THREE-DIMENSIONAL DYNAMIC ANALYSIS FOR THE LOWER EXTREMITY DURING FASTBALL BASEBALL PITCH

Five collegiate baseball pitchers, who have different types of delivery, were videotaped and analyzed using three-dimensional videography and ground reaction force (GRF) anaysis. Just before stride foot contact, a peak vertical GRF of 1.28 BW for pivot foot was produced, resulting from the joint torques for the knee and hip extensors. A peak forward GRF of 0.67 BW also appeared. This GRF may result in the ankle plantar flexors. Immediately after stride foot contact, the joint torques of hip’s extension, abduction and internal rotation, knee’s extension and valgus, ankle’s plantar flexion for the striding leg were generated in order to resist the resultant of vertical and backward GRFs

Borcherds symmetries in M-theory

It is well known but rather mysterious that root spaces of the $E_k$ Lie groups appear in the second integral cohomology of regular, complex, compact, del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms) of toroidal compactifications of M theory. Their Borel subgroups are actually subgroups of supergroups of finite dimension over the Grassmann algebra of differential forms on spacetime that have been shown to preserve the self-duality equation obeyed by all bosonic form-fields of the theory. We show here that the corresponding duality superalgebras are nothing but Borcherds superalgebras truncated by the above choice of Grassmann coefficients. The full Borcherds' root lattices are the second integral cohomology of the del Pezzo surfaces. Our choice of simple roots uses the anti-canonical form and its known orthogonal complement. Another result is the determination of del Pezzo surfaces associated to other string and field theory models. Dimensional reduction on $T^k$ corresponds to blow-up of $k$ points in general position with respect to each other. All theories of the Magic triangle that reduce to the $E_n$ sigma model in three dimensions correspond to singular del Pezzo surfaces with $A_{8-n}$ (normal) singularity at a point. The case of type I and heterotic theories if one drops their gauge sector corresponds to non-normal (singular along a curve) del Pezzo's. We comment on previous encounters with Borcherds algebras at the end of the paper.Comment: 30 pages. Besides expository improvements, we exclude by hand real fermionic simple roots when they would naively aris

Classification of singular Q-homology planes. I. Structure and singularities

A Q-homology plane is a normal complex algebraic surface having trivial rational homology. We obtain a structure theorem for Q-homology planes with smooth locus of non-general type. We show that if a Q-homology plane contains a non-quotient singularity then it is a quotient of an affine cone over a projective curve by an action of a finite group respecting the set of lines through the vertex. In particular, it is contractible, has negative Kodaira dimension and only one singular point. We describe minimal normal completions of such planes.Comment: improved results from Ph.D. thesis (University of Warsaw, 2009), 25 pages, to appear in Israel J. Mat

Decaying shock studies of phase transitions in MgOSiO2 systems: implications for the Super-Earths interiors

We report an experimental study of the phase diagrams of periclase (MgO), enstatite (MgSiO3) and forsterite (Mg2SiO4) at high pressures. We investigated with laser driven decaying shocks the pressure/temperature curves of MgO, MgSiO3 and Mg2SiO4 between 0.2-1.2 TPa, 0.12-0.5 TPa and 0.2-0.85 TPa respectively. A melting signature has been observed in MgO at 0.47 TPa and 9860 K, while no phase changes were observed neither in MgSiO3 nor in Mg2SiO4. An increasing of reflectivity of MgO, MgSiO3 and Mg2SiO4 liquids have been detected at 0.55 TPa -12 760 K, 0.15 TPa - 7540 K, 0.2 TPa - 5800 K, respectively. In contrast to SiO2, melting and metallization of these compounds do not coincide implying the presence of poor electrically conducting liquids close to the melting lines. This has important implications for the generation of dynamos in Super-earths mantles