a = semimajor axis b = magnetic field vector e = eccentricity e = orbital element vector e · = matrix exponential f = true anomaly h = angular momentum magnitude i = inclination J = cost Jn = nth zonal harmonic coefficient M = mean anomaly m = mass m = magnetic dipole vector N − 1 = number of thrusts n = mean motion p = semilatus rectum q = electrical charge r = orbit radius magnitude r = posit...

Recall that our mechanical worm (MW) model used in the simulation portion of our study is constructed from a chain of spherical beads of radius a. Each bead, indexed by n, is centered at Yn, and has an orientation vector t̂n. The vector t̂n is also used as the unit tangent to the worm’s centerline. Each bead is also subject to several forces and torques which sum to zero at each moment in the dyn...

Schreiber and Yukich [Ann. Probab. 36 (2008) 363–396] establish an asymptotic representation for random convex polytope geometry in the unit ball Bd , d ≥ 2, in terms of the general theory of stabilizing functionals of Poisson point processes as well as in terms of generalized paraboloid growth processes. This paper further exploits this connection, introducing also a dual object termed the par...

In the design of support vector machines an important step is to select the optimal hyperparameters. One of the most used estimators of the performance is the Radius-Margin bound. Some modifications of this bound have been made to adapt it to soft margin problems, giving a convex optimization problem for the L2 soft margin formulation. However, it is still interesting to consider the L1 case du...

OJp = tether cross-sectional area = surface magnetic field intensity at equator = motional electric field projected along the tether = Lorentz force = average dimensionless current = dimensionless current at the load = tether length = electron mass, m, = 9.10938188 x lO^^' kg = perimeter of the tether cross section = electron charge, q, = 1.60217646 x lO"' ' C) = planet radius = orbit radius = ...

The nucleon’s strange-quark vector current form factors are studied from the perspective of chiral symmetry. It is argued that chiral perturbation theory cannot yield a prediction for the strangeness radius and magnetic moment. Arrival at definite predictions requires the introduction of additional, modeldependent assumptions which go beyond the framework of chiral perturbation theory. A variet...

The Ludvigsen–Vickers and two recently suggested quasi-local spin-angular momentum expressions, based on holomorphic and anti-holomorphic spinor fields, are calculated for small spheres of radius r about a point o. It is shown that, apart from the sign in the case of anti-holomorphic spinors in non-vacuum, the leading terms of all these expressions coincide. In non-vacuum spacetimes this common...

We show the universal seesaw in the extra dimension setup, where three extra vector-like fields exist in the 5D bulk with heavy masses. We take the framework of the left-right symmetric model. The universal seesaw formula is easily obtained as a replacement of the vector-like mass in 4D case Mi to 2M∗ tan[πRMi] (M∗: 5D Planck scale, Mi: vector-like bulk mass, and R: compactification radius). Th...

carbon nanotubes (cnts) are specific structures with valuable characteristics. in general, the structure of each nanotube is defined by a unique chiral vector. in this paper, different structures of short single-walled cnts are simulated and their mechanical properties are determined using finite element method. for this aim, a simple algorithm is presented which is able to model the geometry o...

Laser stripe center extraction is a key step for the profile measurement of line structured light sensors (LSLS). To accurately obtain the center coordinates at sub-pixel level, an improved gray-gravity method (IGGM) was proposed. Firstly, the center points of the stripe were computed using the gray-gravity method (GGM) for all columns of the image. By fitting these points using the moving leas...