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A lower bound on local energy of partial sum of eigenfunctions for Laplace-Beltrami operators

Qi Lü (2013)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, a lower bound is established for the local energy of partial sum of eigenfunctions for Laplace-Beltrami operators (in Riemannian manifolds with low regularity data) with general boundary condition. This result is a consequence of a new pointwise and weighted estimate for Laplace-Beltrami operators, a construction of some nonnegative function with arbitrary given critical point location in the manifold, and also two interpolation results for solutions of elliptic equations with lateral...

A Lyapunov functional for a system with a time-varying delay

Józef Duda (2012)

International Journal of Applied Mathematics and Computer Science

The paper presents a method to determine a Lyapunov functional for a linear time-invariant system with an interval timevarying delay. The functional is constructed for the system with a time-varying delay with a given time derivative, which is calculated on the system trajectory. The presented method gives analytical formulas for the coefficients of the Lyapunov functional.

A Lyapunov-based design tool of impedance controllers for robot manipulators

Marco Mendoza, Isela Bonilla, Fernando Reyes, Emilio González-Galván (2012)

Kybernetika

This paper presents a design tool of impedance controllers for robot manipulators, based on the formulation of Lyapunov functions. The proposed control approach addresses two challenges: the regulation of the interaction forces, ensured by the impedance error converging to zero, while preserving a suitable path tracking despite constraints imposed by the environment. The asymptotic stability of an equilibrium point of the system, composed by full nonlinear robot dynamics and the impedance control,...

A mathematical framework for learning and adaption: (generalized) random systems with complete connections.

Ulrich Herkenrath, Radu Theodorescu (1981)

Trabajos de Estadística e Investigación Operativa

The aim of this paper is to show that the theory of (generalized) random systems with complete connection may serve as a mathematical framework for learning and adaption. Chapter 1 is of an introductory nature and gives a general description of the problems with which one is faced. In Chapter 2 the mathematical model and some results about it are explained. Chapter 3 deals with special learning and adaption models.

A mathematical model for file fragment diffusion and a neural predictor to manage priority queues over BitTorrent

Christian Napoli, Giuseppe Pappalardo, Emiliano Tramontana (2016)

International Journal of Applied Mathematics and Computer Science

BitTorrent splits the files that are shared on a P2P network into fragments and then spreads these by giving the highest priority to the rarest fragment. We propose a mathematical model that takes into account several factors such as the peer distance, communication delays, and file fragment availability in a future period also by using a neural network module designed to model the behaviour of the peers. The ensemble comprising the proposed mathematical model and a neural network provides a solution...

A mathematical model for fluid-glucose-albumin transport in peritoneal dialysis

Roman Cherniha, Joanna Stachowska-Piętka, Jacek Waniewski (2014)

International Journal of Applied Mathematics and Computer Science

A mathematical model for fluid and solute transport in peritoneal dialysis is constructed. The model is based on a threecomponent nonlinear system of two-dimensional partial differential equations for fluid, glucose and albumin transport with the relevant boundary and initial conditions. Our aim is to model ultrafiltration of water combined with inflow of glucose to the tissue and removal of albumin from the body during dialysis, by finding the spatial distributions of glucose and albumin concentrations...

A mathematical model of HIV-1 infection including the saturation effect of healthy cell proliferation

Mahiéddine Kouche, Bedr'eddine Ainseba (2010)

International Journal of Applied Mathematics and Computer Science

In this paper we derive a model describing the dynamics of HIV-1 infection in tissue culture where the infection spreads directly from infected cells to healthy cells trough cell-to-cell contact. We assume that the infection rate between healthy and infected cells is a saturating function of cell concentration. Our analysis shows that if the basic reproduction number does not exceed unity then infected cells are cleared and the disease dies out. Otherwise, the infection is persistent with the existence...

A matrix inequality based design method for consensus problems in multi-agent systems

Shohei Okuno, Joe Imae, Tomoaki Kobayashi (2009)

International Journal of Applied Mathematics and Computer Science

In this paper, we study a consensus problem in multi-agent systems, where the entire system is decentralized in the sense that each agent can only obtain information (states or outputs) from its neighbor agents. The existing design methods found in the literature are mostly based on a graph Laplacian of the graph which describes the interconnection structure among the agents, and such methods cannot deal with complicated control specification. For this purpose, we propose to reduce the consensus...

A Maturity-Structured Mathematical Model of Mutation, Acquisition in the Absence of Homeostatic Regulation

S. N. Gentry, R. Ashkenazi, T. L. Jackson (2009)

Mathematical Modelling of Natural Phenomena

Most mammalian tissues are organized into a hierarchical structure of stem, progenitor, and differentiated cells. Tumors exhibit similar hierarchy, even if it is abnormal in comparison with healthy tissue. In particular, it is believed that a small population of cancer stem cells drives tumorigenesis in certain malignancies. These cancer stem cells are derived from transformed stem cells or mutated progenitors that have acquired stem-cell qualities, specifically the ability to self-renew. Similar...

A method for sensor placement taking into account diagnosability criteria

Abed Alrahim Yassine, Stéphane Ploix, Jean-Marie Flaus (2008)

International Journal of Applied Mathematics and Computer Science

This paper presents a new approach to sensor placement based on diagnosability criteria. It is based on the study of structural matrices. Properties of structural matrices regarding detectability, discriminability and diagnosability are established in order to be used by sensor placement methods. The proposed approach manages any number of constraints modelled by linear or nonlinear equations and it does not require the design of analytical redundancy relations. Assuming that a constraint models...

A mixed active and passive GLR test for a fault tolerant control system

Hicham Jamouli, Mohamed Amine El Hail, Dominique Sauter (2012)

International Journal of Applied Mathematics and Computer Science

This paper presents an adaptive Generalized Likelihood Ratio (GLR) test for multiple Faults Detection and Isolation (FDI) in stochastic linear dynamic systems. Based on the work of Willsky and Jones (1976), we propose a modified generalized likelihood ratio test, allowing detection, isolation and estimation of multiple sequential faults. Our contribution aims to maximise the good decision rate of fault detection using another updating strategy. This is based on a reference model updated on-line...

A model-based approach to fault-tolerant control

Hans Henrik Niemann (2012)

International Journal of Applied Mathematics and Computer Science

A model-based controller architecture for Fault-Tolerant Control (FTC) is presented in this paper. The controller architecture is based on a general controller parameterization. The FTC architecture consists of two main parts, a Fault Detection and Isolation (FDI) part and a controller reconfiguration part. The theoretical basis for the architecture is given followed by an investigation of the single parts in the architecture. It is shown that the general controller parameterization is central in...

A model-based fault detection and diagnosis scheme for distributed parameter systems : a learning systems approach

Michael A. Demetriou (2002)

ESAIM: Control, Optimisation and Calculus of Variations

In this note, fault detection techniques based on finite dimensional results are extended and applied to a class of infinite dimensional dynamical systems. This special class of systems assumes linear plant dynamics having an abrupt additive perturbation as the fault. This fault is assumed to be linear in the (unknown) constant (and possibly functional) parameters. An observer-based model estimate is proposed which serves to monitor the system’s dynamics for unanticipated failures, and its well...

A Model-Based Fault Detection and Diagnosis Scheme for Distributed Parameter Systems: A Learning Systems Approach

Michael A. Demetriou (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this note, fault detection techniques based on finite dimensional results are extended and applied to a class of infinite dimensional dynamical systems. This special class of systems assumes linear plant dynamics having an abrupt additive perturbation as the fault. This fault is assumed to be linear in the (unknown) constant (and possibly functional) parameters. An observer-based model estimate is proposed which serves to monitor the system's dynamics for unanticipated failures, and its well...

A modified convolution and product theorem for the linear canonical transform derived by representation transformation in quantum mechanics

Navdeep Goel, Kulbir Singh (2013)

International Journal of Applied Mathematics and Computer Science

The Linear Canonical Transform (LCT) is a four parameter class of integral transform which plays an important role in many fields of signal processing. Well-known transforms such as the Fourier Transform (FT), the FRactional Fourier Transform (FRFT), and the FreSnel Transform (FST) can be seen as special cases of the linear canonical transform. Many properties of the LCT are currently known but the extension of FRFTs and FTs still needs more attention. This paper presents a modified convolution...

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