Children's performance estimation in mathematics and science tests over a school year: A pilot study

The metacognitve ability to accurately estimate ones performance in a test, is assumed to be of central importance for initializing task-oriented effort. In addition activating adequate problem-solving strategies, and engaging in efficient error detection and correction. Although school children's' ability to estimate their own performance has been widely investigated, this was mostly done under highly-controlled, experimental set-ups including only one single test occasion. Method: The aim of this study was to investigate this metacognitive ability in the context of real achievement tests in mathematics. Developed and applied by a teacher of a 5th grade class over the course of a school year these tests allowed the exploration of the variability of performance estimation accuracy as a function of test difficulty. Results: Mean performance estimations were generally close to actual performance with somewhat less variability compared to test performance. When grouping the children into three achievement levels, results revealed higher accuracy of performance estimations in the high achievers compared to the low and average achievers. In order to explore the generalization of these findings, analyses were also conducted for the same children's tests in their science classes revealing a very similar pattern of results compared to the domain of mathematics. Discussion and Conclusion: By and large, the present study, in a natural environment, confirmed previous laboratory findings but also offered additional insights into the generalisation and the test dependency of students' performances estimations.

A new model construction by making a detour via intuitionistic theories II: Interpretability lower bound of Feferman's explicit mathematics T0

We partially solve a long-standing problem in the proof theory of explicit mathematics or the proof theory in general. Namely, we give a lower bound of Feferman’s system T0 of explicit mathematics (but only when formulated on classical logic) with a concrete interpretat ion of the subsystem Σ12-AC+ (BI) of second order arithmetic inside T0. Whereas a lower bound proof in the sense of proof-theoretic reducibility or of ordinalanalysis was already given in 80s, the lower bound in the sense of interpretability we give here is new. We apply the new interpretation method developed by the author and Zumbrunnen (2015), which can be seen as the third kind of model construction method for classical theories, after Cohen’s forcing and Krivine’s classical realizability. It gives us an interpretation between classical theories, by composing interpretations between intuitionistic theories.

State Convergence Theory Applied to a Delayed Teleoperation System

State convergence is a control strategy that was proposed in the early 2000s to ensure stability and transparency in a teleoperation system under specific control gains values. This control strategy has been implemented for a linear system with or without time delay. This paper represents the first attempt at demonstrating, theoretically and experimentantally, that this control strategy can also be applied to a nonlinear teleoperation system with n degrees of freedom and delay in the communication channel. It is assumed that the human operator applies a constant force on the local manipulator during the teleoperation. In addition, the interaction between the remote manipulator and the environment is considered passive. Communication between the local and remote sites is made by means of a communication channel with variable time delay. In this article the theory of Lyapunov-Krasovskii was used to demonstrate that the local-remote teleoperation system is asymptotically stable.

Earth’s Rotation: A Challenging Problem in Mathematics and Physics

A suitable knowledge of the orientation and motion of the Earth in space is a common need in various fields. That knowledge has been ever necessary to carry out astronomical observations, but with the advent of the space age, it became essential for making observations of satellites and predicting and determining their orbits, and for observing the Earth from space as well. Given the relevant role it plays in Space Geodesy, Earth rotation is considered as one of the three pillars of Geodesy, the other two being geometry and gravity. Besides, research on Earth rotation has fostered advances in many fields, such as Mathematics, Astronomy and Geophysics, for centuries. One remarkable feature of the problem is in the extreme requirements of accuracy that must be fulfilled in the near future, about a millimetre on the tangent plane to the planet surface, roughly speaking. That challenges all of the theories that have been devised and used to-date; the paper makes a short review of some of the most relevant methods, which can be envisaged as milestones in Earth rotation research, emphasizing the Hamiltonian approach developed by the authors. Some contemporary problems are presented, as well as the main lines of future research prospected by the International Astronomical Union/International Association of Geodesy Joint Working Group on Theory of Earth Rotation, created in 2013.

Computational Mathematics Abstracts /

Mode of access: Internet.

The Messenger of mathematics

Mode of access: Internet.

Engineering applications of higher mathematics,

Bibliography at end of each volume.

Journal of mathematics and physics /

Published: Baltimore, Md., -1968.

Sensitivity Analysis of Some Applied Probability Models

2000 Mathematics Subject Classi cation: Primary 90C31. Secondary 62C12, 62P05, 93C41.

A Didactic Model of Computer Supported Education in Higher Mathematics

Report published in the Proceedings of the National Conference on "Education and Research in the Information Society", Plovdiv, May, 2016

A fizikai matematika legújabb eredményei mint a közgazdaság-tudomány lehetséges vizsgálati eszközei (The newest results of physical mathematics as the possible investigation tools of economics)

A közgazdaság-tudomány számos problémája a fizika analóg modelljeinek segítségével nyert megoldást. A közgazdászok körében erőteljesen megoszlanak a vélemények, hogy a közgazdasági modellek mennyire redukálhatók a fizika, vagy más természettudományok eredményeire. Vannak,akik pontosan ezzel magyarázzák,hogy a mai mainstream közgazdasági elmélet átalakult alkalmazott matematikává,ami a gazdasági kérdéseket csak a társadalom-tudományi vonatkozásaitól eltekintve képes vizsgálni. Mások, e tanulmányszerzője is, viszont úgy vélekednek, hogy a közgazdasági problémák egy része, ahol lehetőség van a mérésre, jól modellezhetők a természettudományok technikai arzenáljával. A másik része, amelyekben nem lehet mérni,s tipikusan ilyenek a társadalomtudományi kérdések, ott sokkal komplexebb technikákra lesz szükség. Etanulmány célkitűzése, hogy felvázolja a fizika legújabb, az irreverzibilis dinamika, a relativitáselmélet és a kvantummechanika sztochasztikus matematikai összefüggéseit, amelyekből a közgazdászok választhatnak egy-egy probléma megfogalmazásában és megoldásában. Például az időoperátorok pontos értelmezése jelentős fordulatot hozhat a makroökonómiai elméletekben; vagy az eddigi statikus egyensúlyi referencia pontokat felválthatják a dinamikus,időben változó sztochasztikus egyensúlyi referenciafüggvények, ami forradalmian új megvilágításba helyezhet számos társadalomtudományi, s főleg nemegyensúlyi közgazdasági kérdést.A termodinamika és a biológiai evolúció fogalmait és definícióit Paul A. Samuelson (1947) már adaptálta a közgazdaságtanban, viszont a kvantummechanika legújabb eredményeit, az időoperátorokat stb. nem érintette. E cikk azokat a legújabb fizikai, kémiai és biológiai matematikai összefüggéseket foglalja össze,amelyek hasznosak lehetnek a közgazdasági modellek komplexebb megfogalmazásához. ___________________ The aim of this paper is to out line the newest results of physics,i.e.,the stochastic mathematical relations of relativity theory and quantum mechanics as well as irreversible dynamics which can be applied for some economic problems.For example,the correct interpretation of time operators using for the macroeconomic theories may provide a serious improvement in approach to the reality.The stochastic dynamic equilibrium reference functions will take over the role of recent static equilibrium reference points,which may also reveal some nonequilibrium questions of macroeconomics.The concepts and definitions of thermodynamics and biological evolution have been adopted in economics by Paul A. Samuelson, but he did not concern the newest results of quantum mechanics, e.g., the time operators. Now we do it.In addition, following Samuelson,we show that von Neumann growth model cannot be explained as a peculiar extension of thermodynamic irreversibility.

A mathematical resolution to log transformations and the binning effect in applied processing of data in flow cytometry

This dissertation develops a new mathematical approach that overcomes the effect of a data processing phenomenon known as “histogram binning” inherent to flow cytometry data. A real-time procedure is introduced to prove the effectiveness and fast implementation of such an approach on real-world data. The histogram binning effect is a dilemma posed by two seemingly antagonistic developments: (1) flow cytometry data in its histogram form is extended in its dynamic range to improve its analysis and interpretation, and (2) the inevitable dynamic range extension introduces an unwelcome side effect, the binning effect, which skews the statistics of the data, undermining as a consequence the accuracy of the analysis and the eventual interpretation of the data. ^ Researchers in the field contended with such a dilemma for many years, resorting either to hardware approaches that are rather costly with inherent calibration and noise effects; or have developed software techniques based on filtering the binning effect but without successfully preserving the statistical content of the original data. ^ The mathematical approach introduced in this dissertation is so appealing that a patent application has been filed. The contribution of this dissertation is an incremental scientific innovation based on a mathematical framework that will allow researchers in the field of flow cytometry to improve the interpretation of data knowing that its statistical meaning has been faithfully preserved for its optimized analysis. Furthermore, with the same mathematical foundation, proof of the origin of such an inherent artifact is provided. ^ These results are unique in that new mathematical derivations are established to define and solve the critical problem of the binning effect faced at the experimental assessment level, providing a data platform that preserves its statistical content. ^ In addition, a novel method for accumulating the log-transformed data was developed. This new method uses the properties of the transformation of statistical distributions to accumulate the output histogram in a non-integer and multi-channel fashion. Although the mathematics of this new mapping technique seem intricate, the concise nature of the derivations allow for an implementation procedure that lends itself to a real-time implementation using lookup tables, a task that is also introduced in this dissertation. ^