Optical communications system Patent

Specifications and drawings for semipassive optical communication syste

Electronic motor control system Patent

Electronic circuit system for controlling electric motor spee

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

How Wide is the Scope of Hold-Up-Based Theories? Contractual Form and Market Thickness in Trucking

How far do the contractual implications of hold-up-based theories (Klein, Crawford, and Alchian (1978), Williamson (1979, 1985)) extend? I investigate this in the context of trucking. Quasi-rents in trucking are generally smaller than in the contexts studied in the previous empirical literature. They vary with hauls' distance and the thickness of local markets. I find that doubling the thickness of the market increases the likelihood that simple spot arrangements govern transactions by about 30% for long hauls. I find weaker evidence of relationships between local market thickness and contractual form for short hauls -- hauls for which quasi-rents are particularly small. Contracts' role as protectors of quasi-rents becomes less important as quasi-rents decrease, but exists over a surprisingly large range.

Quantum Calculations On The Vibrational Predissociation Of NeBr2: Evidence For Continuum Resonances

Quantum mechanical calculations on the vibrational predissociation dynamics of NeBr2 in the B electronic state have been performed and the results compared with both experimental data and other computational studies. For vibrational levels with v less than or equal to 20 we find that the vibrational state dependence of the predissociation lifetimes is in qualitative agreement with experimental measurements, as are the calculated Br-2 fragment rotational distributions. For higher vibrational levels, the B \u3c-- X excitation profiles are well represented by a sum of two Lorentzian line shapes. We attribute this result to the presence of long-lived resonances in the dissociative continuum that are reminiscent of long-lived dissociative trajectories in previous classical studies of NeBr2. (C) 2000 American Institute of Physics. [S0021-9606(00)00205-1]

Evaluating matrix functions for exponential integrators via Carathéodory-Fejér approximation and contour integrals

Among the fastest methods for solving stiff PDE are exponential integrators, which require the evaluation of $f(A)$, where $A$ is a negative definite matrix and $f$ is the exponential function or one of the related ``$\varphi$ functions'' such as $\varphi_1(z) = (e^z-1)/z$. Building on previous work by Trefethen and Gutknecht, Gonchar and Rakhmanov, and Lu, we propose two methods for the fast evaluation of $f(A)$ that are especially useful when shifted systems $(A+zI)x=b$ can be solved efficiently, e.g. by a sparse direct solver. The first method method is based on best rational approximations to $f$ on the negative real axis computed via the Carathéodory-Fejér procedure, and we conjecture that the accuracy scales as $(9.28903\dots)^{-2n}$, where $n$ is the number of complex matrix solves. In particular, three matrix solves suffice to evaluate $f(A)$ to approximately six digits of accuracy. The second method is an application of the trapezoid rule on a Talbot-type contour

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

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