Nature of quantum measurement for quantities not represented by Hermitian operators

In the case of a simple quantum system, we investigate the possibility of defining meaningful probabilities for a quantity that cannot be represented by a Hermitian operator. We find that the consistent-histories approach, recently applied to the case of quantum traversal time [N. Yamada, Phys. Rev. Lett. 83, 3350 (1999)], does not provide a suitable criterion and we dispute Yamada's claim of finding a simple solution to the tunneling-time problem. Rather, we define the probabilities for certain types of generally nonorthogonal decomposition of the system's quantum state. These relate to the interaction between the system and its environment, can be observed in a generalized von Neumann measurement, and are consistent with a particular class of positive-operator-valued measures.

De la cooperativa agroalimentaria a la "learning netchain". Hacia un planteamiento teorico interorganizativo e interpersonal

Se propone un planteamiento teórico/conceptual para determinar si las relaciones interorganizativas e interpersonales de la netchain de las cooperativas agroalimentarias evolucionan hacia una learning netchain. Las propuestas del trabajo muestran que el mayor grado de asociacionismo y la mayor cooperación/colaboración vertical a lo largo de la cadena están positivamente relacionados con la posición horizontal de la empresa focal más cercana del consumidor final. Esto requiere una planificación y una resolución de problemas de manera conjunta, lo que está positivamente relacionado con el mayor flujo y diversidad de la información/conocimiento obtenido y diseminado a lo largo de la netchain. Al mismo tiempo se necesita desarrollar un contexto social en el que fluya la información/conocimiento y las nuevas ideas de manera informal y esto se logra con redes personales y, principalmente, profesionales y con redes internas y, principalmente, externas. Todo esto permitirá una mayor satisfacción de los socios de la cooperativa agroalimentaria y de sus distribuidores y una mayor intensidad en I+D, convirtiéndose la netchain de la cooperativa agroalimentaria, así, en una learning netchain.

The Teaching Space Allocation Problem with splitting

A standard problem within universities is that of teaching space allocation which can be thought of as the assignment of rooms and times to various teaching activities. The focus is usually on courses that are expected to fit into one room. However, it can also happen that the course will need to be broken up, or ‘split’, into multiple sections. A lecture might be too large to fit into any one room. Another common example is that of seminars or tutorials. Although hundreds of students may be enrolled on a course, it is often subdivided into particular types and sizes of events dependent on the pedagogic requirements of that particular course. Typically, decisions as to how to split courses need to be made within the context of limited space requirements. Institutions do not have an unlimited number of teaching rooms, and need to effectively use those that they do have. The efficiency of space usage is usually measured by the overall ‘utilisation’ which is basically the fraction of the available seat-hours that are actually used. A multi-objective optimisation problem naturally arises; with a trade-off between satisfying preferences on splitting, a desire to increase utilisation, and also to satisfy other constraints such as those based on event location and timetabling conflicts. In this paper, we explore such trade-offs. The explorations themselves are based on a local search method that attempts to optimise the space utilisation by means of a ‘dynamic splitting’ strategy. The local moves are designed to improve utilisation and satisfy the other constraints, but are also allowed to split, and un-split, courses so as to simultaneously meet the splitting objectives.

An analogue of the Magnus problem for associative algebras

We prove an analogue of Magnus theorem for associative algebras without unity over arbitrary fields. Namely, if an algebra is given by $n+k$ generators and $k$ relations and has an $n$-element system of generators, then this algebra is a free algebra of rank $n$.