380,505 research outputs found
Existence and Uniqueness of Weak Homotopy Moment Maps
In this paper we show that the classical results on the existence and
uniqueness of moment maps in symplectic geometry generalize directly to weak
homotopy moment maps in multisym- plectic geometry. In particular, we show that
their existence and uniqueness is governed by a Lie algebra cohomology complex
which reduces to the Chevalley-Eilenberg complex in the symplectic setupComment: Incorporated the referee's suggestions and fixed some typos. To
appear in Journal of Geometry and Physic
Optimal Control of Nonlocal Thermistor Equations
We are concerned with the optimal control problem of the well known nonlocal
thermistor problem, i.e., in studying the heat transfer in the resistor device
whose electrical conductivity is strongly dependent on the temperature.
Existence of an optimal control is proved. The optimality system consisting of
the state system coupled with adjoint equations is derived, together with a
characterization of the optimal control. Uniqueness of solution to the
optimality system, and therefore the uniqueness of the optimal control, is
established. The last part is devoted to numerical simulations.Comment: Submitted 21-March-2012; revised 11-June-2012; accepted 13-June-2012;
for publication in the International Journal of Contro
Countable Random Sets: Uniqueness in Law and Constructiveness
The first part of this article deals with theorems on uniqueness in law for
\sigma-finite and constructive countable random sets, which in contrast to the
usual assumptions may have points of accumulation. We discuss and compare two
approaches on uniqueness theorems: First, the study of generators for
\sigma-fields used in this context and, secondly, the analysis of hitting
functions. The last section of this paper deals with the notion of
constructiveness. We will prove a measurable selection theorem and a
decomposition theorem for constructive countable random sets, and study
constructive countable random sets with independent increments.Comment: Published in Journal of Theoretical Probability
(http://www.springerlink.com/content/0894-9840/). The final publication is
available at http://www.springerlink.co
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