Consider the tangential trace of a vector polynomial on the surface of a tetrahedron. We construct an extension operator that extends such a trace function into a polynomial on the tetrahedron. This operator can be continuously extended to the trace space of H(curl ). Furthermore, it satisfies a commutativity property with an extension operator we constructed in Part I of this series. Such exte...

We generalize the imaginary-chemical-potential quantum Monte Carlo (QMC) method proposed by Dagotto [Phys. Rev. B 41, R811 (1990)] to systems without particle-hole symmetry. The generalized method is tested by comparing the results of the QMC simulations and exact diagonalization on small Hubbard molecules, such as tetrahedron and truncated tetrahedron. Results of the application of the method ...

A generalized tetrahedron group is defined to be a group admitting the following presentation: 〈x, y, z | xl = ym = zn = W p 1 (x, y) = W q 2 (y, z) = W r 3 (x, z) = 1〉, 2 ≤ l, m, n, p, q, r, where each Wi(a, b) is a cyclically reduced word involving both a and b. These groups appear in many contexts, not least as fundamental groups of certain hyperbolic orbifolds or as subgroups of generalized...

SUMMARY 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 funct...

A classical 6j-symbol is a real number which can be associated to a labelling of the six edges of a tetrahedron by irreducible representations of SU(2). This abstract association is traditionally used simply to express the symmetry of the 6j-symbol, which is a purely algebraic object; however, it has a deeper geometric significance. Ponzano and Regge, expanding on work of Wigner, gave a strikin...

We present a method for discovering dense packings of general convex hard particles and apply it to study the dense packing behavior of a one-parameter family of particles with tetrahedral symmetry representing a deformation of the ideal mathematical tetrahedron into a less ideal, physical, tetrahedron and all the way to the sphere. Thus, we also connect the two well-studied problems of sphere ...

This paper presents a concept of voltage-vector in three-dimensional space vector modulation for four-leg active filter which are developed based on Euler angle rotation method, and its produces a skewed rod shape consisting of twelve-pairs of asymmetrical tetrahedron nonzero switching vector in which voltage-vector reference is determined by four-pairs of its tetrahedron. Voltage-vector refere...

Abstract Ba 3 Yb 2 Zn 5 O 11 is exceptional among breathing pyrochlore compounds for being in the nearly-decoupled limit where inter-tetrahedron interactions are weak, hosting isolated clusters or molecular magnet-like tetrahedra of magnetic ytterbium (Yb 3+ ) ions. In this work, we present study carried out on single-crystal samples , using a variety magnetometry and neutron scattering techniq...