can modulate the electrophysiological properties of cardiac tissue. We present systematic numerical studies of such modulation of electrophysiological properties in mathematical models for (a) single myocyte-fibroblast (MF) units and (b) two-dimensional (2D) arrays of such units; our models build on earlier ones and allow for zero-, ...

Fourteen linguistically-motivated numerical indicators are evaluated for their ability to categorize verbs as either states or events. The values for each indicator are computed automatically across a corpus of text. To improve classification performance, machine learning techniques are employed to combine multiple indicators. Three machine learning methods are compared for this task: decision ...

We introduce an answer typing strategy specific to quantifiable how questions. Using the web as a data source, we automatically collect answer units appropriate to a given how-question type. Experimental results show answer typing with these units outperforms traditional fixedcategory answer typing and other strategies based on the occurrences of numerical entities in text.

This paper mainly tends to utilize [Formula: see text]-type function to investigate p-th moment and almost sure stability for a class of stochastic switched nonlinear systems. Based on the multiple Lyapunov functions approach, some sufficient conditions are derived to check the stability criteria of stochastic switched nonlinear systems. One numerical example is provided to demonstrate the effe...