Quantum Backflow States from Eigenstates of the Regularized Current Operator

We present an exhaustive class of states with quantum backflow -- the phenomenon in which a state consisting entirely of positive momenta may have negative current and the probability flows in the opposite direction to the momentum. They are characterized by a general function of momenta subject to very weak conditions. Such a family of states is of interest in the light of a recent experimental proposal to measure backflow. We find one particularly simple state which has surprisingly large backflow -- about 41 percent of the lower bound on flux derived by Bracken and Melloy. We study the eigenstates of a regularized current operator and we show how some of these states, in a certain limit, lead to our class of backflow states. This limit also clarifies the correspondence between the spectrum of the regularized current operator, which has just two non-zero eigenvalues in our chosen regularization, and the usual current operator.Comment: 16 pages, 2 figure

Indecomposable modules and Gelfand rings

It is proved that a commutative ring is clean if and only if it is Gelfand with a totally disconnected maximal spectrum. Commutative rings for which each indecomposable module has a local endomorphism ring are studied. These rings are clean and elementary divisor rings

Developing a multi-pollutant conceptual framework for the selection and targeting of interventions in water industry catchment management schemes

In recent years water companies have started to adopt catchment management to reduce diffuse pollution in drinking water supply areas. The heterogeneity of catchments and the range of pollutants that must be removed to meet the EU Drinking Water Directive (98/83/EC) limits make it difficult to prioritise areas of a catchment for intervention. Thus conceptual frameworks are required that can disaggregate the components of pollutant risk and help water companies make decisions about where to target interventions in their catchments to maximum effect. This paper demonstrates the concept of generalising pollutants in the same framework by reviewing key pollutant processes within a source-mobilisation-delivery context. From this, criteria are developed (with input from water industry professionals involved in catchment management) which highlights the need for a new water industry specific conceptual framework. The new CaRPoW (Catchment Risk to Potable Water) framework uses the Source-Mobilisation-Delivery concept as modular components of risk that work at two scales, source and mobilisation at the field scale and delivery at the catchment scale. Disaggregating pollutant processes permits the main components of risk to be ascertained so that appropriate interventions can be selected. The generic structure also allows for the outputs from different pollutants to be compared so that potential multiple benefits can be identified. CaRPow provides a transferable framework that can be used by water companies to cost-effectively target interventions under current conditions or under scenarios of land use or climate change

Rings of Quotients of Rings of Functions

From the original PREFACE: The rings of quotients recently introduced by Johnson and Utumi are applied to the ring $C(X)$ of all continuous real-valued functions on a completely regular space $X$. Let $Q(X)$ denote the maximal ring of quotients of $C(X)$; then $Q(X)$ may be realized as the ring of all continuous functions on the dense open sets of $X$ (modulo an obvious equivalence relation). In special cases (e.g., for metric $X$), $Q(X)$ reduces to the classical ring of quotients of $C(X)$ (formed with respect to the regular elements), but in general, the classical ring is only a proper sub-ring of $Q(X)$.Comment: 72 pages, Typeset copy of 1966 original, long out of prin

Jay\u27s Collectibles

There is growing interest in collectibles of many types, as indicated by the popularity of television programs such as the History Channel’s Pawn Stars and American Pickers and the Public Broadcasting Service’s Antiques Road Show. The availability of online auction sites such as eBay has enabled many people to collect items of interest as a hobby and to sell parts of their collection as a business or for extra income. As a collection grows, it becomes increasingly difficult to track through manual methods, and it is often useful to develop a computer-based system for this purpose. This case raises the possibility of developing an information system to manage a collection of sports autographs. This case may be used in a systems analysis and design, database, or systems development course to address a number of important topics such as: systems scope identification, problem and opportunity analysis, requirements analysis, data modeling, and application development. The case is designed to provoke interest and raise a sufficient level of complexity to challenge students to apply a range of systems development and database concepts. While the case addresses sports collectibles, its concepts may be applicable other types of systems, especially those involving other types of collections or “one of a kind” items. Since many students are likely to have at least some experience using online auction sites, following professional sports, seeing television programs about collectibles, or attending flea markets where collectibles are sold, the case builds in some way on their life experience. This teaching case enables students to discover how systems development and database concepts are applicable to a practical problem solving scenario

Artifacts with uneven sampling of red noise

The vast majority of sampling systems operate in a standard way: at each tick of a fixed-frequency master clock a digitizer reads out a voltage that corresponds to the value of some physical quantity and translates it into a bit pattern that is either transmitted, stored, or processed right away. Thus signal sampling at evenly spaced time intervals is the rule: however this is not always the case, and uneven sampling is sometimes unavoidable. While periodic or quasi-periodic uneven sampling of a deterministic signal can reasonably be expected to produce artifacts, it is much less obvious that the same happens with noise: here I show that this is indeed the case only for long-memory noise processes, i.e., power-law noises $1/f^\alpha$ with $\alpha > 2$. The resulting artifacts are usually a nuisance although they can be eliminated with a proper processing of the signal samples, but they could also be turned to advantage and used to encode information.Comment: 5 figure