			Home About us Contact

Functional Equations (functional + equation)

Distribution by Scientific Domains

Engineering	55%

Selected Abstracts

STABILITY CONDITION OF DISTRIBUTED DELAY SYSTEMS BASED ON AN ANALYTIC SOLUTION TO LYAPUNOV FUNCTIONAL EQUATIONS

ASIAN JOURNAL OF CONTROL, Issue 1 2006
Young Soo Suh
ABSTRACT An analytic solution to Lyapunov functional equations for distributed delay systems is derived. The analytic solution is computed using a matrix exponential function, while conventional computation has been relied on numerical approximations. Based on the analytic solution, a necessary and sufficient stability condition for distributed delay systems with unknown but bounded constant delay is proposed. [source]

The one-level functional equation of multi-rate loss systems

EUROPEAN TRANSACTIONS ON TELECOMMUNICATIONS, Issue 2 2003
Harro L. Hartmann
Motivated by the discrete multi-rate Kaufmann,Roberts recurrence relations, we derive a functional equation (FE), which covers nonintegral states. This FE implies a unique effective step parameter d, which defines an equivalent one-level recurrence depth, or bit-rate, at each state under progress. This state-dependent depth results from the equality requirement of the multi-rate and the one-level model in the moment-generating function transform domain. By this method it is possible to model d by a few moments of the original multi-rate statistic. In this case we obtain an explicit FE solution covering the entire (global) state space. Next we verify that the resulting state probability density incorporates iteratively enumerated discrete state probabilities, including the state-dependent depth. With a system capacity C the iterations then need time complexities between O(C) and O(C2). In contrast to this each FE state, is performed at a time complexity O(1). By the efficient coverage of the whole state space, fast optimizations of multi-rate networks and multi-resource systems can be improved. Copyright © 2003 AEI. [source]

Some Learning Methods in Functional Networks

COMPUTER-AIDED CIVIL AND INFRASTRUCTURE ENGINEERING, Issue 6 2000
Enrique Castillo
This article is devoted to learning functional networks. After a short introduction and motivation of functional networks using a CAD problem, four steps used in learning functional networks are described: (1) selection of the initial topology of the network, which is derived from the physical properties of the problem being modeled, (2) simplification of this topology, using functional equations, (3) estimation of the parameters or weights, using least squares and minimax methods, and (4) selection of the subset of basic functions leading to the best fit to the available data, using the minimum-description-length principle. Several examples are presented to illustrate the learning procedure, including the use of a separable functional network to recover the missing data of the significant wave height records in two different locations, based on a complete record from a third location where the record is complete. [source]

On the difference of fuzzy sets

INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS, Issue 3 2008
Claudi Alsina
We formulate and solve a collection of functional equations arising in the framework of fuzzy logic when modeling the concept of a difference operation between couples of fuzzy sets. © 2008 Wiley Periodicals, Inc. [source]

Symbolic methods for invariant manifolds in chemical kinetics

INTERNATIONAL JOURNAL OF QUANTUM CHEMISTRY, Issue 1 2006
Simon J. Fraser
Abstract Chemical reactions show a separation of time scales in transient decay due to the stiffness of the ordinary differential equations (ODEs) that describe their evolution. This evolution can be represented as motion in the phase space spanned by the concentration variables of the chemical reaction. Transient decay corresponds to a collapse of the "compressible fluid" representing the continuum of possible dynamical states of the system. Collapse occurs sequentially through a hierarchy of nested, attracting, slow invariant manifolds (SIMs), i.e., sets that map into themselves under the action of the phase flow, eventually reaching the asymptotic attractor of the system. Using a symbolic manipulative language, explicit formulas for the SIMs can be found by iterating functional equations obtained from the system's ODEs. Iteration converges geometrically fast to a SIM at large concentrations and, if necessary, can be stabilized at small concentrations. Three different chemical models are examined in order to show how finding the SIM for a model depends on its underlying dynamics. For every model the iterative method provides a global SIM formula; however, formal series expansions for the SIM diverge in some models. Repelling SIMs can be also found by iterative methods because of the invariance of trajectory geometry under time reversal. © 2005 Wiley Periodicals, Inc. Int J Quantum Chem, 2006 [source]

An approximation to the solution of telegraph equation by variational iteration method

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2009
J. Biazar
Abstract The variational iteration method (VIM) has been applied to solve many functional equations. In this article, this method is applied to obtain an approximate solution for the Telegraph equation. Some examples are presented to show the ability of the proposed method. The results of applying VIM are exactly the same as those obtained by Adomian decomposition method. It seems less computation is needed in proposed method.© 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009 [source]

Optimal control for non-linear integrodifferential functional equations

OPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 1 2003
Jin-Mun Jeong
Abstract An optimal control problem for a non-linear control system with a hemicontinuous and coercive operator is studied. The existence, uniqueness, and a variation of solutions of the system are also given. An example is presented to illustrate the theory. Copyright © 2003 John Wiley & Sons, Ltd. [source]

The practice of non-parametric estimation by solving inverse problems: the example of transformation models

THE ECONOMETRICS JOURNAL, Issue 3 2010
Frédérique Fève
Summary, This paper considers a semi-parametric version of the transformation model , (Y) =,,X+U under exogeneity or instrumental variables assumptions (E(U,X) = 0 or . This model is used as an example to illustrate the practice of the estimation by solving linear functional equations. This paper is specially focused on the data-driven selection of the regularization parameter and of the bandwidths. Simulations experiments illustrate the relevance of this approach. [source]