Delay differential equations driven by Levy processes: stationarity and Feller properties

We consider a stochastic delay differential equation driven by a general Levy process. Both, the drift and the noise term may depend on the past, but only the drift term is assumed to be linear. We show that the segment process is eventually Feller, but in general not eventually strong Feller on the Skorokhod space. The existence of an invariant measure is shown by proving tightness of the segments using semimartingale characteristics and the Krylov-Bogoliubov method. A counterexample shows that the stationary solution in completely general situations may not be unique, but in more specific cases uniqueness is established.Comment: 28 page

Laser radar studies: A study of the feasibility of remote measurement of atmospheric density and turbidity by means of rotational Raman scattering of laser light

A remote sensing technique is described which utilizes elastic scattering and rotational Raman scattering of laser light in the atmosphere to obtain soundings of turbidity, transmissivity and density. A scheme is devised whereby, through selective weighting of the rotational Raman lines, the effect of atmospheric temperature structure may be eliminated. The close spectral proximity of the elastic and Raman-scattered signals, combined with the fact that the Raman scattering is quite weak, produces special requirements for the spectroscopic and light-gathering components of a rotational Raman laser radar system. These requirements are investigated. A computation of typical signal-to-noise ratios is made. It is shown that daytime signal-to-noise ratios greater than 10 db are to be expected for observation heights of 5 km and below. For nighttime work, 10 db signal-to-noise ratios are achievable to altitudes as high as 15 km

Effect of load introduction on graphite epoxy compression specimens

Compression testing of modern composite materials is affected by the manner in which the compressive load is introduced. Two such effects are investigated: (1) the constrained edge effect which prevents transverse expansion and is common to all compression testing in which the specimen is gripped in the fixture; and (2) nonuniform gripping which induces bending into the specimen. An analytical model capable of quantifying these foregoing effects was developed which is based upon the principle of minimum complementary energy. For pure compression, the stresses are approximated by Fourier series. For pure bending, the stresses are approximated by Legendre polynomials

Osmotic force resisting chain insertion in a colloidal suspension

We consider the problem of inserting a stiff chain into a colloidal suspension of particles that interact with it through excluded volume forces. The free energy of insertion is associated with the work of creating a cavity devoid of colloid and sufficiently large to accomodate the chain. The corresponding work per unit length is the force that resists the entry of the chain into the colloidal suspension. In the case of a hard sphere fluid, this work can be calculated straightforwardly within the scaled particle theory; for solutions of flexible polymers, on the other hand, we employ simple scaling arguments. The forces computed in these ways are shown, for nanometer chain and colloid diameters, to be of the order of tens of pN for solution volume fraction for biophysical processes such as the ejection of DNA from viral capsids into the cell cytoplasm.Comment: 16 pages,3 figures. Accepted for publication in European Physical Journal

Transaction Costs in Dealer Markets: Evidence From The London Stock Exchange

This paper describes regularities in the intraday spreads and prices quoted by dealers on the London Stock Exchange. It develops a measure of spread-related transaction costs, one that recognizes dealers' willingness to price trades within their quoted spreads. This measure of transaction costs shows that trading costs are systematically related to a trade's size, characteristics of the trading counterparties, and security characteristics. Customers pay the full spread on small trades while medium to large trades receive more favorable execution. Market makers only discount very large customer trades while dealers regularly discount medium to large trades. Inter-dealer trades generally receive favorable execution, and discounts increase in size. Market makers do not discount trades with each other over the phone, but do discount when trading anonymously using inter-dealer-brokers. Quoted and touch spreads are falling in the number of market makers. The rate of decline is interpreted as reflecting economies of scale in market making.

Anomalous Hall effect in the Co-based Heusler compounds Co2_{2}FeSi and Co2_{2}FeAl

The anomalous Hall effect (AHE) in the Heusler compounds Co$_{2}$FeSi and Co$_{2}$FeAl is studied in dependence of the annealing temperature to achieve a general comprehension of its origin. We have demonstrated that the crystal quality affected by annealing processes is a significant control parameter to tune the electrical resistivity $\rho_{xx}$ as well as the anomalous Hall resistivity $\rho_{ahe}$. Analyzing the scaling behavior of $\rho_{ahe}$ in terms of $\rho_{xx}$ points to a temperature-dependent skew scattering as the dominant mechanism in both Heusler compounds

Strong Magnetization Measured in the Cool Cores of Galaxy Clusters

Tangential discontinuities, seen as X-ray edges known as cold fronts (CFs), are ubiquitous in cool-core galaxy clusters. We analyze all 17 deprojected CF thermal profiles found in the literature, including three new CFs we tentatively identify (in clusters A2204 and 2A0335). We discover small but significant thermal pressure drops below all nonmerger CFs, and argue that they arise from strong magnetic fields below and parallel to the discontinuity, carrying 10%-20% of the pressure. Such magnetization can stabilize the CFs, and explain the CF-radio minihalo connection.Comment: PRL accepted, additional control tests adde

The use of AI in education: Practicalities and ethical considerations

There is a wide diversity of views on the potential for artificial intelligence (AI), ranging from overenthusiastic pronouncements about how it is imminently going to transform our lives to alarmist predictions about how it is going to cause everything from mass unemployment to the destruction of life as we know it. In this article, I look at the practicalities of AI in education and at the attendant ethical issues it raises. My key conclusion is that AI in the near- to medium-term future has the potential to enrich student learning and complement the work of (human) teachers without dispensing with them. In addition, AI should increasingly enable such traditional divides as ‘school versus home’ to be straddled with regard to learning. AI offers the hope of increasing personalization in education, but it is accompanied by risks of learning becoming less social. There is much that we can learn from previous introductions of new technologies in school to help maximize the likelihood that AI can help students both to flourish and to learn powerful knowledge. Looking further ahead, AI has the potential to be transformative in education, and it may be that such benefits will first be seen for students with special educational needs. This is to be welcomed