We present a new shape measure for tetrahedral elements that is optimal in that it gives the distance of a tetrahedron from the set of inverted elements. This measure is constructed from the condition number of the linear transformation between a unit equilateral tetrahedron and any tetrahedron with positive volume. Using this shape measure, we formulate two optimization objective functions tha...

On a regular tetrahedron in spherical space there exist the finite number of simple closed geodesics. For any pair coprime integers $(p,q)$ it was found numbers $\alpha_1$ and $\alpha_2$ depending on $p$, $q$ satisfying inequalities $\pi/3< \alpha_1 < \alpha_2 2\pi/3$ such that with faces angle $\alpha \in \left( \pi/3, \right)$ exists unique, up to rigid motion tetrahedron, geodesic type $(p,q...

The microstructure constitutes one of the pillars materials tetrahedron [...]

We present a succinct way of obtaining all possible higher dimensional generalization of Quantum Yang-Baxter Equation (QYBE). Using the scheme, we could generate the two popular three-simplex equations, namely: Zamolodchikov’s tetrahedron equation (ZTE) and Frenkel and Moore equation (FME). E-mail address: [email protected] E-mail address: [email protected] The Quantum Yang-Baxter Equation (Q...