Sentence examples for to four dimensional from inspiring English sources

If (mathcal{R}_{0}>1), then the endemic equilibrium is globally asymptotically stable with the help of the Li and Muldowney geometric approach applied to four dimensional systems.

The main purpose of this paper is to derive the expression for the basic reproduction number and further show the global stability of disease-free as well as endemic equilibria by the aid of Lyapunov function and Li Muldowney geometric approach applied to four dimensional systems.

Self-organizing maps are another way to reduce dimensionality by mapping multidimensional data to two dimensional space.

It's about moving from two dimensions to three dimensional".

(b) Fit to three dimensional displacement data.

Analytical assessments are performed in according to three dimensional finite element modeling.

Finite size and interface effects may cause fundamentally different behavior compared to three dimensional macroscopic systems.

Our method also applies to two dimensional problems on Cartesian meshes.

Then, it is extended to three dimensional model by adding commodity type and then, different types of transportation modes are added to make it four dimensional model.

Performing this for each detected photon in a standard CSI scan would lead to three dimensional image formation.

Cu deposition at stepped, Pt(111) vicinal surfaces gives rise to three dimensional clusters.