The application of a numerical integration procedure developed by erwin fehlberg to the restricted problem of three bodies

Application of numerical integration procedures to restricted three-body proble

A VLSI pipeline design of a fast prime factor DFT on a finite field

A conventional prime factor discrete Fourier transform (DFT) algorithm is used to realize a discrete Fourier-like transform on the finite field, GF(q sub n). A pipeline structure is used to implement this prime factor DFT over GF(q sub n). This algorithm is developed to compute cyclic convolutions of complex numbers and to decode Reed-Solomon codes. Such a pipeline fast prime factor DFT algorithm over GF(q sub n) is regular, simple, expandable, and naturally suitable for VLSI implementation. An example illustrating the pipeline aspect of a 30-point transform over GF(q sub n) is presented

A parallel VLSI architecture for a digital filter of arbitrary length using Fermat number transforms

A parallel architecture for computation of the linear convolution of two sequences of arbitrary lengths using the Fermat number transform (FNT) is described. In particular a pipeline structure is designed to compute a 128-point FNT. In this FNT, only additions and bit rotations are required. A standard barrel shifter circuit is modified so that it performs the required bit rotation operation. The overlap-save method is generalized for the FNT to compute a linear convolution of arbitrary length. A parallel architecture is developed to realize this type of overlap-save method using one FNT and several inverse FNTs of 128 points. The generalized overlap save method alleviates the usual dynamic range limitation in FNTs of long transform lengths. Its architecture is regular, simple, and expandable, and therefore naturally suitable for VLSI implementation

Resonances Width in Crossed Electric and Magnetic Fields

We study the spectral properties of a charged particle confined to a two-dimensional plane and submitted to homogeneous magnetic and electric fields and an impurity potential. We use the method of complex translations to prove that the life-times of resonances induced by the presence of electric field are at least Gaussian long as the electric field tends to zero.Comment: 3 figure

Observations of Hierarchical Solar-Type Multiple Star Systems

Twenty multiple stellar systems with solar-type primaries were observed at high angular resolution using the PALM-3000 adaptive optics system at the 5 m Hale telescope. The goal was to complement the knowledge of hierarchical multiplicity in the solar neighborhood by confirming recent discoveries by the visible Robo-AO system with new near-infrared observations with PALM-3000. The physical status of most, but not all, of the new pairs is confirmed by photometry in the Ks band and new positional measurements. In addition, we resolved for the first time five close sub-systems: the known astrometric binary in HIP 17129AB, companions to the primaries of HIP 33555, and HIP 118213, and the companions to the secondaries in HIP 25300 and HIP 101430. We place the components on a color-magnitude diagram and discuss each multiple system individually.Comment: Accepted to Astronomical Journa

A Number-Theoretic Error-Correcting Code

In this paper we describe a new error-correcting code (ECC) inspired by the Naccache-Stern cryptosystem. While by far less efficient than Turbo codes, the proposed ECC happens to be more efficient than some established ECCs for certain sets of parameters. The new ECC adds an appendix to the message. The appendix is the modular product of small primes representing the message bits. The receiver recomputes the product and detects transmission errors using modular division and lattice reduction

Local energy decay of massive Dirac fields in the 5D Myers-Perry metric

We consider massive Dirac fields evolving in the exterior region of a 5-dimensional Myers-Perry black hole and study their propagation properties. Our main result states that the local energy of such fields decays in a weak sense at late times. We obtain this result in two steps: first, using the separability of the Dirac equation, we prove the absence of a pure point spectrum for the corresponding Dirac operator; second, using a new form of the equation adapted to the local rotations of the black hole, we show by a Mourre theory argument that the spectrum is absolutely continuous. This leads directly to our main result.Comment: 40 page

VLSI architectures for computing multiplications and inverses in GF(2-m)

Finite field arithmetic logic is central in the implementation of Reed-Solomon coders and in some cryptographic algorithms. There is a need for good multiplication and inversion algorithms that are easily realized on VLSI chips. Massey and Omura recently developed a new multiplication algorithm for Galois fields based on a normal basis representation. A pipeline structure is developed to realize the Massey-Omura multiplier in the finite field GF(2m). With the simple squaring property of the normal-basis representation used together with this multiplier, a pipeline architecture is also developed for computing inverse elements in GF(2m). The designs developed for the Massey-Omura multiplier and the computation of inverse elements are regular, simple, expandable and, therefore, naturally suitable for VLSI implementation

Wave operator bounds for 1-dimensional Schr\"odinger operators with singular potentials and applications

Boundedness of wave operators for Schr\"odinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.Comment: 16 pages, 0 figure

Know the Star, Know the Planet. III. Discovery of Late-Type Companions to Two Exoplanet Host Stars

We discuss two multiple star systems that host known exoplanets: HD 2638 and 30 Ari B. Adaptive optics imagery revealed an additional stellar companion to both stars. We collected multi-epoch images of the systems with Robo-AO and the PALM-3000 adaptive optics systems at Palomar Observatory and provide relative photometry and astrometry. The astrometry indicates that the companions share common proper motion with their respective primaries. Both of the new companions have projected separations less than 30 AU from the exoplanet host star. Using the projected separations to compute orbital periods of the new stellar companions, HD 2638 has a period of 130 yrs and 30 Ari B has a period of 80 years. Previous studies have shown that the true period is most likely within a factor of three of these estimated values. The additional component to the 30 Ari makes it the second confirmed quadruple system known to host an exoplanet. HD 2638 hosts a hot Jupiter and the discovery of a new companion strengthens the connection between hot Jupiters and binary stars. We place the systems on a color-magnitude diagram and derive masses for the companions which turn out to be roughly 0.5 solar mass stars.Comment: Accepted to Astronomical Journal, 16 pages, 5 Figure