Results 1 to 10 of about 1,325,951 (324)

Laplace's equation on convex polyhedra via the unified method. [PDF]

Proc Math Phys Eng Sci, 2015
We provide a new method to study the classical Dirichlet problem for Laplace's equation on a convex polyhedron. This new approach was motivated by Fokas’ unified method for boundary value problems. The central object in this approach is the global relation: an integral equation which couples the known boundary data and the unknown boundary values. This
Ashton AC.
europepmc   +5 more sources

The Unified Method: III Non-Linearizable Problems on the Interval [PDF]

Journal of Physics A: Mathematical and Theoretical, 2011
Boundary value problems for integrable nonlinear evolution PDEs formulated on the finite interval can be analyzed by the unified method introduced by one of the authors and used extensively in the literature.
A S Fokas, Fokas A S, Fokas A S, J Lenells, Lenells J   +4 more
core   +4 more sources

The Unified Method: I Non-Linearizable Problems on the Half-Line [PDF]

Journal of Physics A: Mathematical and Theoretical, 2011
Boundary value problems for integrable nonlinear evolution PDEs formulated on the half-line can be analyzed by the unified method introduced by one of the authors and used extensively in the literature.
A S Fokas, Bikbaev R F, Bona J L, Boutet de Monvel A, Coddington E A, Deconinck B Trogdon T Vasan V, Doschoris M, Fokas A S, Fokas A S, Fokas A S, Fokas A S, Fokas A S, Fokas A S, Fokas A S, Fokas A S Pelloni B, Habibullin I T, Its A R, J Lenells, Lenells J, Lenells J, Lenells J, Lenells J, Pelloni B, Smith D A, Smith D A, Tarasov V O, Vetra S   +26 more
core   +4 more sources

Application of the unified method to solve the Biswas–Arshed model

Results in Physics, 2022
We apply the unified method to retrieve optical soliton solutions of the Biswas–Arshed model (BAM) with the Kerr law nonlinearity in this paper. We first derive the ordinary differential form of this model from its partial differential form via a ...
Mohammad Safi Ullah, Alrazi Abdeljabbar, Harun-Or Roshid, M. Zulfikar Ali   +3 more
doaj   +2 more sources

Application of the unified method to solve the ion sound and Langmuir waves model

Heliyon, 2022
We present the unified method and use it to integrate the ion sound and Langmuir waves (ISLW) model to retrieve optical soliton solutions. Some new dynamical optical solitons involving the combo of rational, trigonometric, and hyperbolic function ...
Dulal Chandra Nandi, Mohammad Safi Ullah, Harun-Or- Roshid, M. Zulfikar Ali   +3 more
doaj   +2 more sources

The projection method: a unified formalism for community detection

Frontiers in Complex Systems
We present the class of projection methods for community detection that generalizes many popular community detection methods. In this framework, we represent each clustering (partition) by a vector on a high-dimensional hypersphere. A community detection
Martijn Gösgens, Remco van der Hofstad, Nelly Litvak   +2 more
doaj   +4 more sources

The Unified and Holistic Method Gamma (γ) for Inter-Annotator Agreement Measure and Alignment

Computational Linguistics, 2021
Agreement measures have been widely used in computational linguistics for more than 15 years to check the reliability of annotation processes. Although considerable effort has been made concerning categorization, fewer studies address unitizing, and when
Yann Mathet, Antoine Widlöcher, Jean-Philippe Métivier   +2 more
doaj   +2 more sources

The unified transform method for the Sasa–Satsuma equation on the half-line [PDF]

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2013
We implement the unified transform method to the initial-boundary value (IBV) problem of the Sasa–Satsuma equation on the half line. In addition to presenting the basic Riemann–Hilbert formalism, which linearizes this IBV problem, we also analyse the associated general Dirichlet to Neumann map using the so-called global relation.
Jian Xu, E. Fan
semanticscholar   +3 more sources

A new application of the unified method

New Trends in Mathematical Science, 2018
S. Akcagil, T. Aydemir
semanticscholar   +2 more sources

A unified method of data assimilation and turbulence modeling for separated flows at high Reynolds numbers [PDF]

The Physics of Fluids, 2022
In recent years, machine learning methods represented by deep neural networks (DNN) have been a new paradigm of turbulence modeling. However, in the scenario of high Reynolds numbers, there are still some bottlenecks, including the lack of high-fidelity ...
Zhiyuan Wang, Weiwei Zhang
semanticscholar   +1 more source