Search results for "linear system"

Reliable numerical solution of a class of nonlinear elliptic problems generated by the Poisson-Boltzmann equation

2020

We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson-Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in [S. Repin, A posteriori error estimation for variational problems with uniformly convex functionals. Math. Comp., 69:481-500, 2000] for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computa…

Harmonic Balance Method and Stability of Discontinuous Systems

2019

The development of the theory of discontinuous dynamical systems and differential inclusions was not only due to research in the field of abstract mathematics but also a result of studies of particular problems in mechanics. One of first methods, used for the analysis of dynamics in discontinuous mechanical systems, was the harmonic balance method developed in the thirties of the 20th century. In our work the results of analysis obtained by the method of harmonic balance, which is an approximate method, are compared with the results obtained by rigorous mathematical methods and numerical simulation. peerReviewed

Parabolic equations with nonlinear singularities

2011

Abstract We show the existence of positive solutions u ∈ L 2 ( 0 , T ; H 0 1 ( Ω ) ) for nonlinear parabolic problems with singular lower order terms of the asymptote-type. More precisely, we shall consider both semilinear problems whose model is { u t − Δ u + u 1 − u = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , and quasilinear problems having natural growth with respect to the gradient, whose model is { u t − Δ u + ∣ ∇ u ∣ 2 u γ = f ( x , t ) in Ω × ( 0 , T ) , u ( x , 0 ) = u 0 ( x ) in Ω , u ( x , t ) = 0 on ∂ Ω × ( 0 , T ) , with γ > 0 . Moreover, we prove a comparison principle and, as an application, we study the asymptotic behav…

Global linear feedback control for the generalized Lorenz system

2006

Abstract In this paper we show how the chaotic behavior of the Chen system can be controlled via feedback technique. We design both a nonlinear feedback controller and a linear one which globally regulate the closed-loop system states to a given point. We finally show that our approach works also for the whole family of the generalized Lorenz system.

On GPU-accelerated fast direct solvers and their applications in image denoising

2015

Nonlinear Feedback Control and Stability Analysis of a Proof-of-Work Blockchain

2017

In this paper a novel feedback controller and stability analysis of a blockchain implementation is developed by using a control engineering perspective. The controller output equals the difficulty adjustment in the mining process while the feedback variable is the average block time over a certain time period. The computational power (hash rate) of the miners is considered a disturbance in the model. The developed controller is tested against a simulation model with constant disturbance, step and ramp responses as well as with a high-frequency sinusoidal disturbance. Stability and a fast response is demonstrated in all these cases with a controller which adjusts it's output at every new blo…

Nonlinear radial-harmonic correlation using binary decomposition for scale-invariant pattern recognition

2003

We introduce a new scale-invariant pattern-recognition method that uses nonlinear correlation. We applied several common linear correlations to images decomposed into disjoint binary images, which is very discriminant even when the target is embedded in strong noise. We combine our sliced orthogonal nonlinear generalized correlation method and the radial-harmonic expansion in order to achieve scale-invariant pattern recognition. The information from a radial harmonic for each binary slice of the reference object is combined with binary slices of the target. The method avoids the time-consuming process of finding expansion centers for the radial harmonics. The stability of the correlation pe…

Interlacing multiplexing techniques for optical morphological correlation

2006

We propose a novel approach to implement nonlinear morphological correlation. Previous implementation was based on a time sequential approach that consists on displaying different binary image decomposition in a joint transform correlator adding each joint power spectra sequentially. A second Fourier transformation of the sum of joint power spectra gives the correlation output. In this paper, we propose to interlace the different binary images into one single distribution. Then, we introduce the distribution in a conventional joint transform correlator. The correlation output gives the morphological correlation at a specific location. The advantage is important considering that no sequentia…

Assessment of qualitative judgements for conditional events in expert systems

1991

Comprehensive Strategy for Proton Chemical Shift Prediction: Linear Prediction with Nonlinear Corrections

2014

A fast 3D/4D structure-sensitive procedure was developed and assessed for the chemical shift prediction of protons bonded to sp3carbons, which poses the maybe greatest challenge in the NMR spectral parameter prediction. The LPNC (Linear Prediction with Nonlinear Corrections) approach combines three well-established multivariate methods viz. the principal component regression (PCR), the random forest (RF) algorithm, and the k nearest neighbors (kNN) method. The role of RF is to find nonlinear corrections for the PCR predicted shifts, while kNN is used to take full advantage of similar chemical environments. Two basic molecular models were also compared and discussed: in the MC model the desc…