Financing Canadian Innovation: Why Canada Should End Roadblocks to Foreign Private Equity

Canada’s cross-border tax laws raise barriers that needlessly discourage investment in Canadian private equity firms. We examine the harm these barriers cause, and propose ways of reducing them.cross-border taxation

Final Calibration of the Berkeley Extreme and Far-Ultraviolet Spectrometer on the ORFEUS-SPAS I and II Missions

The Berkeley Extreme and Far-Ultraviolet Spectrometer (BEFS) flew as part of the ORFEUS telescope on the ORFEUS-SPAS I and II space-shuttle missions in 1993 and 1996, respectively. The data obtained by this instrument have now entered the public domain. To facilitate their use by the astronomical community, we have re-extracted and re-calibrated both data sets, converted them into a standard (FITS) format, and placed them in the Multimission Archive at Space Telescope (MAST). Our final calibration yields improved wavelength scales and effective-area curves for both data sets.Comment: To appear in the January 2002 issue of the PASP. 17 pages with 9 embedded postscript figures; uses emulateapj5.st

Lower bounds for polynomials using geometric programming

We make use of a result of Hurwitz and Reznick, and a consequence of this result due to Fidalgo and Kovacec, to determine a new sufficient condition for a polynomial $f\in\mathbb{R}[X_1,...,X_n]$ of even degree to be a sum of squares. This result generalizes a result of Lasserre and a result of Fidalgo and Kovacec, and it also generalizes the improvements of these results given in [6]. We apply this result to obtain a new lower bound $f_{gp}$ for $f$, and we explain how $f_{gp}$ can be computed using geometric programming. The lower bound $f_{gp}$ is generally not as good as the lower bound $f_{sos}$ introduced by Lasserre and Parrilo and Sturmfels, which is computed using semidefinite programming, but a run time comparison shows that, in practice, the computation of $f_{gp}$ is much faster. The computation is simplest when the highest degree term of $f$ has the form $\sum_{i=1}^n a_iX_i^{2d}$, $a_i>0$, $i=1,...,n$. The lower bounds for $f$ established in [6] are obtained by evaluating the objective function of the geometric program at the appropriate feasible points

Structural change in multipartite entanglement sharing: a random matrix approach

We study the typical entanglement properties of a system comprising two independent qubit environments interacting via a shuttling ancilla. The initial preparation of the environments is modeled using random-matrix techniques. The entanglement measure used in our study is then averaged over many histories of randomly prepared environmental states. Under a Heisenberg interaction model, the average entanglement between the ancilla and one of the environments remains constant, regardless of the preparation of the latter and the details of the interaction. We also show that, upon suitable kinematic and dynamical changes in the ancilla-environment subsystems, the entanglement-sharing structure undergoes abrupt modifications associated with a change in the multipartite entanglement class of the overall system's state. These results are invariant with respect to the randomized initial state of the environments.Comment: 10 pages, RevTeX4 (Minor typo's corrected. Closer to published version

Solving magnetostatic field problems with NASTRAN

Determining the three-dimensional magnetostatic field in current-induced situations has usually involved vector potentials, which can lead to excessive computational times. How such magnetic fields may be determined using scalar potentials is reviewed. It is shown how the heat transfer capability of NASTRAN level 17 was modified to take advantage of the new method

Distribution of interference in random quantum algorithms

We study the amount of interference in random quantum algorithms using a recently derived quantitative measure of interference. To this end we introduce two random circuit ensembles composed of random sequences of quantum gates from a universal set, mimicking quantum algorithms in the quantum circuit representation. We show numerically that these ensembles converge to the well--known circular unitary ensemble (CUE) for general complex quantum algorithms, and to the Haar orthogonal ensemble (HOE) for real quantum algorithms. We provide exact analytical formulas for the average and typical interference in the circular ensembles, and show that for sufficiently large numbers of qubits a random quantum algorithm uses with probability close to one an amount of interference approximately equal to the dimension of the Hilbert space. As a by-product, we offer a new way of efficiently constructing random operators from the Haar measures of CUE or HOE in a high dimensional Hilbert space using universal sets of quantum gates.Comment: 14 pages revtex, 11 eps figure

The symplectic origin of conformal and Minkowski superspaces

Supermanifolds provide a very natural ground to understand and handle supersymmetry from a geometric point of view; supersymmetry in $d=3,4,6$ and $10$ dimensions is also deeply related to the normed division algebras. In this paper we want to show the link between the conformal group and certain types of symplectic transformations over division algebras. Inspired by this observation we then propose a new\,realization of the real form of the 4 dimensional conformal and Minkowski superspaces we obtain, respectively, as a Lagrangian supermanifold over the twistor superspace $\mathbb{C}^{4|1}$ and a big cell inside it. The beauty of this approach is that it naturally generalizes to the 6 dimensional case (and possibly also to the 10 dimensional one) thus providing an elegant and uniform characterization of the conformal superspaces.Comment: 15 pages, references added, minor change

Lag synchronization and scaling of chaotic attractor in coupled system

We report a design of delay coupling for lag synchronization in two unidirectionally coupled chaotic oscillators. A delay term is introduced in the definition of the coupling to target any desired lag between the driver and the response. The stability of the lag synchronization is ensured by using the Hurwitz matrix stability. We are able to scale up or down the size of a driver attractor at a response system in presence of a lag. This allows compensating the attenuation of the amplitude of a signal during transmission through a delay line. The delay coupling is illustrated with numerical examples of 3D systems, the Hindmarsh-Rose neuron model, the R\"ossler system and a Sprott system and, a 4D system. We implemented the coupling in electronic circuit to realize any desired lag synchronization in chaotic oscillators and scaling of attractors.Comment: 10 pages, 7 figure

Method of constructing exactly solvable chaos

We present a new systematic method of constructing rational mappings as ergordic transformations with nonuniform invariant measures on the unit interval [0,1]. As a result, we obtain a two-parameter family of rational mappings that have a special property in that their invariant measures can be explicitly written in terms of algebraic functions of parameters and a dynamical variable. Furthermore, it is shown here that this family is the most generalized class of rational mappings possessing the property of exactly solvable chaos on the unit interval, including the Ulam=Neumann map y=4x(1-x). Based on the present method, we can produce a series of rational mappings resembling the asymmetric shape of the experimentally obtained first return maps of the Beloussof-Zhabotinski chemical reaction, and we can match some rational functions with other experimentally obtained first return maps in a systematic manner.Comment: 12 pages, 2 figures, REVTEX. Title was changed. Generalized Chebyshev maps including the precise form of two-parameter generalized cubic maps were added. Accepted for publication in Phys. Rev. E(1997

Mathematical determination of geometrical image aberrations in single and double mirror systems

Mathematical determination of geometrical image aberrations in single and double mirror system