Multipole Born series approach to light scattering by Mie-resonant nanoparticle structures

Exciting optical effects such as polarization control, imaging, and holography were demonstrated at the nanoscale using the complex and irregular structures of nanoparticles with the multipole Mie-resonances in the optical range. The optical response of such particles can be simulated either by full wave numerical simulations or by the widely used analytical coupled multipole method (CMM), however, an analytical solution in the framework of CMM can be obtained only in a limited number of cases. In this paper, a modification of the CMM in the framework of the Born series and its applicability for simulation of light scattering by finite nanosphere structures, maintaining both dipole and quadrupole resonances, are investigated. The Born approximation simplifies an analytical consideration of various systems and helps shed light on physical processes ongoing in that systems. Using Mie theory and Green’s functions approach, we analytically formulate the rigorous coupled dipole-quadrupole equations and their solution in the different-order Born approximations. We analyze in detail the resonant scattering by dielectric nanosphere structures such as dimer and ring to obtain the convergence conditions of the Born series and investigate how the physical characteristics such as absorption in particles, type of multipole resonance, and geometry of ensemble influence the convergence of Born series and its accuracy.

Sliding Mode Control of Flexible Articulated Manipulator Based on Robust Observer

In this paper, a robust observer-based sliding mode control algorithm is proposed to address the modelling and measurement inaccuracies, load variations, and external disturbances of flexible articulated manipulators. Firstly, a sliding mode observer was designed with exponential convergence to observe system state accurately and to overcome the measuring difficulty of the state variables, unmeasurable quantities, and external disturbances. Next, a robust sliding mode controller was developed based on the observer, such that the output error of the system converges to zero in finite time. In this way, the whole system achieves asymptotic stability. Finally, the convergence conditions of the observer were theoretically analyzed to verify the convergence of the proposed algorithm, and simulation was carried out to confirm the effectiveness of the proposed method.

Extended local convergence for Newton-type solver under weak conditions

We present the local convergence of a Newton-type solver for equations involving Banach space valued operators. The eighth order of convergence was shown earlier in the special case of the k-dimensional Euclidean space, using hypotheses up to the eighth derivative although these derivatives do not appear in the method. We show convergence using only the rst derivative. This way we extend the applicability of the methods. Numerical examples are used to show the convergence conditions. Finally, the basins of attraction of the method, on some test problems are presented.

A novel PID-like particle swarm optimizer: on terminal convergence analysis

In this paper, a novel proportion-integral-derivative-like particle swarm optimization (PIDLPSO) algorithm is presented with improved terminal convergence of the particle dynamics. A derivative control term is introduced into the traditional particle swarm optimization (PSO) algorithm so as to alleviate the overshoot problem during the stage of the terminal convergence. The velocity of the particle is updated according to the past momentum, the present positions (including the personal best position and the global best position), and the future trend of the positions, thereby accelerating the terminal convergence and adjusting the search direction to jump out of the area around the local optima. By using a combination of the Routh stability criterion and the final value theorem of the Z-transformation, the convergence conditions are obtained for the developed PIDLPSO algorithm. Finally, the experiment results reveal the superiority of the designed PIDLPSO algorithm over several other state-of-the-art PSO variants in terms of the population diversity, searching ability and convergence rate.

Modelling and Prediction of the Spread of COVID-19 in Cameroon and Assessing the Governmental Measures (March–September 2020)

COVID-19 is an acute respiratory illness in humans caused by a coronavirus, capable of producing severe symptoms and, in some cases, death, especially in older people and those with underlying health conditions. It was originally identified in China in 2019 and became a pandemic in 2020. On 6 March 2020, Cameroon recorded its first cases of infection with COVID-19. The Government of Cameroon (GOC) took 13 barrier measures on 18 March 2020. On 1 May 2020, 19 new measures were adopted, easing restrictions and encouraging economic activity. On 1 June, schools and universities were reopened, after which massive screening began to take place throughout the country. In this study, we have modelled the COVID-19 epidemic in Cameroon in order to assess the governmental measures of response and predict the behaviour of epidemic As a result of these measures, the pandemic evolved in three phases. The first phase began on 18 March and ended on 15 May 2020. During this phase, the actual curve of cumulative positive cases based on field data closely fit the theoretical curve resulting from mathematical modelling. In the beginning of May, we predicted that nearly 3000 positive cases would be declared by mid-May 2020. The actual data confirmed these predictions: there were 2954 cases as of 15 May 2020. The second phase, beyond mid-May 2020, encompasses the period when the GOC’s relaxation of measures takes effect. This phase was marked by an acceleration of the cumulative number of positive cases starting in the third week of May, postponing the expected peak by two weeks. Under Phase 2 conditions, the onset of the peak will occur in early June and extend through the first two weeks of June. However, a third phase occurs in the first week of June, with the reopening of schools and universities combined with massive screening; the peak is therefore expected in the second week of June (around 15 June). The GOC should, at this stage, strengthen its response plan by tripling the current coverage capacity to regain the first phase convergence conditions associated with the first 13 measures. The pandemic will begin its descent in the month of august, but COVID-19 will remain endemic for at least one year.

Uniform Stochastic Convergence

This chapter concerns random sequences of functions on metric spaces. The main issue is the distinction between convergence at all points of the space (pointwise) and uniform convergence, where limit points are also taken into account. The role of the stochastic equicontinuity property is highlighted. Generic uniform convergence conditions are given and linked to the question of uniform laws of large numbers.

Application of Fuzzy Finite Difference Scheme for the Non-homogeneous Fuzzy Heat Equation

A numerical framework based on fuzzy finite difference is presented for approximating fuzzy triangular solutions of fuzzy partial differential equations by considering the type of $[gH-p]-$differentiability. The fuzzy triangle functions are expanded using full fuzzy Taylor expansion to develop a new fuzzy finite difference method. By considering the type of gH-differentiability, we approximate the fuzzy derivatives with a new fuzzy finite-difference. In particular, we propose using this method to solve non-homogeneous fuzzy heat equation with triangular initial-boundary conditions. We examine the truncation error and the convergence conditions of the proposed method. Several numerical examples are presented to demonstrate the performance of the methods. The final results demonstrate the efficiency and the ability of the new fuzzy finite difference method to produce triangular fuzzy numerical results which are more consistent with existing reality.