Conflicts in the learning of real numbers and limits

question: "Is 0.999... (nought point nine recurring) equal to one, or just less than one?". Many answers contained infinitesimal concepts: "The same, because the difference between them is infinitely small." " The same, for at infinity it comes so close to one it can be considered the same." "Just less than one, but it is the nearest you can get to one without actually saying it is one." "Just less than one, but the difference between it and one is infinitely small." The majority of students thought that 0.999... was less than one. It may be that a few students had been taught using infinitesimal concepts, or that the phrase “just less than one ” had connotations for the students different from those intended by the questioner; but it seems more likely that the answers represent the students ’ own rationalisations made in an attempt to resolve conflicts inherent in the students ’ previous experience of limiting processes. Some conscious and subconscious conflicts Most of the mathematics met in secondary school consists of sophisticated idea

Concept image and concept definition in mathematics with particular reference to limits and continuity

The concept image consists of all the cognitive structure in the individual's mind that is associated with a given concept. This may not be globally coherent and may have aspects which are quite different from the formal concept definition. The development of limits and continuity, as taught in secondary school and university, are considered. Various investigations are reported which demonstrate individual concept images differing from the formal theory and containing factors which cause cognitive conflict

Symmetry of Magnetically Ordered Quasicrystals

The notion of magnetic symmetry is reexamined in light of the recent observation of long range magnetic order in icosahedral quasicrystals [Charrier et al., Phys. Rev. Lett. 78, 4637 (1997)]. The relation between the symmetry of a magnetically-ordered (periodic or quasiperiodic) crystal, given in terms of a ``spin space group,'' and its neutron diffraction diagram is established. In doing so, an outline of a symmetry classification scheme for magnetically ordered quasiperiodic crystals is provided. Predictions are given for the expected diffraction patterns of magnetically ordered icosahedral crystals, provided their symmetry is well described by icosahedral spin space groups.Comment: 5 pages. Accepted for publication in Phys. Rev. Letter

A Uniform Approach to Antiferromagnetic Heisenberg Spins on Low Dimensional Lattices

Using group theoretical methods we show for both the triangular and square lattices that in the continuum limit the antiferromagnetic order parameter lives on SO3 without respect of the initial lattice. For the antiferromagnetic chain we recover the Haldane decomposition. This order parameter interacts with a local gauge field rather than with a global one as implicitly suggested in the literature which in our approach appears in a rather natural manner. In fact this merely corresponds to a novel extension of the spin group by a local gauge field. This analysis based on the real division algebras applies to low dimensional lattices.Comment: 5 pages; REVTeX

Diffractive point sets with entropy

After a brief historical survey, the paper introduces the notion of entropic model sets (cut and project sets), and, more generally, the notion of diffractive point sets with entropy. Such sets may be thought of as generalizations of lattice gases. We show that taking the site occupation of a model set stochastically results, with probabilistic certainty, in well-defined diffractive properties augmented by a constant diffuse background. We discuss both the case of independent, but identically distributed (i.i.d.) random variables and that of independent, but different (i.e., site dependent) random variables. Several examples are shown.Comment: 25 pages; dedicated to Hans-Ude Nissen on the occasion of his 65th birthday; final version, some minor addition

Ecological genomics: steps towards unraveling the genetic basis of inducible defenses in Daphnia

Little is known about the genetic mechanisms underlying inducible defenses. Recently, the genome of Daphnia pulex, a model organism for defense studies, has been sequenced. Building on the genome information, recent preliminary studies in BMC Developmental Biology and BMC Molecular Biology have assessed gene response profiles in Daphnia under predation pressure. We review the significance of the findings and highlight future research perspectives

Methodological considerations in the analysis of fecal glucocorticoid metabolites in tufted capuchins (Cebus apella)

Analysis of fecal glucocorticoid (GC) metabolites has recently become the standard method to monitor adrenocortical activity in primates noninvasively. However, given variation in the production, metabolism, and excretion of GCs across species and even between sexes, there are no standard methods that are universally applicable. In particular, it is important to validate assays intended to measure GC production, test extraction and storage procedures, and consider the time course of GC metabolite excretion relative to the production and circulation of the native hormones. This study examines these four methodological aspects of fecal GC metabolite analysis in tufted capuchins (Cebus apella). Specifically, we conducted an adrenocorticotrophic hormone (ACTH) challenge on one male and one female capuchin to test the validity of four GC enzyme immunoassays (EIAs) and document the time course characterizing GC me- tabolite excretion in this species. In addition, we compare a common field-friendly technique for extracting fecal GC metabolites to an established laboratory extraction methodology and test for effects of storing “field extracts” for up to 1 yr. Results suggest that a corticosterone EIA is most sensitive to changes in GC production, provides reliable measures when extracted according to the field method, and measures GC metabolites which remain highly stable after even 12 mo of storage. Further, the time course of GC metabolite excretion is shorter than that described yet for any primate taxa. These results provide guidelines for studies of GCs in tufted capuchins, and underscore the importance of validating methods for fecal hormone analysis for each species of interest

Cluster analysis of higher-education competitiveness in selected European countries

The subject of research in this paper is higher-education competitiveness on account of its impact on the enhancement of social and economic competitiveness, as well as on the growth of human capital and creation of social knowledge. The purpose of this paper is to group the selected European countries according to higher-education competitiveness, by means of the hierarchical cluster analysis method, with a special focus on the position of Serbia. Higher-education competitiveness in the chosen countries is analysed by means of three indicators of competitiveness: the ratio of the number of students per number of inhabitants, the number of students per number of employed, as well as the amount of budgetary funds allocated per student. The research results indicate different higher-education competitiveness in the analysed countries and also the fact that, according to this analysis, Serbia is in the group of countries with low competitiveness of higher education

Diffusion in liquid mixtures

The understanding of transport and mixing in fluids in the presence and in the absence of external fields and reactions represents a challenging topic of strategic relevance for space exploration. Indeed, mixing and transport of components in a fluid are especially important during long-term space missions where fuels, food and other materials, needed for the sustainability of long space travels, must be processed under microgravity conditions. So far, the processes of transport and mixing have been investigated mainly at the macroscopic and microscopic scale. Their investigation at the mesoscopic scale is becoming increasingly important for the understanding of mass transfer in confined systems, such as porous media, biological systems and microfluidic systems. Microgravity conditions will provide the opportunity to analyze the effect of external fields and reactions on optimizing mixing and transport in the absence of the convective flows induced by buoyancy on Earth. This would be of great practical applicative relevance to handle complex fluids under microgravity conditions for the processing of materials in space