Attitude determination and sensor alignment via weighted least squares affine transformations

Attitude determination and sensor alignment via weighted least squares affine transformation

A vector approach to the algebra of rotations with applications

Vector analysis approach to algebra of rotations with applications to least-squares rotation and rigid body motio

Algorithm for in-flight gyroscope calibration

An optimal algorithm for the in-flight calibration of spacecraft gyroscope systems is presented. Special consideration is given to the selection of the loss function weight matrix in situations in which the spacecraft attitude sensors provide significantly more accurate information in pitch and yaw than in roll, such as will be the case in the Hubble Space Telescope mission. The results of numerical tests that verify the accuracy of the algorithm are discussed

In-flight determination of spacecraft magnetic bias independent of attitude

A simple algorithm for the in-flight determination of the magnetic bias of a spacecraft is presented. The algorithm, developed for use during the Hubble Space Telescope mission, determines this bias independently of any attitude estimates and requires no spacecraft sensor data other than that from the spacecraft magnetometer(s). Estimates of the algorithm's accuracy and results from a number of numerical studies on the use of this algorithm are also presented

Open circular billiards and the Riemann hypothesis

A comparison of escape rates from one and from two holes in an experimental container (e.g. a laser trap) can be used to obtain information about the dynamics inside the container. If this dynamics is simple enough one can hope to obtain exact formulas. Here we obtain exact formulas for escape from a circular billiard with one and with two holes. The corresponding quantities are expressed as sums over zeroes of the Riemann zeta function. Thus we demonstrate a direct connection between recent experiments and a major unsolved problem in mathematics, the Riemann hypothesis.Comment: 5 pages, 4 embedded postscript figures; v2: more explicit on how the Reimann Hypothesis arises from a comparison of one and two hole escape rate

The Proposed Biological Station at the Tortugas

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The least common multiple of a sequence of products of linear polynomials

Let $f(x)$ be the product of several linear polynomials with integer coefficients. In this paper, we obtain the estimate: $\log {\rm lcm}(f(1), ..., f(n))\sim An$ as $n\rightarrow\infty$, where $A$ is a constant depending on $f$.Comment: To appear in Acta Mathematica Hungaric

Mesoscopic motion of atomic ions in magnetic fields

We introduce a semiclassical model for moving highly excited atomic ions in a magnetic field which allows us to describe the mixing of the Landau orbitals of the center of mass in terms of the electronic excitation and magnetic field. The extent of quantum energy flow in the ion is investigated and a crossover from localization to delocalization with increasing center of mass energy is detected. It turns out that our model of the moving ion in a magnetic field is closely connected to models for transport in disordered finite-size wires.Comment: 4 pages, 2 figures, subm. to Phys.Rev.A, Rap.Co

Rings of real functions in pointfree topology

AbstractThis paper deals with the algebra F(L) of real functions on a frame L and its subclasses LSC(L) and USC(L) of, respectively, lower and upper semicontinuous real functions. It is well known that F(L) is a lattice-ordered ring; this paper presents explicit formulas for its algebraic operations which allow to conclude about their behaviour in LSC(L) and USC(L).As applications, idempotent functions are characterized and previous pointfree results about strict insertion of functions are significantly improved: general pointfree formulations that correspond exactly to the classical strict insertion results of Dowker and Michael regarding, respectively, normal countably paracompact spaces and perfectly normal spaces are derived.The paper ends with a brief discussion concerning the frames in which every arbitrary real function on the α-dissolution of the frame is continuous