Search results for "Rational number"
showing 10 items of 31 documents
Problemas multiplicativos relacionados con la división de fracciones : un estudio sobre su enseñanza y aprendizaje
2013
Los estudiantes tienen dificultades para asociar el enunciado de un problema multiplicativo con la operación que permite resolverlo; esta investigación identifica los tipos de problemas multiplicativos que los estudiantes reconocen como de división de fracciones. Mediante el análisis histórico-epistemológico de textos de enseñanza sobre tres épocas históricas y ocho períodos diferentes, se obtiene un listado de variables de enseñanza (algoritmos, sentidos de uso de fracción y de división de fracciones, representaciones, problemas), así como los valores de dichas variables. Se localizan en los textos consultados algunas reglas particulares y seis algoritmos generales, cuyo predominio ha vari…
Hartmanis-Stearns Conjecture on Real Time and Transcendence
2012
Hartmanis-Stearns conjecture asserts that any number whose decimal expansion can be computed by a multitape Turing machine is either rational or transcendental. After half a century of active research by computer scientists and mathematicians the problem is still open but much more interesting than in 1965.
Decision Under Uncertainty: An Experimental View
2010
This work (experimental research) is based on Prospect theory, which was developed by D. Kahneman and A. Tversky in 1979. This is one the most quoted and best-documented point of view in economic psychology. First of all, it replaces, once again, the notion of utility with value. But value is defined in terms of gains and losses and this, according with an irrational human tendency to be less willing to gamble with profits than with losses. So, we discover the great importance of these assumptions in the field of risk individual decision-making. n experimental study was conducted to examine the influence of elaboration and the way in which alternatives are phased on decision. Subjects were …
STURMIAN WORDS AND AMBIGUOUS CONTEXT-FREE LANGUAGES
1990
If x is a rational number, 0<x≤1, then A(x)c is a context-free language, where A(x) is the set of factors of the infinite Sturmian words with asymptotic density of 1’s smaller than or equal to x. We also prove a “gap” theorem i.e. A(x) can never be an unambiguous co-context-free language. The “gap” theorem is established by proving that the counting generating function of A(x) is transcendental. We show some links between Sturmian words, combinatorics and number theory.
Central idempotents and units in rational group algebras of alternating groups
1998
Let ℚAn be the group algebra of the alternating group over the rationals. By exploiting the theory of Young tableaux, we give an explicit description of the minimal central idempotents of ℚAn. As an application we construct finitely many generators for a subgroup of finite index in the centre of the group of units of ℚAn.
«Widrige Winde»: Der Abbruch der schonischen Expedition aus der Sicht des preußischen Gesandten, des Freiherrn Friedrich Ernst von Cnyphausen
2017
There are two interpretations of Peter the Great’s motives for refusing to land on the Swedish island of Schonen in historiography: that the tsar feared unforeseen military risks and that he did not trust his allies, Denmark and Great Britain. In this article, the author attempts to analyse in a more detailed way the reasons and consequences for the mistrust in the Northern Alliance by looking at communications by Baron Friedrich Ernst von Cnyphausen, the Prussian ambassador in Copenhagen. It is shown that the Russophobic hysteria which grasped the Danish royal court in September 1716 looks completely irrational when we consider parallel attitudes in the Prussian court. Cnyphausen does not …
Resonance between Cantor sets
2007
Let $C_a$ be the central Cantor set obtained by removing a central interval of length $1-2a$ from the unit interval, and continuing this process inductively on each of the remaining two intervals. We prove that if $\log b/\log a$ is irrational, then \[ \dim(C_a+C_b) = \min(\dim(C_a) + \dim(C_b),1), \] where $\dim$ is Hausdorff dimension. More generally, given two self-similar sets $K,K'$ in $\RR$ and a scaling parameter $s>0$, if the dimension of the arithmetic sum $K+sK'$ is strictly smaller than $\dim(K)+\dim(K') \le 1$ (``geometric resonance''), then there exists $r<1$ such that all contraction ratios of the similitudes defining $K$ and $K'$ are powers of $r$ (``algebraic resonance…
Codimension growth of two-dimensional non-associative algebras
2007
Let F be a field of characteristic zero and let A be a two-dimensional non-associative algebra over F. We prove that the sequence c n (A), n =1,2,..., of codimensions of A is either bounded by n + 1 or grows exponentially as 2 n . We also construct a family of two-dimensional algebras indexed by rational numbers with distinct T-ideals of polynomial identities and whose codimension sequence is n + 1, n > 2.
Burrows-Wheeler transform and Run-Length Enconding
2017
In this paper we study the clustering effect of the Burrows-Wheeler Transform (BWT) from a combinatorial viewpoint. In particular, given a word w we define the BWT-clustering ratio of w as the ratio between the number of clusters produced by BWT and the number of the clusters of w. The number of clusters of a word is measured by its Run-Length Encoding. We show that the BWT-clustering ratio ranges in ]0, 2]. Moreover, given a rational number \(r\,\in \,]0,2]\), it is possible to find infinitely many words having BWT-clustering ratio equal to r. Finally, we show how the words can be classified according to their BWT-clustering ratio. The behavior of such a parameter is studied for very well-…
Learning with confidence
1996
Herein we investigate learning in the limit where confidence in the current conjecture accrues with time. Confidence levels are given by rational numbers between 0 and 1. The traditional requirement that for learning in the limit is that a device must converge (in the limit) to a correct answer. We further demand that the associated confidence in the answer (monotonically) approach 1 in the limit. In addition to being a more realistic model of learning, our new notion turns out to be a more powerful as well. In addition, we give precise characterizations of the classes of functions that are learnable in our new model(s).