Propriedades dos sistemas de numeração: uma sequência didática em uma abordagem histórica

This paper aims to describe the construction and validation of a notebook of activities whose content is a didactic sequence that makes use of the study of ancient numbering systems as compared to the object of our decimal positional numbering system Arabic. This is on the assumption that the comparison with a system different from our own might provide a better understanding of our own numbering system, but also help in the process of arithmetic operations of addition, subtraction and multiplication, since it will force us to think in ways that are not routinely object of our attention. The systems covered in the study were the Egyptian hieroglyphic system of numbering, the numbering system Greek alphabet and Roman numbering system, always compared to our numbering system. The following teachung is presented structured in the form of our activities, so-called exercise set and common tasks around a former same numbering system. In its final stage of preparation, the sequence with the participation of 26 primary school teachers of basic education

Memórias das aritméticas da Emília: o ensino de aritmética entre 1920 e 1940

Pós-graduação em Educação Matemática - IGCE

Education pamphlets

A collection of miscellaneous pamphlets.

A singular function and its relation with the number systems involved in its definition

Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.

A novel approach to reducing number of sensing units for wearable gait analysis systems.

Gait analysis methods to estimate spatiotemporal measures, based on two, three or four gyroscopes attached on lower limbs have been discussed in the literature. The most common approach to reduce the number of sensing units is to simplify the underlying biomechanical gait model. In this study, we propose a novel method based on prediction of movements of thighs from movements of shanks. Datasets from three previous studies were used. Data from the first study (ten healthy subjects and ten with Parkinson's disease) were used to develop and calibrate a system with only two gyroscopes attached on shanks. Data from two other studies (36 subjects with hip replacement, seven subjects with coxarthrosis, and eight control subjects) were used for comparison with the other methods and for assessment of error compared to a motion capture system. Results show that the error of estimation of stride length compared to motion capture with the system with four gyroscopes and our new method based on two gyroscopes was close ( -0.8 ±6.6 versus 3.8 ±6.6 cm). An alternative with three sensing units did not show better results (error: -0.2 ±8.4 cm). Finally, a fourth that also used two units but with a simpler gait model had the highest bias compared to the reference (error: -25.6 ±7.6 cm). We concluded that it is feasible to estimate movements of thighs from movements of shanks to reduce number of needed sensing units from 4 to 2 in context of ambulatory gait analysis.

Tightened Lieb-Oxford Bound for Systems of Fixed Particle Number

The Lieb-Oxford bound is a constraint upon approximate exchange-correlation functionals. We explore a nonempirical tightening of that bound in both universal and electron number-dependent form. The test functional is PBE. Regarding both atomization energies (slightly worsened) and bond lengths (slightly improved), we find the PBE functional to be remarkably insensitive to the value of the Lieb-Oxford bound. This both rationalizes the use of the original Lieb-Oxford constant in PBE and suggests that enhancement factors more sensitive to sharpened constraints await discovery.

Stochastic stability for Markovian jump linear systems associated with a finite number of jump times

This paper deals with a stochastic stability concept for discrete-time Markovian jump linear systems. The random jump parameter is associated to changes between the system operation modes due to failures or repairs, which can be well described by an underlying finite-state Markov chain. In the model studied, a fixed number of failures or repairs is allowed, after which, the system is brought to a halt for maintenance or for replacement. The usual concepts of stochastic stability are related to pure infinite horizon problems, and are not appropriate in this scenario. A new stability concept is introduced, named stochastic tau-stability that is tailored to the present setting. Necessary and sufficient conditions to ensure the stochastic tau-stability are provided, and the almost sure stability concept associated with this class of processes is also addressed. The paper also develops equivalences among second order concepts that parallels the results for infinite horizon problems. (C) 2003 Elsevier B.V. All rights reserved.

Design of a reconfigurable pseudorandom number generator for use in intelligent systems

This paper deals with the design of a network-on-chip reconfigurable pseudorandom number generation unit that can map and execute meta-heuristic algorithms in hardware. The unit can be configured to implement one of the following five linear generator algorithms: a multiplicative congruential, a mixed congruential, a standard multiple recursive, a mixed multiple recursive, and a multiply-with-carry. The generation unit can be used both as a pseudorandom and a message passing-based server, which is able to produce pseudorandom numbers on demand, sending them to the network-on-chip blocks that originate the service request. The generator architecture has been mapped to a field programmable gate array, and showed that millions of numbers in 32-, 64-, 96-, or 128-bit formats can be produced in tens of milliseconds. (C) 2011 Elsevier B.V. All rights reserved.

On the number of critical periods for planar polynomial systems

In this paper we get some lower bounds for the number of critical periods of families of centers which are perturbations of the linear one. We give a method which lets us prove that there are planar polynomial centers of degree l with at least 2[(l - 2)/2] critical periods as well as study concrete families of potential, reversible and Lienard centers. This last case is studied in more detail and we prove that the number of critical periods obtained with our approach does not. increases with the order of the perturbation. (C) 2007 Elsevier Ltd. All rights reserved.

On the number of limit cycles in discontinuous piecewise linear differential systems with two pieces separated by a straight line

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Structure-activity relationship of mastoparan analogs: effects of the number and positioning of Lys residues on secondary structure, interaction with membrane-mimetic systems and biological activity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)