15,494 research outputs found
The Primary Pretenders
We call a composite number q such that there exists a positive integer b with
b^p == b (mod q) a prime pretender to base b. The least prime pretender to base
b is the primary pretender q_b. It is shown that there are only 132 distinct
primary pretenders, and that q_b is a periodic function of b whose period is
the 122-digit number
19568584333460072587245340037736278982017213829337604336734362-
294738647777395483196097971852999259921329236506842360439300.Comment: 7 page
Tele-autonomous control involving contacts: The applications of a high precision laser line range sensor
The object localization algorithm based on line-segment matching is presented. The method is very simple and computationally fast. In most cases, closed-form formulas are used to derive the solution. The method is also quite flexible, because only few surfaces (one or two) need to be accessed (sensed) to gather necessary range data. For example, if the line-segments are extracted from boundaries of a planar surface, only parameters of one surface and two of its boundaries need to be extracted, as compared with traditional point-surface matching or line-surface matching algorithms which need to access at least three surfaces in order to locate a planar object. Therefore, this method is especially suitable for applications when an object is surrounded by many other work pieces and most of the object is very difficult, is not impossible, to be measured; or when not all parts of the object can be reached. The theoretical ground on how to use line range sensor to located an object was laid. Much work has to be done in order to be really useful
A NASA high-power space-based laser research and applications program
Applications of high power lasers are discussed which might fulfill the needs of NASA missions, and the technology characteristics of laser research programs are outlined. The status of the NASA programs or lasers, laser receivers, and laser propulsion is discussed, and recommendations are presented for a proposed expanded NASA program in these areas. Program elements that are critical are discussed in detail
A Thin HI Circumnuclear Disk in NGC4261
We report on high sensitivity, spectral line VLBI observations of the HI
absorption feature in the radio galaxy NGC4261. Although absorption is only
detectable on the most sensitive baseline, it can be unambiguously associated
with the counterjet and is interpreted to originate in a thin atomic
circumnuclear disk. This structure is probably a continuation of the dusty
accretion disk inferred from HST imaging, which could be feeding the massive
black hole. HI column densities in front of the counterjet of the order of
10^{21}(T_sp/100 K) cm^{-2} are derived, consistent with X-ray data and VLBI
scale free-free absorption. The data presented here are the result of the first
scientific project processed on the new EVN MkIV data processor.Comment: 4 pages, 3 postscript figures, Astronomy and Astrophysics Letters, in
pres
Quaternionic Root Systems and Subgroups of the
Cayley-Dickson doubling procedure is used to construct the root systems of
some celebrated Lie algebras in terms of the integer elements of the division
algebras of real numbers, complex numbers, quaternions and octonions. Starting
with the roots and weights of SU(2) expressed as the real numbers one can
construct the root systems of the Lie algebras of SO(4),SP(2)=
SO(5),SO(8),SO(9),F_{4} and E_{8} in terms of the discrete elements of the
division algebras. The roots themselves display the group structures besides
the octonionic roots of E_{8} which form a closed octonion algebra. The
automorphism group Aut(F_{4}) of the Dynkin diagram of F_{4} of order 2304, the
largest crystallographic group in 4-dimensional Euclidean space, is realized as
the direct product of two binary octahedral group of quaternions preserving the
quaternionic root system of F_{4}.The Weyl groups of many Lie algebras, such
as, G_{2},SO(7),SO(8),SO(9),SU(3)XSU(3) and SP(3)X SU(2) have been constructed
as the subgroups of Aut(F_{4}). We have also classified the other non-parabolic
subgroups of Aut(F_{4}) which are not Weyl groups. Two subgroups of orders192
with different conjugacy classes occur as maximal subgroups in the finite
subgroups of the Lie group of orders 12096 and 1344 and proves to be
useful in their constructions. The triality of SO(8) manifesting itself as the
cyclic symmetry of the quaternionic imaginary units e_{1},e_{2},e_{3} is used
to show that SO(7) and SO(9) can be embedded triply symmetric way in SO(8) and
F_{4} respectively
On the fundamental representation of Borcherds algebras with one imaginary simple root
Borcherds algebras represent a new class of Lie algebras which have almost
all the properties that ordinary Kac-Moody algebras have, and the only major
difference is that these generalized Kac-Moody algebras are allowed to have
imaginary simple roots. The simplest nontrivial examples one can think of are
those where one adds ``by hand'' one imaginary simple root to an ordinary
Kac-Moody algebra. We study the fundamental representation of this class of
examples and prove that an irreducible module is given by the full tensor
algebra over some integrable highest weight module of the underlying Kac-Moody
algebra. We also comment on possible realizations of these Lie algebras in
physics as symmetry algebras in quantum field theory.Comment: 8 page
Discovery of circularly polarised radio emission from SS 433
We report the discovery of circularly polarised radio emission from the
radio-jet X-ray binary SS 433 with the Australia Telescope Compact Array. The
flux density spectrum of the circular polarization, clearly detected at four
frequencies between 1 - 9 GHz, has a spectral index of (-0.9 +/- 0.1). Multiple
components in the source and a lack of very high spatial resolution do not
allow a unique determination of the origin of the circular polarization, nor of
the spectrum of fractional polarization. However, we argue that the emission is
likely to arise in the inner regions of the binary, possibly via
propagation-induced conversion of linear to circular polarization, and the
fractional circular polarization of these regions may be as high as 10%.
Observations such as these have the potential to investigate the composition,
whether pairs or baryonic, of the ejecta from X-ray binaries.Comment: Accepted for publication in ApJ Letter
Empirical logic of finite automata: microstatements versus macrostatements
We compare the two approaches to the empirical logic of automata. The first,
called partition logic (logic of microstatements), refers to experiments on
individual automata. The second one, the logic of simulation (logic of
macrostatements), deals with ensembles of automata.Comment: late
Algebraic approach to quantum field theory on non-globally-hyperbolic spacetimes
The mathematical formalism for linear quantum field theory on curved
spacetime depends in an essential way on the assumption of global
hyperbolicity. Physically, what lie at the foundation of any formalism for
quantization in curved spacetime are the canonical commutation relations,
imposed on the field operators evaluated at a global Cauchy surface. In the
algebraic formulation of linear quantum field theory, the canonical commutation
relations are restated in terms of a well-defined symplectic structure on the
space of smooth solutions, and the local field algebra is constructed as the
Weyl algebra associated to this symplectic vector space. When spacetime is not
globally hyperbolic, e.g. when it contains naked singularities or closed
timelike curves, a global Cauchy surface does not exist, and there is no
obvious way to formulate the canonical commutation relations, hence no obvious
way to construct the field algebra. In a paper submitted elsewhere, we report
on a generalization of the algebraic framework for quantum field theory to
arbitrary topological spaces which do not necessarily have a spacetime metric
defined on them at the outset. Taking this generalization as a starting point,
in this paper we give a prescription for constructing the field algebra of a
(massless or massive) Klein-Gordon field on an arbitrary background spacetime.
When spacetime is globally hyperbolic, the theory defined by our construction
coincides with the ordinary Klein-Gordon field theory on aComment: 21 pages, UCSBTH-92-4
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