Covariant Quantum Fields on Noncommutative Spacetimes

A spinless covariant field $\phi$ on Minkowski spacetime \M^{d+1} obeys the relation $U(a,\Lambda)\phi(x)U(a,\Lambda)^{-1}=\phi(\Lambda x+a)$ where $(a,\Lambda)$ is an element of the Poincar\'e group \Pg and $U:(a,\Lambda)\to U(a,\Lambda)$ is its unitary representation on quantum vector states. It expresses the fact that Poincar\'e transformations are being unitary implemented. It has a classical analogy where field covariance shows that Poincar\'e transformations are canonically implemented. Covariance is self-reproducing: products of covariant fields are covariant. We recall these properties and use them to formulate the notion of covariant quantum fields on noncommutative spacetimes. In this way all our earlier results on dressing, statistics, etc. for Moyal spacetimes are derived transparently. For the Voros algebra, covariance and the *-operation are in conflict so that there are no covariant Voros fields compatible with *, a result we found earlier. The notion of Drinfel'd twist underlying much of the preceding discussion is extended to discrete abelian and nonabelian groups such as the mapping class groups of topological geons. For twists involving nonabelian groups the emergent spacetimes are nonassociative.Comment: 20 page

Attracting Interest: Dynamic Displays of Proceptivity Increase the Attractiveness of Men and Women

Proceptive signals may influence judgments of opposite-sex attractiveness because these signals indicate high mate quality and/or non-threatening behavior but they may also signal high probable rate of return for mating effort. If so, individuals observing these signals may be sensitive to where the signals are directed to; signals directed toward other individuals may not predict what signals would be directed toward the observer. To explore these possibilities I made use of video stimuli composed of mock interviews with actors. Each actor did one proceptive and one unreceptive interview. Each interview was presented as being directed toward participants or toward an opposite sex interviewer. Proceptivity enhanced the attractiveness of opposite-sex actors and an interaction between proceptive state and signal direction was found, with this pattern varying substantially between actors. The possibility that this variation is mediated by the physical attractiveness and sex of the actors will be discussed

Extremal Problems in Bergman Spaces and an Extension of Ryabykh's Theorem

We study linear extremal problems in the Bergman space $A^p$ of the unit disc for $p$ an even integer. Given a functional on the dual space of $A^p$ with representing kernel $k \in A^q$, where $1/p + 1/q = 1$, we show that if the Taylor coefficients of $k$ are sufficiently small, then the extremal function $F \in H^{\infty}$. We also show that if $q \le q_1 < \infty$, then $F \in H^{(p-1)q_1}$ if and only if $k \in H^{q_1}$. These results extend and provide a partial converse to a theorem of Ryabykh.Comment: 16 pages. To appear in the Illinois Journal of Mathematic

A decision support model for construction cash flow management

The excessive level of construction business failures and their association with financial difficulties has placed financial management in the forefront of many business imperatives. This has highlighted the importance of cash flow forecasting and management that has given rise to the development of several forecasting models. The traditional approach to the use of project financial models has been largely a project-oriented perspective. However, the dominating role of “project economics” in shaping “corporate economics” tends to place the corporate strategy at the mercy of the projects. This article approaches the concept of cash flow forecasting and management from a fresh perspective. Here, the use of forecasting models is extended beyond their traditional role as a guideline for monitoring and control of progress. They are regarded as tools for driving the project in the direction of corporate goals. The work is based on the premise that the main parties could negotiate the terms and attempt to complement their priorities. As part of this approach, a model is proposed for forecasting and management of project cash flow. The mathematical component of the model integrates three modules: an exponential and two fourth-degree polynomials. The model generates a forecast by potentially combining the outcome of data analysis with the experience and knowledge of the forecaster/organization. In light of corporate objectives, the generated forecast is then manipulated and replaced by a range of favorable but realistic cash flow profiles. Finally, through a negotiation with other parties, a compromised favorable cash flow is achieved. This article will describe the novel way the model is used as a decision support tool. Although the structure of the model and its mathematical components are described in detail, the data processing and analysis parts are briefly described and referenced accordingly. The viability of the model and the approach are demonstrated by means of a scenario