Strings and D-Branes with Boundaries

The covariant field equations of ten-dimensional super D-branes are obtained by considering fundamental strings whose ends lie in the superworldsurface of the D-brane. By considering in a similar fashion Dp-branes ending on D(p+2)-branes we derive equations describing D-branes with dual potentials, as well as the vector potentials.Comment: 12 pages, Late

3-Point Functions in N=4 Yang-Mills

Three-point functions of analytic (chiral primary) operators in N=4 Yang-Mills theory in four dimensions are calculated using the harmonic superspace formulation of this theory. In the case of the energy-momentum tensor multiplet anomaly considerations determine the coefficient. Analyticity in N=2 harmonic superspace is explicitly checked in a two-loop calculation.Comment: This file requires the feynman.tex macro Some references are adde

The Six Dimensional Self-Dual Tensor

The equations of motion for a self-interacting self-dual tensor in six dimensions are extracted from the equations describing the M-theory five-brane. These equations are presented in a self-contained, six-dimensional Lorentz-covariant form. In particular, it is shown that the field-strength tensor satisfies a non-linear generalised self-duality constraint. The self-duality equation is rewritten in five-dimensional notation and shown to be identical to the corresponding equation in the non-covariant formalism.Comment: 8 pages, late

New methods for bounding the number of points on curves over finite fields

We provide new upper bounds on N_q(g), the maximum number of rational points on a smooth absolutely irreducible genus-g curve over F_q, for many values of q and g. Among other results, we find that N_4(7) = 21 and N_8(5) = 29, and we show that a genus-12 curve over F_2 having 15 rational points must have characteristic polynomial of Frobenius equal to one of three explicitly given possibilities. We also provide sharp upper bounds for the lengths of the shortest vectors in Hermitian lattices of small rank and determinant over the maximal orders of small imaginary quadratic fields of class number 1. Some of our intermediate results can be interpreted in terms of Mordell-Weil lattices of constant elliptic curves over one-dimensional function fields over finite fields. Using the Birch and Swinnerton-Dyer conjecture for such elliptic curves, we deduce lower bounds on the orders of certain Shafarevich-Tate groups.Comment: LaTeX, 35 page

On Brane Actions and Superembeddings

Actions for branes, with or without worldsurface gauge fields, are discussed in a unified framework. A simple algorithm is given for constructing the component Green-Schwarz actions. Superspace actions are also discussed. Three examples are given to illustrate the general procedure: the membrane in D=11 and the D2-brane, which both have on-shell worldsurface supermultiplets, and the membrane in D=4, which has an off-shell multiplet.Comment: 19 pages, late

Open Superbranes

Open branes ending on other branes, which may be referred to as the host branes, are studied in the superembedding formalism. The open brane, host brane and the target space in which they are both embedded are all taken to be supermanifolds. It is shown that the superspace constraints satisfied by the open brane are sufficient to determine the corresponding superspace constraints for the host branes, whose dynamics are determined by these constraints. As a byproduct, one also obtains information about the boundary of the open brane propagating in the host brane.Comment: 12 pages, late

Voluntary activation of quadriceps femoris in patients with unilateral anterior cruciate ligament rupture within 6 months of injury: a cross-sectional observational study

Background: Deficits in quadriceps femoris strength and voluntary activation have been well documented in chronic anterior cruciate ligament (ACL) injuries, but less is known about the acute or early phase after injury. Objectives: The aim of this study was to evaluate and compare the levels of quadriceps voluntary activation (VA) and strength in both limbs of participants with unilateral ACL ruptures (complete tears) within 6 months of injury. Design: Cross-sectional observational study. Method: Seventeen participants, 12 male, mean age 30 (17-45) years, performed maximal voluntary isometric contractions with the interpolated twitch technique. Results: Mean (SD) peak VA was significantly lower in the injured limb 76.5 (15.0) % than the uninjured limb 85.9 (6.7) % (p = 0.02). Mean (SD) peak torque in the injured limb was significantly lower 162.7 (74.1) Nm than the uninjured limb 240.5 (81.0) Nm (p &lt; 0.01). Conclusions: This between-limb difference in VA has not previously been observed in patients within 6 months of ACL rupture. Our findings suggest that early rehabilitation programs for adults with ACL rupture should focus on reducing VA deficits to facilitate improvement of the quadriceps femoris muscle strength in the injured limb to comparable values of the uninjured limb.</p

Computer considerations for real time simulation of a generalized rotor model

Scaled equations were developed to meet requirements for real time computer simulation of the rotor system research aircraft. These equations form the basis for consideration of both digital and hybrid mechanization for real time simulation. For all digital simulation estimates of the required speed in terms of equivalent operations per second are developed based on the complexity of the equations and the required intergration frame rates. For both conventional hybrid simulation and hybrid simulation using time-shared analog elements the amount of required equipment is estimated along with a consideration of the dynamic errors. Conventional hybrid mechanization using analog simulation of those rotor equations which involve rotor-spin frequencies (this consititutes the bulk of the equations) requires too much analog equipment. Hybrid simulation using time-sharing techniques for the analog elements appears possible with a reasonable amount of analog equipment. All-digital simulation with affordable general-purpose computers is not possible because of speed limitations, but specially configured digital computers do have the required speed and consitute the recommended approach

D=11, p=5

The equations of motion of the super five-brane in D=11 dimensions are derived using the formalism of superembeddings. The equations describe highly nonlinear self-interactions of a tensor multiplet in the six dimensional worlsurface, and they have manifest worldsurface local supersymmetry. The geometry of the target space corresponds to D=11 supergravity.Comment: 7 pages, late