We present a new type of strange attractors generated by an odd-symmetric three-dimensional vector field with a saddle-focus having two homoclinic orbits at the origin. This type of attractors is intimately related to the double scroll. We present the mathematical properties which prove rigorously the chaotic nature of this strange attractor to be different from that of a Lorenz-type attractor or a quasiattractor. In particular, we proved that for certain nonempty intervals of parameters, our two-dimensional map has a strange attractor with no stable orbits. Unlike other known attractors, this strange attractor contains not only a Cantor set structure of hyperbolic points typical of horseshoe maps, but also unstable points (i.e., stable in reverse time). This implies that the points from the stable manifolds of the hyperbolic points must necessarily attract the unstable points.
We present results of optical follow-up observations of ultraluminous X-ray source (ULX) candidates. A published ROSAT catalog of 87 ULX candidates named 19 of these as having optical counterparts in Digitized Sky Survey (DSS) images. Using Keck optical spectroscopy, we classify 16 ULX candidates in this subset as well as one other ULX candidate from the catalog with a counterpart in the DSS. This is one of the largest sets of optical identifications of such objects thus far. Fifteen are background active galactic nuclei (AGNs); two are foreground stars in our Galaxy. These findings are consistent with background and foreground object expectations, as derived from log N - log S relations. The logarithmic X-ray to optical flux ratios of these objects are also typical of background and foreground objects. Finally, we discuss the nature of ULX candidates outside the optical extent of their apparent host galaxies.
In 1974, Hawking showed 1 that Black Holes can evaporate by the emission of low temperature thermal radiation, now named Hawking Radiation. Shortly thereafter, a closely related effect called Unruh Radiation became apparent. According to Unruh 2 and Davies 2 , observers of the electromagnetic field in an accelerating reference frame should see thermal radiation at a temperature T: where a is the acceleration relative to an inertial frame, c is the speed of light and ħ and K are Planck's and Boltzmann's constant respectively. In a frame accelerating at g= 980 cm/sec 2 , equivalent to the acceleration experienced at the earth's surface 3 , this thermal radiation is at a temperature of only 4× 10 −20 °K. Therefore, physicists hoping to observe this radiation, have sought out systems being subjected to extreme acceleration. For example, J. S. Bell has suggested 4 that the spin depolarization of electrons accelerating around a synchrotron storage ring may be interpreted as being due to such radiation.
Systematic methods for synthesising nonlinear networks having a prescribed scalar or multidimensional piecewise-linear function are described. In the scalar case, precision active-circuit building blocks using operational amplifiers, transistors, diodes, and resistors are given for realising piecewise-linear drivingpoint and transfer characteristic plots. In the multidimensional case, methods are given for realising a multiterminal nonlinear network having a multidimensional piecewise-linear transfer function. Finally, these methods are generalised for synthesising nonlinear n-ports having a prescribed multidimensional piecewiselinear driving-point function. Although most of the basic building blocks are grounded active networks, convertor networks are developed for transforming such grounded networks into floating networks having the same properties. By slight modifications of these convertor networks, other useful conversion properties are also presented
This paper provides a rigorous mathematical proof that the double scroll is indeed chaotic. Our approach is to derive a linearly equivalent class of piecewise-linear differential equations which includes the double scroll as a special case. A necessary and sufficient condition for two such piecewise-linear vector fields to be linearly equivalent is that their respective eigenvalues be a scaled version of each other. In the special case where they are identical, we have exact equivalence in the sense of linear conjugacy. An explicit normalform equation in the context of global bifurcation is derived and parametrized by their eigenvalues. Analytical expressions for various Poincaré maps are then derived and used to characterize the birth and the death of the double scroll, as well as to derive an approximate one-dimensional map in analytic form which is useful for further bifurcation analysis. In particular, the analytical expressions characterizing various half-return maps associated with the Poincaré map are used in a crucial way to prove the existence of a Shilnikov-type homoclinic orbit, thereby establishing rigorously the chaotic nature of the double scroll. These analytical expressions are also fundamental in our in-depth analysis of the birth (onset of the double scroll) and death (extinction of chaos) of the double scroll. The unifying theme throughout this paper is to analyze the double scroll system as an unfolding of a large family of piecewise-linear vector fields in <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">R^3</tex> . Using this approach, we were able to prove that the chaotic dynamics of the double scroll is quite common, and is robust because the associated horseshoes predicted from Shilnikov's theorem are structurally stable. In fact, it is exhibited by a large family (in fact, infinitely many linearlyequivalent circuits) of vector fields whose associated piecewise-linear differential equations bear no resemblance to each other. It is therefore remarkable that the normalized eigenvalues, which is a local concept, completely determine the system's global qualitative behavior.
In this paper, we present an object recognition technique using scanline information. Objects are scanned using a small number of on/off light sensors. The times when the beams break and unbreak constrain the object's identity, position, and orientation. We study this type of sensor because they are inexpensive, compact, very precise, and insensitive to ambient light, and so well-adapted to manufacturing environments. The information provided by the sensor is very sparse however, consisting of isolated points on the object boundary without normal information. Conventional model-based matching techniques, such as the alignment method, take O(n<SUP>3</SUP>) time for this problem. We describe an O(A + n) correspondence algorithm for objects with convex polygonal silhouettes, where n is the silhouette's complexity, and A is the total number of consistent edge pair matches for pairs of scanline points, which is O(n<SUP>2</SUP>) in the worst case, but typically O(n). Our algorithm works also for non-convex objects, but the quantity A has a somewhat larger typical value, and a worst case value of O(n<SUP>3</SUP>). The object's position and orientation can be easily computed given the correspondence information.
The completion of the Arabidopsis sequence will be followed by a new ten-year project that will determine the function of all angiosperm genes. Funding for the U.S. component of this multinational project will originate from a new initiative from the U.S. National Science Foundation called the 2010 Project. Progress toward completion of this ambitious project will necessitate significant changes in how the plant biology community selects and approaches research objectives. The plan envisions that the project will facilitate the development of a computational model of a virtual plant that will allow predictive queries about basic mechanisms underlying plant growth and development.
