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1
Article
 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…

2
Article
 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 implicitlydefined 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…

3
Article
 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…

4
Article
 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 predictorcorrector 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)qinvariant open spin½ 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 TemperleyLieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)qmodules. These formulas include corrections that appear if two or more tilting …

 Author(s):
 Andrew Sommese, Azat M. Gainutdinov, Wenrui Hao, Rafael I. Nepomechie
 Abstract:
We consider the sl(2)qinvariant open spin½ 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 TemperleyLieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)qmodules. These formulas include corrections that appear if two or more tilting …

 Author(s):
 Andrew Sommese
 Abstract:
We consider the sl(2)qinvariant open spin½ 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 TemperleyLieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)qmodules. These formulas include corrections that appear if two or more tilting …

 Author(s):
 Andrew Sommese
 Abstract:
We consider the sl(2)qinvariant open spin½ 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 TemperleyLieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)qmodules. These formulas include corrections that appear if two or more tilting …

 Author(s):
 Andrew Sommese
 Abstract:
We consider the sl(2)qinvariant open spin½ 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 TemperleyLieb algebra; and a formula for the degeneracies of the transfer matrix eigenvalues in terms of dimensions of tilting sl(2)qmodules. These formulas include corrections that appear if two or more tilting …

 Author(s):
 Parker Ladwig, Andrew Sommese
 Abstract:
“Supplying accurate CPU [costperserial use] information to faculty and appropriate marketing of the alternate modes of delivery … become the key to achieving an optimal costefficient serials collection in an academic library.” (Marisa Scigliano, “Serial Use in a Small Academic Library: Determining Costeffectiveness,” Serials Review 26 (2000): 43–52.)
A model is presented for adjusting use statistics using a journal’s ISI Journal Citation Reports cited halflife.The goal is to improve t…