Nonassociative structures and 3-Sasakian homogeneous manifolds

The 3-Sasakian homogeneous spaces are certain contact manifolds whose geometric structure is very well codified in Lie theoretical terms. This fact can be used to find interesting invariant affine connections, with nice properties or special holonomies. The more fruitful results arise in the particular case of the 7-dimensional 3-Sasakian homogeneous manifolds, that is, the corresponding sphere and the Aloff-Wallach space, although the target is to find a good connection independently of the dimension. A nonassociative structure related to Lie algebras appears through this study, that one of symplectic triple system. In particular the curvature of an affine connection can be written by means of the binary and ternary products in this triple system. Also, for some distinguished connections, the holonomy algebra can be described in a unified form, what helps to find a suitable candidate for a best affine connection adapted to the geometry of the 3-Sasakian manifold, which necessarily will have nonzero torsion.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tec

Strengthening Your Hip Muscles: Some Exercises May Be Better Than Others

Weak hip muscles lead to poor hip motion, and poor hip motion can cause knee, hip, and back pain. Strengthening hip muscles that control how hips move may reduce pain in these parts of the body. This undergraduate research project compared hip abductor muscle activity during selected exercises using electromyography in order to determine which exercises are best for activating the gluteus medius and the superior portion of the gluteus maximus, while minimizing activity of the tensor fascia lata. Participants in this study included nine healthy female soccer players between the ages of 18 and 21. Using an electromyogram (EMG), the muscle activity of the nine subjects was recorded during the following 11 exercises: hip abduction in sidelying, clam with elastic resistance around thighs, bilateral bridge, unilateral bridge, hip extension in quadruped on elbows with knee extending, hip extension in quadruped on elbows with knee flexed, forward lunge with erect trunk, squat, sidestep with elastic resistance in a squatted position, hip hike, and forward step-up. At this time, data collection and analysis continues; however, it is hypothesized that both gluteal muscles were significantly more active than the TFL in unilateral and bilateral bridging, quadruped hip extension, the clam, sidestepping, and squatting

Lattice HQET Calculation of the Isgur-Wise Function

We calculate the Isgur-Wise function on the lattice, simulating the light quark with the Wilson action and the heavy quark with a direct lattice implementation of the heavy-quark effective theory. Improved smearing functions produced by a variational technique, MOST, are used to reduce the statistical errors and to minimize excited-state contamination of the ground-state signal. Calculating the required matching factors, we obtain $\xi'(1)=-0.64(13)$ for the slope of the Isgur-Wise function in continuum-HQET in the \barMS scheme at a scale of $4.0$GeV.Comment: 3 Pages, LaTeX, Poster at Lattice '9

BB Meson Matrix Elements from Various Heavy Quark Effective Theories

Various properties of heavy-light mesons are determined, including decay constants, the $B_{B}$-parameter, and the Isgur-Wise function. The heavy (bottom) quark is simulated with the static, NRQCD and/or (fixed-velocity) lattice-HQET effective theories, using optimally-smeared sources as produced by the ``Maximal Operator Smearing Technique''.Comment: To appear in the proceedings of the Lattice '95 conference. 4 pages, uuencoded-compressed PostScript fil