Search results for "Recursion"
showing 10 items of 61 documents
Strategien bei Problemen mit rekursiver Lösung
1989
Recursion is not only a means for describing mathematical concepts, it is also an important problem solving tool in both mathematics and computer sciences. Recursion is the object of interest in our research project. In this article, we are going to report on an investigation aiming at the identification of strategies 7th and 8th graders use while coping with the recursive TOWER OFHANOI problem. Our hypothesis is that there are preliminary concepts for the concept of recursion which may vary for different students. We will describe some preliminary concepts in this paper.
Rasiowa–Sikorski Sets and Forcing
2018
The paper is concerned with the problem of building models for first-order languages from the perspective of the classic paper of Rasiowa and Sikorski (1950). The central idea, due to Rasiowa and Sikorski and developed in this paper, is constructing first-order models from individual variables. The notion of a Rasiowa–Sikorski set of formulas of an arbitrary language L is introduced. Investigations are confined to countable languages. Each Rasiowa–Sikorski set defines a countable model for L. Conversely, each countable model for L is determined, up to isomorphism, by some Rasiowa–Sikorski set. Consequences of these facts are investigated.
Tridiagonality, supersymmetry and non self-adjoint Hamiltonians
2019
In this paper we consider some aspects of tridiagonal, non self-adjoint, Hamiltonians and of their supersymmetric counterparts. In particular, the problem of factorization is discussed, and it is shown how the analysis of the eigenstates of these Hamiltonians produce interesting recursion formulas giving rise to biorthogonal families of vectors. Some examples are proposed, and a connection with bi-squeezed states is analyzed.
On the impact of forgetting on learning machines
1995
People tend not to have perfect memories when it comes to learning, or to anything else for that matter. Most formal studies of learning, however, assume a perfect memory. Some approaches have restricted the number of items that could be retained. We introduce a complexity theoretic accounting of memory utilization by learning machines. In our new model, memory is measured in bits as a function of the size of the input. There is a hierarchy of learnability based on increasing memory allotment. The lower bound results are proved using an unusual combination of pumping and mutual recursion theorem arguments. For technical reasons, it was necessary to consider two types of memory : long and sh…
Logic, Computing and Biology
2015
Logic and Computing are appropriate formal languages for Biology, and we may well be surprised by the strong analogy between software and DNA, and between hardware and the protein machinery of the cell. This chapter examines to what extent any biological entity can be described by an algorithm and, therefore, whether the Turing machine and the halting problem concepts apply. Last of all, I introduce the concepts of recursion and algorithmic complexity, both from the field of computer science, which can help us understand and conceptualise biological complexity.
Bicommutants of reduced unbounded operator algebras
2009
The unbounded bicommutant $(\mathfrak M_{E'})''$ of the {\em reduction} of an O*-algebra $\MM$ via a given projection $E'$ weakly commuting with $\mathfrak M$ is studied, with the aim of finding conditions under which the reduction of a GW*-algebra is a GW*-algebra itself. The obtained results are applied to the problem of the existence of conditional expectations on O*-algebras.
Induced and reduced unbounded operator algebras
2012
The induction and reduction precesses of an O*-vector space \({{\mathfrak M}}\) obtained by means of a projection taken, respectively, in \({{\mathfrak M}}\) itself or in its weak bounded commutant \({{\mathfrak M}^\prime_{\rm w}}\) are studied. In the case where \({{\mathfrak M}}\) is a partial GW*-algebra, sufficient conditions are given for the induced and the reduced spaces to be partial GW*-algebras again.
Reduction of the glass transition temperature in polymer films: A molecular-dynamics study
2001
We present results of molecular dynamics (MD) simulations for a non-entangled polymer melt confined between two completely smooth and repulsive walls, interacting with inner particles via the potential $U_{\rm wall}\myeq (\sigma/z)^9$, where $z \myeq |z_{\rm particle}-z_{\rm wall}|$ and $\sigma$ is (roughly) the monomer diameter. The influence of this confinement on the dynamic behavior of the melt is studied for various film thicknesses (wall-to-wall separations) $D$, ranging from about 3 to about 14 times the bulk radius of gyration. A comparison of the mean-square displacements in the film and in the bulk shows an acceleration of the dynamics due to the presence of the walls. %Consistent…
Understanding the challenges of rapid digital transformation : the case of COVID-19 pandemic in higher education
2021
Rapid digital transformation is taking place due to the COVID-19 pandemic, forcing organisations and higher educational institutions to change their working and learning culture. This study explores the challenges of rapid digital transformation arising during the pandemic in the higher education context. This research used the Q-methodology to understand the nine challenges that higher education encountered, perceived differently as four main patterns: (1) Digital-nomad enterprise; (2) Corporate-collectivism; (3) Well-being-oriented; and (4) Pluralistic. This study broadens the current understanding of digital transformation, especially in higher education. The nine challenges and four pat…
Stationary sets of the mean curvature flow with a forcing term
2020
We consider the flat flow approach for the mean curvature equation with forcing in an Euclidean space $\mathbb R^n$ of dimension at least 2. Our main results states that tangential balls in $\mathbb R^n$ under any flat flow with a bounded forcing term will experience fattening, which generalizes the result by Fusco, Julin and Morini from the planar case to higher dimensions. Then, as in the planar case, we are able to characterize stationary sets in $\mathbb R^n$ for a constant forcing term as finite unions of equisized balls with mutually positive distance.