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 P

Flowing sand - a possible physical realization of Directed Percolation

A simple model for flowing sand on an inclined plane is introduced. The model is related to recent experiments by Douady and Daerr [Nature 399, 241 (1999)] and reproduces some of the experimentally observed features. Avalanches of intermediate size appear to be compact, placing the critical behavior of the model into the universality class of compact directed percolation. On very large scales, however, the avalanches break up into several branches leading to a crossover from compact to ordinary directed percolation. Thus, systems of flowing granular matter on an inclined plane could serve as a first physical realization of directed percolation.Comment: 9 pages, 12 eps figure

Язык духов: параллели между рифмованной прозой (саджʻ) доисламских арабских прорицателей и речевым поведением шаманов

The speech behavior of soothsayers (kuhhān), who lived in pre-Islamic Arabia, was characterized by the use of rhymed and rhythmic prose, the formulaic structure of utterances and their enigmatic nature. Furthermore, their speech was ecstatically performed and featured a specific language that was different from the generally accepted mode of everyday communication. As a consequence, their utterances were perceived by their audiences as emanating from supernatural beings. The article draws a parallel between the speech peculiarities of the kuhhān and texts that serve for ‘communication’ with spirits in shamanic/shamanistic cultures. From a functional point of view, in both cases the texts exhibit a number of distinctive properties that mark sacred pronouncements dictated by otherworldly forces. There are also similarities in the contexts and circumstances of text production of soothsayers and shamans. The conclusions of the article can serve as another argument in favor of a typological affinity between these two groups of religious specialists. This affinity has previously been examined mainly through the prism of their social functions and non-verbal behavior. This article, on the other hand, emphasizes the linguistic characteristics of this affinity

GluA2-lacking AMPA receptors in hippocampal CA1 cell synapses: evidence from gene-targeted mice

The GluA2 subunit in heteromeric alpha-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) receptor channels restricts Ca2+ permeability and block by polyamines, rendering linear the current-voltage relationship of these glutamate-gated cation channels. Although GluA2-lacking synaptic AMPA receptors occur in GABA-ergic inhibitory neurons, hippocampal CA1 pyramidal cell synapses are widely held to feature only GluA2 containing AMPA receptors. A controversy has arisen from reports of GluA2-lacking AMPA receptors at hippocampal CA3-to-CA1 cell synapses and a study contesting these findings. Here we sought independent evidence for the presence of GluA2-lacking AMPA receptors in CA1 pyramidal cell synapses by probing the sensitivity of their gated cation channels in wild-type (WT) mice and gene-targeted mouse mutants to philanthotoxin, a specific blocker of GluA2-lacking AMPA receptors. The mutants either lacked GluA2 for maximal philanthotoxin sensitivity, or, for minimal sensitivity, expressed GluA1 solely in a Q/R site-edited version or not at all. Our comparative electrophysiological analyses provide incontrovertible evidence for the presence in wild-type CA1 pyramidal cell synapses of GluA2-less AMPA receptor channels. This article is part of a Special Issue entitled “Calcium permeable AMPARs in synaptic plasticity and disease.

On Diurnal and Annual Variations of Directional Detection Rates of Dark Matter

Direction sensitive direct detection of Weakly Interacting Massive Particles (WIMPs) as dark matter would provide an unambiguous non-gravitational signature of dark matter (DM). The diurnal variation of DM signal due to earth's rotation around its own axis can be a significant signature for galactic WIMPs. Because of particular orientation of earth's axis of rotation with respect to WIMP wind direction, the apparent direction of WIMP wind as observed at a detector can alter widely over a day. In this work we calculate the directional detection rates with their daily and yearly modulations in earth-bound dark matter experiments considering detailed features of the geometry and dynamics of the earth-sun system along with the solar motion in galactic frame. A separate halo model namely the dark disc model other than the usual standard halo model for dark matter halo is also considered and the results for two models are compared. We demonstrate the results for two types of gas detectors namely DRIFT (target material CS2) and NEWAGE (target material CF4) that use Time Projection Chamber techniques for measuring directionality of the recoil nucleus. The WIMP mass and recoil energy dependence of the daily variation of event rates are computed for specific detector and the sensitive ranges of mass and recoil energies for the considered detector are probed.Comment: 11 pages, 17 figure