Electronic motor control system Patent

Electronic circuit system for controlling electric motor spee

Optical communications system Patent

Specifications and drawings for semipassive optical communication syste

Care Planning and Review for Looked After Children: Fifteen Years of Slow Progress?

This Critical Commentary reviews progress in research into planning and reviewing for children in care in England and Wales since the publication of two major studies in the late 1990s (roughly coinciding with the New Labour period). It briefly considers the changing context of law, regulation and guidance and the aims and objectives of the care planning and review system. It then reviews the limited research literature available, in relation to a series of key topics. Consideration is also given to guides for children and practitioners on the subject. The commentary concludes by suggesting that this is an area in which research has failed to keep pace with changes in policy and practice, and recommends a more systematic approach

Hodge theory and derived categories of cubic fourfolds

Cubic fourfolds behave in many ways like K3 surfaces. Certain cubics - conjecturally, the ones that are rational - have specific K3s associated to them geometrically. Hassett has studied cubics with K3s associated to them at the level of Hodge theory, and Kuznetsov has studied cubics with K3s associated to them at the level of derived categories. These two notions of having an associated K3 should coincide. We prove that they coincide generically: Hassett's cubics form a countable union of irreducible Noether-Lefschetz divisors in moduli space, and we show that Kuznetsov's cubics are a dense subset of these, forming a non-empty, Zariski open subset in each divisor.Comment: 37 pages. Applications to algebraic cycles added, and other improvements following referees' suggestions. This is a slightly expanded version of the paper to appear in Duke Math

Computing the Gamma function using contour integrals and rational approximations

Some of the best methods for computing the gamma function are based on numerical evaluation of Hankel's contour integral. For example, Temme evaluates this integral based on steepest-decent contours by the trapezoid rule. Here we investigate a different approach to the integral: the application of the trapezoid rule on Talbot-type contours using optimal parameters recently derived by Weideman for computing inverse Laplace transforms. Relatedly, we also investigate quadrature formulas derived from best approximations to exp(z) on the negative real axis, following Cody, Meinardus and Varga. The two methods are closely related and both converge geometrically. We find that the new methods are competitive with existing ones, even though they are based on generic tools rather than on specific analysis of the gamma function

Resolving Distributed Knowledge

Distributed knowledge is the sum of the knowledge in a group; what someone who is able to discern between two possible worlds whenever any member of the group can discern between them, would know. Sometimes distributed knowledge is referred to as the potential knowledge of a group, or the joint knowledge they could obtain if they had unlimited means of communication. In epistemic logic, the formula D_G{\phi} is intended to express the fact that group G has distributed knowledge of {\phi}, that there is enough information in the group to infer {\phi}. But this is not the same as reasoning about what happens if the members of the group share their information. In this paper we introduce an operator R_G, such that R_G{\phi} means that {\phi} is true after G have shared all their information with each other - after G's distributed knowledge has been resolved. The R_G operators are called resolution operators. Semantically, we say that an expression R_G{\phi} is true iff {\phi} is true in what van Benthem [11, p. 249] calls (G's) communication core; the model update obtained by removing links to states for members of G that are not linked by all members of G. We study logics with different combinations of resolution operators and operators for common and distributed knowledge. Of particular interest is the relationship between distributed and common knowledge. The main results are sound and complete axiomatizations.Comment: In Proceedings TARK 2015, arXiv:1606.0729