Community articles — Math

This is an informal set of comments on the HoTT Book.

Group Isomorphisms

We describe what mimetic interpolation is and why it is critical for some pre- and post-processing tasks. A simple test case shows how using bilinear interpolation for a flux calculation introduces numerical errors that depend on the grid, the number of segments and the number of quadrature points. In contrast, mimetic interpolation will return the exact result regardless of the grid resolution and the number of segments.

Calculating the value of Ck ∈ {1, ∞} class of smoothness real-valued function's derivative in point of R+ in radius of convergence of its Taylor polynomial (or series), applying an analog of Newton's binomial theorem and q-difference operator. (P,q)-power difference introduced in section 5. Additionally, by means of Newton's interpolation formula, the discrete analog of Taylor series, interpolation using q-difference and p,q-power difference is shown.

In this paper, we derive and prove, by means of Binomial theorem and Faulhaber's formula, the following identity between $m$-order polynomials in \(T\) \(\sum_{k=1}^{\ell}\sum_{j=0}^m A_{m,j}k^j(T-k)^j=\sum_{k=0}^{m}(-1)^{m-k}U_m(\ell,k)\cdot T^k=T^{2m+1}, \ \ell=T\in\mathbb{N}.\)

The main aim of this paper to establish the relations between forward, backward and central finite (divided) differences (that is discrete analog of the derivative) and partial & ordinary high-order derivatives of the polynomials.

Cour 1 ere AS

Primality Tests and Factoring Algorithms

Two Snow Plows Problem