Comment on "Geometric phases for mixed states during cyclic evolutions"

It is shown that a recently suggested concept of mixed state geometric phase in cyclic evolutions [2004 {\it J. Phys. A} {\bf 37} 3699] is gauge dependent.Comment: Comment to the paper L.-B. Fu and J.-L. Chen, J. Phys. A 37, 3699 (2004); small changes; journal reference adde

Inverse problems connected with two-point boundary value problems

For the purpose of studying those properties of a nonlinear function $f(u)$ for which the two-point boundary value problem $u''+\lambda f(u)=0 (00$, the authors construct a number of kinds of special examples. "Inverse" in the title refers to the fact that the multiplicity is specified first and then a suitable function $f$ is constructed

Local search methods for the discrete time/resource trade-off problem in project networks.

Abstract: In this paper we consider the discrete time/resource trade-off problem in project networks. Given a project network consisting of nodes (activities) and arcs (technological precedence relations specifying that an activity can only start when al of its predecessors have been completed), in which the duration of the activities is a discrete, on-increasing function of the amount of a single renewable resource committed to it, the discrete time/resource trade-off problem minimizes the project makespan subject to precedence constraints and a single renewable resource constraint. For each activity a work content is specified such that all execution modes (duration-resource pairs) for performing the activity are allowed as long as the product of the duration and the resource requirement is at least as large as the specified work content. We present a tabu search procedure which is based on subdividing the problem into a mode assignment phase and a resource-constrained project scheduling phase with fixed mode assignments. Extensive computational experience, including a comparison with other local search methods, is reported.Scheduling; Methods; Networks; Product; Assignment;

Bounding the Probability of Error for High Precision Recognition

We consider models for which it is important, early in processing, to estimate some variables with high precision, but perhaps at relatively low rates of recall. If some variables can be identified with near certainty, then they can be conditioned upon, allowing further inference to be done efficiently. Specifically, we consider optical character recognition (OCR) systems that can be bootstrapped by identifying a subset of correctly translated document words with very high precision. This "clean set" is subsequently used as document-specific training data. While many current OCR systems produce measures of confidence for the identity of each letter or word, thresholding these confidence values, even at very high values, still produces some errors. We introduce a novel technique for identifying a set of correct words with very high precision. Rather than estimating posterior probabilities, we bound the probability that any given word is incorrect under very general assumptions, using an approximate worst case analysis. As a result, the parameters of the model are nearly irrelevant, and we are able to identify a subset of words, even in noisy documents, of which we are highly confident. On our set of 10 documents, we are able to identify about 6% of the words on average without making a single error. This ability to produce word lists with very high precision allows us to use a family of models which depends upon such clean word lists

Bounds of the rank of the Mordell-Weil group of jacobians of hyperelliptic curves

In this article we extend work of Shanks and Washington on cyclic extensions, and elliptic curves associated to the simplest cubic fields. In particular, we give families of examples of hyperelliptic curves $C: y^2=f(x)$ defined over $\mathbb{Q}$, with $f(x)$ of degree $p$, where $p$ is a Sophie Germain prime, such that the rank of the Mordell--Weil group of the jacobian $J/\mathbb{Q}$ of $C$ is bounded by the genus of $C$ and the $2$-rank of the class group of the (cyclic) field defined by $f(x)$, and exhibit examples where this bound is sharp.Comment: 22 pages, To appear in J. Th\'eor. Nombres Bordeau

How distorting are direct payments?

Agricultural and Food Policy,