Improved estimates for the triangle inequality

Improved estimates for the triangle inequality

We obtain refined estimates of the triangle inequality in a normed space using integrals and the Tapia semi-product. The particular case of an inner product space is discussed in more detail.

On the metric triangle inequality

A non-contradictible axiomatic theory is constructed under the local reversibility of the metric triangle inequality. The obtained notion includes the metric spaces as particular cases and the generated metric topology is T$_{1}$-separated and generally, non-Hausdorff.

Triangle inequality for resistances

Given an electrical circuit each edge e of which is an isotropic conductor with a monomial conductivity function y∗ e = y r e/μ s e. In this formula, ye is the potential difference and y∗ e current in e, while μe is the resistance of e, while r and s are two strictly positive real parameters common for all edges. In 1987, Gvishiani and Gurvich [4] proved that, for every two nodes a, b of the ci...

Improved Estimates of Kinematic Wave Parameters for Circular Channels

The momentum equation in the kinematic wave model is a power-law equation with two parameters. These parameters, which relate the discharge to the flow area, are commonly derived using Manning’s equation. In general, the values of these parameters depend on the flow depth except for some special cross sections. In this paper, improved estimates of the kinematic wave parameters for circular chan...

The Poverty-Growth-Inequality Triangle