Search results for "Numbers"
showing 10 items of 128 documents
Other patterns for the first and second order rational solutions to the KPI equation
2022
We present rational solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of polynomials in x, y and t depending on several real parameters. We get an infinite hierarchy of rational solutions written as a quotient of a polynomial of degree 2N (N + 1) − 2 in x, y and t by a polynomial of degree 2N (N + 1) in x, y and t, depending on 2N − 2 real parameters for each positive integer N. We construct explicit expressions of the solutions in the simplest cases N = 1 and N = 2 and we study the patterns of their modulus in the (x, y) plane for different values of time t and parameters. In particular, in the study of these solutions, we see the appearance not yet observed of three pairs of…
From particular polynomials to rational solutions to the KPI equation
2022
We construct solutions to the Kadomtsev-Petviashvili equation (KPI) from particular polynomials. We obtain rational solutions written as a second derivative with respect to the variable x of a logarithm of a determinant of order n. So we get with this method an infinite hierarchy of rational solutions to the KPI equation. We give explicitly the expressions of these solutions for the first five orders.
Rational solutions of order N to the KPI equation with multi-parameters and the explicit case of order 3
2022
We present multiparametric rational solutions to the Kadomtsev-Petviashvili equation (KPI). These solutions of order N depend on 2N − 2 real parameters. Explicit expressions of the solutions at order 3 are given. They can be expressed as a quotient of a polynomial of degree 2N (N + 1) − 2 in x, y and t by a polynomial of degree 2N (N + 1) in x, y and t, depending on 2N − 2 real parameters. We study the patterns of their modulus in the (x,y) plane for different values of time t and parameters.
Solutions to the Gardner equation with multiparameters and the rational case
2022
We construct solutions to the Gardner equation in terms of trigonometric and hyperbolic functions, depending on several real parameters. Using a passage to the limit when one of these parameters goes to 0, we get, for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 3. We easily deduce solutions to the mKdV equation in terms of wronskians as well as rational solutions depending on 2N real parameters.
Existence de points fixes enlacés à une orbite périodique d'un homéomorphisme du plan
1992
Let f be an orientation-preserving homeomorphism of the plane such that f-Id is contracting. Under these hypotheses, we establish the existence, for every periodic orbit, of a fixed point which has nonzero linking number with this periodic orbit.
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…
Impact of cardiopulmonary resuscitation on a cannot intubate, cannot oxygenate condition: a randomised crossover simulation research study of the int…
2019
ObjectivesDuring a ‘cannot intubate, cannot oxygenate’ situation, asphyxia can lead to cardiac arrest. In this stressful situation, two complex algorithms facilitate decision-making to save a patient’s life: difficult airway management and cardiopulmonary resuscitation. However, the extent to which competition between the two algorithms causes conflicts in the execution of pivotal treatment remains unknown. Due to the rare incidence of this situation and the very low feasibility of such an evaluation in clinical reality, we decided to perform a randomised crossover simulation research study. We propose that even experienced healthcare providers delay cricothyrotomy, a lifesaving approach, d…
Numbers and time doubly dissociate
2011
The magnitude dimensions of number, time and space have been suggested to share some common magnitude processing, which may imply symmetric interaction among dimensions. Here we challenge these suggestions by presenting a double dissociation between two neuropsychological patients with left (JT) and right (CB) parietal lesions and selective impairment of number and time processing respectively. Both patients showed an influence of task-irrelevant number stimuli on time but not space processing. In JT otherwise preserved time processing was severely impaired in the mere presence of task-irrelevant numbers, which themselves could not be processed accurately. In CB, impaired temporal estimatio…
Perceiving numbers alters time perception.
2008
The representation of time, space and numbers are strictly linked in the primate's cognitive system. Here we show that merely looking at number symbols biases a temporal judgment on their duration depending upon the number's magnitude. In a first experiment, a group of healthy subjects was submitted to a time estimation task, requiring to judge whether the duration of a test stimulus was longer or shorter than that of a previous reference fixed stimulus (digit 5; duration 300 ms). Test stimuli were the digits 1, 5 and 9 ranging between 250 and 350 ms. The main results showed that temporal perception was biased according to the magnitude expressed by the digit: low digits (i.e. 1) leading to…
Skaitļu teorija: lekcijas, lasītas Latvijas Universitātes Matemātikas un dabas zinātņu fakultātē
1936
Lekcijas sakārtojis Fogels, Ernests ; rediģējis Lūsis, Arvīds.