The basic method we propose in order to solve analytically the equation of motion of a relativistic single-bunch travelling in a linac, in the presence of wakefields, has been summarized in a preceding report [1]. The extended treatment presented here includes the quadrupole transverse displacements, the chromatic variation of the magnetic focusing, the energy spread along the bunch and possibl...

numerical solutions obtained by the meshless local petrov–galerkin (mlpg) method are presented for two-dimensional steady-state heat conduction problems. the mlpg method is a truly meshless approach, and neither the nodal connectivity nor the background mesh is required for solving the initial-boundary-value problem. the penalty method is adopted to efficiently enforce the essential boundary co...

Second?degree dominance has become a widely accepted criterion for ordering distribution functions according to social welfare. However, it provides only partial ordering, and may fail rank distributions that intersect. To intersecting functions, we propose general approach based on rank?dependent theory. This avoids making arbitrary restrictions or parametric assumptions about welfare allows r...

Networked complex systems in a wide range of physics, biology and social sciences involve synergy among multiple agents beyond pairwise interactions. Higher-order mathematical structures such as hypergraphs have been increasingly popular modelling analysis dynamical behaviours. Here, we study simple three-body consensus model, which favourably incorporates higher-order network interactions, dim...

We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements? The stress is on a comparison of linear and nonlinear approaches. As a model case we use piecewise-constant functions on [0, 1], in particular, the Heaviside...

We address in this paper the following two closely related problems: 1. How to represent functions with singularities (up to a prescribed accuracy) in a compact way? 2. How to reconstruct such functions from a small number of measurements? The stress is on a comparison of linear and nonlinear approaches. As a model case we use piecewise-constant functions on [0, 1], in particular, the Heaviside...