What is an Exponential Function? At its core, an exponential function describes a situation where the rate of growth is proportional to its current value. Imagine a snowball rolling down a hill, ...

In this part you do not have to sketch the graph and you may even be given the sketch of the graph to start with. For a quadratic equation of the form \(y = k{(x - a)^2} + b\), the following diagram ...

The graph below has a turning point (3, -2). Write down the nature of the turning point and the equation of the axis of symmetry. For the parabola \(y=(x+6)(x-4)\) determine the coordinates and nature ...

Graphing an equation is an essential skill in mathematics, as it helps us visualize the relationships between variables. There are several techniques that can be employed to make graphing easier and ...

Advances in Applied Probability, Vol. 50, No. 1 (2018), pp. 272-301 (30 pages) We consider a family of directed exponential random graph models parametrized by edges and outward stars. Much of the ...

We propose the Base-(k+1) Graph, which is finite-time convergence for any number of nodes and maximum degree $k$, Thanks to this property, the Base-(k+1) Graph ...

We study the asymptotics for sparse exponential random graph models where the parameters may depend on the number of vertices of the graph. We obtain exact estimates for the mean and variance of the ...

Abstract: Analyzing and modeling network data have become increasingly important in a wide range of scientific fields. Among popular models, exponential random graph models (ERGM) have been developed ...

Abstract: This paper aims to solve the exponential bipartite consensus problem of linear fractional-order multi-agent system (FOMAS) with signed directed graph. Unlike most of the existing works using ...