AN EVALUATION OF PERFORMANCE OF A DOUBLE-LEG CIRCLE ON A POMMEL HORSE, AND A DESIRABLE PERFOMANCE PROPOSAL

For the evaluation of the performance of a double-leg circle on a pommel horse, we focused on the relation between the horizontal rotation of a body about the vertical axis in the center of a pommel horse and the hip rotation about the longitudinal axis of a body. Several gymnasts having different levels of skill were examined by using a motion capture system. The analysis shows that the horizontal rotation and the hip rotation are in good synchronization for the performance of a well-trained gymnast

Orbital Arrangements and Magnetic Interactions in the Quasi-One-Dimensional Cuprates <i>A</i>CuMoO₄(OH) (<i>A</i> = Na, K)

A new spin-1/2 quasi-one-dimensional antiferromagnet KCuMoO₄(OH) is prepared by the hydrothermal method. The crystal structures of KCuMoO₄(OH) and the already-known Na-analogue NaCuMoO₄(OH) are isotypic, comprising chains of Cu²⁺ ions in edge-sharing CuO₄(OH)₂ octahedra. Despite the structural similarity, their magnetic properties are quite different because of the different arrangements of d_<i>x</i>²_{–<i>y</i>²} orbitals carrying spins. For NaCuMoO₄(OH), d_<i>x</i>²_{–<i>y</i>²} orbitals are linked by superexchange couplings via two bridging oxide ions, which gives a ferromagnetic nearest-neighbor interaction <i>J</i>₁ of −51 K and an antiferromagnetic next-nearest-neighbor interaction <i>J</i>₂ of 36 K in the chain. In contrast, a staggered d_<i>x</i>²_{–<i>y</i>²} orbital arrangement in KCuMoO₄(OH) results in superexchange couplings via only one bridging oxide ion, which makes <i>J</i>₁ antiferromagnetic as large as 238 K and <i>J</i>₂ negligible. This comparison between the two isotypic compounds demonstrates an important role of orbital arrangements in determining the magnetic properties of cuprates