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  • Author(s):
    Rene De Vogelaere
    Abstract:

    Hamilton equations are such that the relation, between the coordinates and momenta at time t and at time t 0, is a contact transformation. Methods of integration of Hamilton equations, which do preserve the contact transformation property are given here. These methods are of first and second order. They are given, for the equation x= f(x,t), then for the case of one degree of freedom, then for the general case. Some of the formulae are implicit.

    Date Published:
    1956-04
  • Author(s):
    Daniel Bates, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Numerical algebraic geometry is the area devoted to the solution and manipulation of polynomial systems by numerical methods, which are mainly based on continuation. Due to the extreme intrinsic parallelism of continuation, polynomial systems may be successfully dealt with that are much larger than is possible with other methods. Singular solutions require special numerical methods called endgames, and the endgames currently used do not take advantage of parallelism. This article gives an ove…

  • Author(s):
    Charles Wampler II, Daniel Bates, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Dedicated to our collaborator, mentor, and friend, Andrew Sommese, by Bates, Hauenstein, and Wampler on the occasion of his sixtieth birthday.

    When numerically tracking implicitly-defined paths, such as is required for homotopy continuation methods, efficiency and reliability are enhanced by using adaptive stepsize and adaptive multiprecision methods. Both efficiency and reliability can be further improved by adapting precision and stepsize simultaneously. This paper presents a strategy fo…

  • Author(s):
    Charles Wampler, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Though numerical methods to find all the isolated solutions of nonlinear systems of multivariate polynomials go back 30 years, it is only over the last decade that numerical methods have been devised for the computation and manipulation of algebraic sets coming from polynomial systems over the complex numbers. Collectively, these algorithms and the underlying theory have come to be known as numerical algebraic geometry. Several software packages are capable of carrying out some of the operati…

  • Author(s):
    Daniel Bates, Andrew Sommese, Jonathan Hauenstein
    Abstract:

    Path tracking is the fundamental computational tool in homotopy continuation and is therefore key in most algorithms in the emerging field of numerical algebraic geometry. Though the basic notions of predictor-corrector methods have been known for years, there is still much to be considered, particularly in the specialized algebraic setting of solving polynomial systems. In this article, the effects of the choice of predictor method on the performance of a tracker is analyzed, and details for…

  • Author(s):
    Andrew Sommese, Azat M. Gainutdinov, Wenrui Hao, Rafael I. Nepomechie
    Abstract:

    We consider the sl(2)q-invariant open spin-½ XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of dimensions of irreducible representations of the Temperley-Lieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)q-modules. These formulas include corrections that appear if two or more tilting …

  • Author(s):
    Michael Wiescher, de Boer, R.J. , Bardayan, D.W., Go¨rres, J.
    Abstract:

    Background: The slowest reaction in the first CNO cycle is 14N(p,γ ) 15O, therefore its rate determines the overall energy production efficiency of the entire cycle. The cross section presents several strong resonance contributions, especially for the ground-state transition. Some of the properties of the corresponding levels in the 15O compound nucleus remain uncertain, which affects the uncertainty in extrapolating the capture cross section to the low energy range of astrophysical interest….

  • Author(s):
    David Severson, Anastasia N. Naumenko, Vladimir A. Timoshevskiy, Nicholas A. Kinney, Alina A. Kokhanenko, Becky S. deBruyn, Diane D. Lovin, Vladimir N. Stegniy, Igor V. Sharakhov, Maria V. Sharakhova
    Abstract:

    The genome assembly of southern house mosquito Cx. quinquefasciatus is represented by a high number of supercontigs with no order or orientation on the chromosomes. Although cytogenetic maps for the polytene chromosomes of this mosquito have been developed, their utilization for the genome mapping remains difficult because of the low number of high-quality spreads in chromosome preparations. Therefore, a simple and robust mitotic-chromosome-based approach for the genome mapping of Cx. quinque…

  • Author(s):
    David Severson, Susanta K. Behura, Consuelo Gomez-Machorro, Brent W. Harker, Becky deBruyn, Diane D. Lovin, Ryan R. Hemme, Akio Mori, Jeanne Romero-Severson
    Abstract:

    Dengue virus is primarily transmitted by Aedes aegypti mosquitoes. Control of the vector mosquito is the major practice to prevent dengue. However, it is not well known how the virus can infect some mosquito strains but fail to do so with other refractory strains. To address that question, we conducted whole genome microarray based gene expression studies between susceptible and refractory strains of A. aegypti to identify gene expression patterns following challenge with dengue virus. Our an…

  • Author(s):
    David Severson, Daniel Lawson, Peter Arensburger, Peter Atkinson, Nora J. Besansky, Robert V. Bruggner, Ryan Butler, Kathryn S. Campbell, George K. Christophides, Scott Christley, Emmanuel Dialynas, Martin Hammond, Catherine A. Hill, Nathan Konopinski, Neil F. Lobo, Robert M. MacCallum, Greg Madey, Karine Megy, Jason Meyer, Seth Redmond, Eric O. Stinson, Pantelis Topalis, Ewan Birney, William M. Gelbart, Fotis C. Kafatos, Christos Louis, Frank H. Collins
    Abstract:

    VectorBase (http://www.vectorbase.org) is an NIAID-funded Bioinformatic Resource Center focused on invertebrate vectors of human pathogens. VectorBase annotates and curates vector genomes providing a web accessible integrated resource for the research community. Currently, VectorBase contains genome information for three mosquito species: Aedes aegypti, Anopheles gambiae and Culex quinquefasciatus, a body louse Pediculus humanus and a tick species Ixodes scapularis. Since our last report Vect…

  • Author(s):
    Parker Ladwig, E. Bruce Williams
    Abstract:

    Review of the book Using the Mathematics Literature, edited by Kristine K. Fowler, New York, Marcel Dekker, 2004. 389 pp., US $165, ISBN 0-8247-5035-7.

    The book’s major drawback is its price—42 cents per page vs. 19 cents for Tucker and Anderson. However, it is still an important addition to your library’s collection, a relevant resource for undergraduate and graduate student advisors, and perhaps a gift for the new librarian who will be working with your department.

  • Author(s):
    Parker Ladwig, Andrew Sommese
    Abstract:

    “Supplying accurate CPU [cost-per-serial use] information to faculty and appropriate marketing of the alternate modes of delivery … become the key to achieving an optimal cost-efficient serials collection in an academic library.” (Marisa Scigliano, “Serial Use in a Small Academic Library: Determining Cost-effectiveness,” Serials Review 26 (2000): 43–52.)

    A model is presented for adjusting use statistics using a journal’s ISI Journal Citation Reports cited half-life.The goal is to improve t…