A gradient estimate for solutions of the heat equation. II

summary:The author obtains an estimate for the spatial gradient of solutions of the heat equation, subject to a homogeneous Neumann boundary condition, in terms of the gradient of the initial data. The proof is accomplished via the maximum principle; the main assumption is that the sufficiently smooth boundary be convex

Elastic and Raman scattering of 9.0 and 11.4 MeV photons from Au, Dy and In

Monoenergetic photons between 8.8 and 11.4 MeV were scattered elastically and in elastically (Raman) from natural targets of Au, Dy and In.15 new cross sections were measured. Evidence is presented for a slight deformation in the 197Au nucleus, generally believed to be spherical. It is predicted, on the basis of these measurements, that the Giant Dipole Resonance of Dy is very similar to that of 160Gd. A narrow isolated resonance at 9.0 MeV is observed in In.Comment: 31 pages, 11 figure

Project management : learning by breaking the rules

The paper explores project management in action in a large public research organisation – NLAT which decided to change its internal organisation from team-based to project-based organisation a few years ago. A systematic and comparative analysis of 8 projects reveals that adherence to the ISO 9000’s standardized rules of project management - specific staffing and project leaders, definition of milestones ex ante, procedure manuals, and formalized learning accumulation mechanisms - had little to do with the organisations success over recent years: Looking for explanations for this success, the paper focuses on the process of transferring from one project to another, enhancing organisational learning through rules breaking. We identify three elements which encourage the accumulation of knowledge and competencies, as organisational learning: low project core staffing levels which stimulates the circulation of engineers and researchers between projects and blurs project boundaries, implementing and managing thematic projects which build on specific competencies developed in dedicated projects and encouraging ‘bricolage’ to hybridise project management with traditional hierarchical management practices.PROJECT MANAGEMENT;R&D;HIGH TECH;MANAGEMENT PRACTICES

Disk-Like Structure in the Semi-Regular Pulsating Star, X Her

The author reports a result of an interferometric observation of the semiragular pulsating star with an unusual narrow molecular line profile, X Her, in the CO J=1-0 line with the Berkeley-Illinois-Maryland array. In the CO spectrum, a double-component profile (including narrow and broad components) is seen as reported by previous observations. The narrow component consists of two spiky peaks. The spatial structure of the board component shows bipolar shape, and that of the narrow component shows an elliptical/spherical shape. The two peaks in the narrow component show a systematic difference in the integrated intensity map. The kinematical and geometrical properties of the narrow component are reminiscent of a Keplerian rotating disk with the central mass of 0.9 M_sun, though an interpretation by an expansion disk seems to be more natural. A secondary bipolar flow instead of the disk cannot be fully excluded as an interpretation of the narrow line.Comment: 12 pages, 4 figues, accepted for publication in Ap

Estimates in Beurling--Helson type theorems. Multidimensional case

We consider the spaces $A_p(\mathbb T^m)$ of functions $f$ on the $m$ -dimensional torus $\mathbb T^m$ such that the sequence of the Fourier coefficients $\hat{f}=\{\hat{f}(k), ~k \in \mathbb Z^m\}$ belongs to $l^p(\mathbb Z^m), ~1\leq p<2$. The norm on $A_p(\mathbb T^m)$ is defined by $\|f\|_{A_p(\mathbb T^m)}=\|\hat{f}\|_{l^p(\mathbb Z^m)}$. We study the rate of growth of the norms $\|e^{i\lambda\varphi}\|_{A_p(\mathbb T^m)}$ as $|\lambda|\rightarrow \infty, ~\lambda\in\mathbb R,$ for $C^1$ -smooth real functions $\varphi$ on $\mathbb T^m$ (the one-dimensional case was investigated by the author earlier). The lower estimates that we obtain have direct analogues for the spaces $A_p(\mathbb R^m)$

Macroscopic objects in quantum mechanics: A combinatorial approach

Why we do not see large macroscopic objects in entangled states? There are two ways to approach this question. The first is dynamic: the coupling of a large object to its environment cause any entanglement to decrease considerably. The second approach, which is discussed in this paper, puts the stress on the difficulty to observe a large scale entanglement. As the number of particles n grows we need an ever more precise knowledge of the state, and an ever more carefully designed experiment, in order to recognize entanglement. To develop this point we consider a family of observables, called witnesses, which are designed to detect entanglement. A witness W distinguishes all the separable (unentangled) states from some entangled states. If we normalize the witness W to satisfy |tr(W\rho)| \leq 1 for all separable states \rho, then the efficiency of W depends on the size of its maximal eigenvalue in absolute value; that is, its operator norm ||W||. It is known that there are witnesses on the space of n qbits for which ||W|| is exponential in n. However, we conjecture that for a large majority of n-qbit witnesses ||W|| \leq O(\sqrt{n logn}). Thus, in a non ideal measurement, which includes errors, the largest eigenvalue of a typical witness lies below the threshold of detection. We prove this conjecture for the family of extremal witnesses introduced by Werner and Wolf (Phys. Rev. A 64, 032112 (2001)).Comment: RevTeX, 14 pages, some additions to the published version: A second conjecture added, discussion expanded, and references adde

Bilateral Proximal Tibial Sleeve Fractures in a Child: A Case Report

Introduction: A sleeve fracture classically describes an avulsion of cartilage or periosteum with or without osseous fragments and usually occurs at the inferior margin of the patella. Tibial tubercle sleeve fractures in the skeletally immature are extremely rare. Case Presentation: In this report the authors describe a 12-year-old boy with no systemic disease and no steroid use who sustained bilateral proximal tibial sleeve fractures whilst playing football. Both ruptures were associated with rupture of the medial patellofemoral ligament and tear of the medial retinaculum. Treatment was performed with primary end-to-end repair, reinforcement with bone anchors and cerclage wires with an excellent outcome. Conclusions: We feel this rare, currently unclassified variant of a tibial tubercle avulsion fracture should be recognised and consideration taken to adding it to existing classification systems

Knowledge Cartography for Controversies: The Iraq Debate

In analysing controversies and debates—which would include reviewing a literature in order to plan research, or assessing intelligence to formulate policy—there is no one worldview which can be mapped, for instance as a single, coherent concept map. The cartographic challenge is to show which facts are agreed and contested, and the different kinds of narrative links that use facts as evidence to define the nature of the problem, what to do about it, and why. We will use the debate around the invasion of Iraq to demonstrate the methodology of using a knowledge mapping tool to extract key ideas from source materials, in order to classify and connect them within and across a set of perspectives of interest to the analyst. We reflect on the value that this approach adds, and how it relates to other argument mapping approaches