On the Asymptotic Behavior of the Ratio between the Numbers of Binary Primitive and Irreducible Polynomials

This work was presented in part at the 8th International Conference on Finite Fields and Applications Fq^8 , Melbourne, Australia, 9-13 July, 2007.

Discriminant Sets of Families of Hyperbolic Polynomials of Degree 4 and 5

∗ Research partially supported by INTAS grant 97-1644

Managing Interval Resources in Automated Planning

In this paper RDPPLan, a model for planning with quantitative resources specified as numerical intervals, is presented. Nearly all existing models of planning with resources require to specify exact values for updating resources modified by actions execution. In other words these models cannot deal with more realistic situations in which the resources quantities are not completely known but are bounded by intervals. The RDPPlan model allow to manage domains more tailored to real world, where preconditions and effects over quantitative resources can be specified by intervals of values, in addition mixed logical/quantitative and pure numerical goals can be posed. RDPPlan is based on non directional search over a planning graph, like DPPlan, from which it derives, it uses propagation rules which have been appropriately extended to the management of resource intervals. The propagation rules extended with resources must verify invariant properties over the planning graph which have been proven by the authors and guarantee the correctness of the approach. An implementation of the RDPPlan model is described with search strategies specifically developed for interval resources.

Percent in a Nutshell …

Ironically, the “learning of percent” is one of the most problematic aspects of school mathematics. In our view, these difficulties are not associated with the arithmetic aspects of the “percent problems”, but mostly with two methodological issues: firstly, providing students with a simple and accurate understanding of the rationale behind the use of percent, and secondly - overcoming the psychological complexities of the fluent and comprehensive understanding by the students of the sometimes specific wordings of “percent problems”. Before we talk about percent, it is necessary to acquaint students with a much more fundamental and important (regrettably, not covered by the school syllabus) classical concepts of quantitative and qualitative comparison of values, to give students the opportunity to learn the relevant standard terminology and become accustomed to conventional turns of speech. Further, it makes sense to briefly touch on the issue (important in its own right) of different representations of numbers. Percent is just one of the technical, but common forms of data representation: p% = p × % = p × 0.01 = p × 1/100 = p/100 = p × 10-2 "Percent problems” are involved in just two cases: I. The ratio of a variation m to the standard M II. The relative deviation of a variation m from the standard M The hardest and most essential in each specific "percent problem” is not the routine arithmetic actions involved, but the ability to figure out, to clearly understand which of the variables involved in the problem instructions is the standard and which is the variation. And in the first place, this is what teachers need to patiently and persistently teach their students. As a matter of fact, most primary school pupils are not yet quite ready for the lexical specificity of “percent problems”. ....Math teachers should closely, hand in hand with their students, carry out a linguistic analysis of the wording of each problem ... Schoolchildren must firmly understand that a comparison of objects is only meaningful when we speak about properties which can be objectively expressed in terms of actual numerical characteristics. In our opinion, an adequate acquisition of the teaching unit on percent cannot be achieved in primary school due to objective psychological specificities related to this age and because of the level of general training of students. Yet, if we want to make this topic truly accessible and practically useful, it should be taught in high school. A final question to the reader (quickly, please): What is greater: % of e or e% of Pi

Services for Content Creation and Presentation in an Iconographical Digital Library

Content creation and presentation are key activities in a multimedia digital library (MDL). The proper design and intelligent implementation of these services provide a stable base for overall MDL functionality. This paper presents the framework and the implementation of these services in the latest version of the “Virtual Encyclopaedia of Bulgarian Iconography” multimedia digital library. For the semantic description of the iconographical objects a tree-based annotation template is implemented. It provides options for autocompletion, reuse of values, bilingual entering of data, automated media watermarking, resizing and conversing. The paper describes in detail the algorithm for automated appearance of dependent values for different characteristics of an iconographical object. An algorithm for avoiding duplicate image objects is also included. The service for automated appearance of new objects in a collection after their entering is included as an important part of the content presentation. The paper also presents the overall service-based architecture of the library, covering its main service panels, repositories and their relationships. The presented vision is based on a long-term observation of the users’ preferences, cognitive goals, and needs, aiming to find an optimal functionality solution for the end users.