10,310 research outputs found
Some of Piaget's questions on moral judgment applied to some children in American schools
Thesis (M.A.)--Boston Universit
Preconditioners for state constrained optimal control problems\ud with Moreau-Yosida penalty function tube
Optimal control problems with partial differential equations play an important role in many applications. The inclusion of bound constraints for the state poses a significant challenge for optimization methods. Our focus here is on the incorporation of the constraints via the Moreau-Yosida regularization technique. This method has been studied recently and has proven to be advantageous compared to other approaches. In this paper we develop preconditioners for the efficient solution of the Newton steps associated with the fast solution of the Moreau-Yosida regularized problem. Numerical results illustrate the competitiveness of this approach. \ud
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Copyright c 2000 John Wiley & Sons, Ltd
All-at-Once Solution if Time-Dependent PDE-Constrained Optimisation Problems
Time-dependent partial differential equations (PDEs) play an important role in applied mathematics and many other areas of science. One-shot methods try to compute the solution to these problems in a single iteration that solves for all time-steps at the same time. In this paper, we look at one-shot approaches for the optimal control of time-dependent PDEs and focus on the fast solution of these problems. The use of Krylov subspace solvers together with an efficient preconditioner allows for minimal storage requirements. We solve only approximate time-evolutions for both forward and adjoint problem and compute accurate solutions of a given control problem only at convergence of the overall Krylov subspace iteration. We show that our approach can give competitive results for a variety of problem formulations
Explicit isogeny descent on elliptic curves
In this note, we consider an l-isogeny descent on a pair of elliptic curves
over Q. We assume that l > 3 is a prime. The main result expresses the relevant
Selmer groups as kernels of simple explicit maps between finite- dimensional
F_l-vector spaces defined in terms of the splitting fields of the kernels of
the two isogenies. We give examples of proving the l-part of the Birch and
Swinnerton-Dyer conjectural formula for certain curves of small conductor.Comment: 17 pages, accepted for publication in Mathematics of Computatio
Preconditioning for Allen-Cahn variational inequalities with non-local constraints
The solution of Allen-Cahn variational inequalities with mass constraints is of interest in many applications. This problem can be solved both in its scalar and vector-valued form as a PDE-constrained optimization problem by means of a primal-dual active set method. At the heart of this method lies the solution of linear systems in saddle point form. In this paper we propose the use of Krylov-subspace solvers and suitable preconditioners for the saddle point systems. Numerical results illustrate the competitiveness of this approach
Rational divisors in rational divisor classes
We discuss the situation where a curve C, defined over a number field K, has a known K-rational divisor class of degree 1, and consider whether this class contains an actual K-rational divisor. When C has points everywhere locally, the local to global principle of the Brauer group gives the existence of such a divisor. In this situation, we give an alternative, more down to earth, approach, which indicates how to compute this divisor in certain situations. We also discuss examples where C does not have points everywhere locally, and where no such K-rational divisor is contained in the K-rational divisor class
Employer Demand for Welfare Recipients by Race
This paper uses new survey data on employers in four large metropolitan areas to examine the determinants of employer demand for welfare recipients. The results suggest a high level of demand for welfare recipients, though such demand appears fairly sensitive to business cycle conditions. A broad range of factors, including skill needs and industry, affect the prospective demand for welfare recipients among employers, while other characteristics that affect the relative supply of welfare recipients to these employers (such as location and employer use of local agencies or welfare-to-work programs) influence the extent to which such demand is realized in actual hiring. Moreover, the conditional demand for black (and to a lesser extent Hispanic) welfare recipients lags behind their representation in the welfare population and seems to be more heavily affected by employers’ location and indicators of preferences than by their skill needs or overall hiring activity. Thus, a variety of factors on the demand side of the labor market continue to limit the employment options of welfare recipients, especially those who are minorities.
On elliptic curves with an isogeny of degree 7
We show that if is an elliptic curve over with a
-rational isogeny of degree 7, then the image of the 7-adic Galois
representation attached to is as large as allowed by the isogeny, except
for the curves with complex multiplication by . The
analogous result with 7 replaced by a prime was proved by the first
author in [7]. The present case has additional interesting
complications. We show that any exceptions correspond to the rational points on
a certain curve of genus 12. We then use the method of Chabauty to show that
the exceptions are exactly the curves with complex multiplication. As a
by-product of one of the key steps in our proof, we determine exactly when
there exist elliptic curves over an arbitrary field of characteristic not 7
with a -rational isogeny of degree 7 and a specified Galois action on the
kernel of the isogeny, and we give a parametric description of such curves.Comment: The revision gives a complete answer to the question considered in
Version 1. Version 3 will appear in the American Journal of Mathematic
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