Search results for "mathematics"
showing 10 items of 22031 documents
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.
On the existence of at least a solution for functional integral equations via measure of noncompactness
2017
In this article, we use fixed-point methods and measure of noncompactness theory to focus on the problem of establishing the existence of at least a solution for the following functional integral equation ¶ \[u(t)=g(t,u(t))+\int_{0}^{t}G(t,s,u(s))\,ds,\quad t\in{[0,+\infty[},\] in the space of all bounded and continuous real functions on $\mathbb{R}_{+}$ , under suitable assumptions on $g$ and $G$ . Also, we establish an extension of Darbo’s fixed-point theorem and discuss some consequences.
Controlled polyhedral sweeping processes: existence, stability, and optimality conditions
2021
This paper is mainly devoted to the study of controlled sweeping processes with polyhedral moving sets in Hilbert spaces. Based on a detailed analysis of truncated Hausdorff distances between moving polyhedra, we derive new existence and uniqueness theorems for sweeping trajectories corresponding to various classes of control functions acting in moving sets. Then we establish quantitative stability results, which provide efficient estimates on the sweeping trajectory dependence on controls and initial values. Our final topic, accomplished in finite-dimensional state spaces, is deriving new necessary optimality and suboptimality conditions for sweeping control systems with endpoint constrain…
Minimality via second variation for microphase separation of diblock copolymer melts
2017
Abstract We consider a non-local isoperimetric problem arising as the sharp interface limit of the Ohta–Kawasaki free energy introduced to model microphase separation of diblock copolymers. We perform a second order variational analysis that allows us to provide a quantitative second order minimality condition. We show that critical configurations with positive second variation are indeed strict local minimizers of the problem. Moreover, we provide, via a suitable quantitative inequality of isoperimetric type, an estimate of the deviation from minimality for configurations close to the minimum in the L 1 {L^{1}} -topology.
Tracking of blood vessels motion from 4D-flow MRI data
2022
This paper presents a novel approach to track objects from 4D Flow MRI data. A salient feature of the proposed method is that it fully exploits the geometrical and dynamical nature of the information provided by this imaging modality. The underlying idea consists in formulating the tracking problem as a data assimilation problem, in which both position and velocity observations are extracted from the 4D Flow MRI data series. Optimal estate estimation is then performed in a sequential fashion via Kalman filtering. The capabilities of the method are extensively assessed in a numerical study involving synthetic and clinical data.
The infrastructure MESSy submodels GRID (v1.0) and IMPORT (v1.0)
2018
The coupling of Earth system model components, which work on different grids, into an Earth System Model (ESM) provokes the necessity to transfer data from one grid to another. Additionally, each of these model components might require data import onto its specific grid. Usually, one of two approaches is used: Either all input data is preprocessed to the employed grid, or the imported data is interpolated on-line, i.e. during model integration to the required grid. For the former, each change in the model resolution requires the re-preprocessing of all data. The latter option implies that in each model integration computing time is required for the grid mapping. If all components of an ESM …
"Table 1" of "First observation of an attractive interaction between a proton and a multi-strange baryon"
2019
The p$-$p $\oplus$ $\overline{\mathrm{p}}-\overline{\mathrm{p}}$ correlation function.
"Table 1" of "Measurement of the (anti-)$^{3}$He elliptic flow in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 5.02 TeV"
2020
Event-plane resolution $R_{\Psi_{2}}$ of the second harmonic as a function of the collision centrality.