Search results for "55"
showing 10 items of 2320 documents
A Geometrical Three-Ring-Based Model for MIMO Mobile-to-Mobile Fading Channels in Cooperative Networks
2011
Published version of an article published in the journal: Eurasip Journal on Advances in Signal Processing. Also available from the publisher at: http://dx.doi.org/10.1155/2011/892871. OA This paper deals with the modeling and analysis of narrowband multiple-input multiple-output (MIMO) mobile-to-mobile (M2M) fading channels in relay-based cooperative networks. In the transmission links from the source mobile station to the destination mobile station via the mobile relay, non-line-of-sight (NLOS) propagation conditions are taken into account. A stochastic narrowband MIMO M2M reference channel model is derived from the geometrical three-ring scattering model, where it is assumed that an infi…
Multicenter clinical trial of ultrasonic circular cyclo coagulation in patients with open-angle glaucoma: One year results
2014
International audience; Purpose: To evaluate the efficacy and safety of the Ultrasonic Circular Cyclo Coagulation (UC3) procedure with one year of follow-up. Methods: Prospective non comparative interventional clinical study performed in 9 French glaucoma centers. Fifty-two eyes of 52 patients with open-angle glaucoma, intraocular pressure (IOP) > 21 mmHg, an average of 1.7 failed previous surgeries and an average of 3.7 hypotensive medications were insonified with a therapy probe comprising 6 piezoelectric transducers. The 6 transducers were activated, 24 patients (group 1) were treated with a 4 seconds exposure time for each shot and 28 patients (group 2) with a 6 seconds exposure time. C…
Solutions of the LPD equation and multi-parametric rogue waves
2022
Quasi-rational solutions to the Lakshmanan Porsezian Daniel equation are presented. We construct explicit expressions of these solutions for the first orders depending on real parameters. We study the patterns of these configurations in the (x, t) plane in function of the different parameters. We observe in the case of order 2, three rogue waves which move according to the two parameters. In the case of order 3, six rogue waves are observed with specific configurations moving according to the four parameters.
From particular polynomials to rational solutions to the mKdV equation
2022
Rational solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of determinants involving certain particular polynomials. This gives a very efficient method to construct solutions. We construct very easily explicit expressions of these rational solutions for the first orders n = 1 until 10.
N order solutions with multi-parameters to the Boussinesq and KP equations and the degenerate rational case
2021
From elementary exponential functions which depend on several parameters, we construct multi-parametric solutions to the Boussinesq equation. When we perform a passage to the limit when one of these parameters goes to 0, we get rational solutions as a quotient of a polynomial of degree N (N + 1) − 2 in x and t, by a polynomial of degree N (N + 1) in x and t for each positive integer N depending on 3N parameters. We restrict ourself to give the explicit expressions of these rational solutions for N = 1 until N = 3 to shortened the paper. We easily deduce the corresponding explicit rational solutions to the Kadomtsev Petviashvili equation for the same orders from 1 to 3.
From particular polynomials to rational solutions to the PII equation
2022
The Painlevé equations were derived by Painlevé and Gambier in the years 1895 − 1910. Given a rational function R in w, w ′ and analytic in z, they searched what were the second order ordinary differential equations of the form w ′′ = R(z, w, w ′) with the properties that the singularities other than poles of any solution or this equation depend on the equation only and not of the constants of integration. They proved that there are fifty equations of this type, and the Painlevé II is one of these. Here, we construct solutions to the Painlevé II equation (PII) from particular polynomials. We obtain rational solutions written as a derivative with respect to the variable x of a logarithm of a…
Multi-parameters rational solutions to the mKdV equation
2021
N-order solutions to the modified Korteweg-de Vries (mKdV) equation are given in terms of a quotient of two wronskians of order N depending on 2N real parameters. When one of these parameters goes to 0, we succeed to get for each positive integer N , rational solutions as a quotient of polynomials in x and t depending on 2N real parameters. We construct explicit expressions of these rational solutions for orders N = 1 until N = 6.
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.