Search results for "Functional analysis"

2014

State estimation problem is considered for a kind of wireless network control system with stochastic uncertainty and time delay. A sliding mode observer is designed for the system under the situation that no missing measurement occurs and system uncertainty happens in a stochastic way. The observer designed for the system can guarantee the system states will be driven onto the sliding surface under control law, and the sliding motion of system states on sliding surface will be stable. By constructing proper Lyapunov-Krasovskii functional, sufficient conditions are acquired via linear matrix inequality. Finally, simulation result is employed to show the effectiveness of the proposed method.

Voltage collapse proximity indicators for radial distribution networks

2007

Based on the single-line equivalent system of a radial distribution network, two simple methods to evaluate two efficient voltage collapse proximity indicators are presented and discussed. The two methods differ on the determination of the parameters which define the equivalent system from which the indicators are derived. Both methods can be conveniently used jointly for on-line applications to assess the state of a distribution system from the viewpoint of voltage stability; the first to monitoring the stability margin of the whole system loading, the second to sharpen the stability analysis at the critical node when the system operating point is in the vicinity of the loadability limit. …

Existence and stability of periodic solutions in a neural field equation

2017

We study the existence and linear stability of stationary periodic solutions to a neural field model, an intergo-differential equation of the Hammerstein type. Under the assumption that the activation function is a discontinuous step function and the kernel is decaying sufficiently fast, we formulate necessary and sufficient conditions for the existence of a special class of solutions that we call 1-bump periodic solutions. We then analyze the stability of these solutions by studying the spectrum of the Frechet derivative of the corresponding Hammerstein operator. We prove that the spectrum of this operator agrees up to zero with the spectrum of a block Laurent operator. We show that the no…

X-ray fluorescence analysis by the fundamental parameters method without explicit knowledge of the excitation beam spectrum

2000

The results of analyses carried out with the fundamental parameters method without explicit knowledge of the beam exciting the sample are presented. The excitation beam is described by means of the fluorescence produced by a set of thick or thin targets of pure chemical elements. The results are compared with those obtained by using a semi-empirical model and an adjusted spectrum model, all sets of results being in turn compared with the actual chemical composition of the samples. It is concluded that the description of the excitation beam by means of the fluorescence produced on targets of pure elements is suitable for use with the fundamental parameters method. Copyright © 2000 John Wiley…

On State Constrained Optimal Shape Design Problems

1987

This paper is concerned with the following optimal design problem with constraints both on the state and on the control: $$MinimizeJ(y,u)$$ (P) subject to $$A\left( u \right)y + \partial \varphi \left( y \right) \mathrel\backepsilon Bu + f,$$ (1.1) $$y \in K,$$ (1.2) $$u \in {U_{ad}}.$$ (1.3)

Contact Shape Optimization

1995

Shape optimization is a branch of the optimal control theory in which the control variable is connected with the geometry of the problem. The aim is to find a shape from an a priori defined class of domains, for wich the corresponding cost functional attains its minimum. Shape optimization of mechanical systems, behaviour of which is described by equations, has been very well analyzed from the mathematical, as well as from the mechanical point of view, see [1], [2], [3] and references therein. The aim of this contribution is to extend results to the case, in which the system is described by the so called variational inequalities. There are two reasons for doing that: 1) The behavior of many…

A New Hybrid Mutation Operator for Multiobjective Optimization with Differential Evolution

2011

Differential evolution has become one of the most widely used evolution- ary algorithms in multiobjective optimization. Its linear mutation operator is a sim- ple and powerful mechanism to generate trial vectors. However, the performance of the mutation operator can be improved by including a nonlinear part. In this pa- per, we propose a new hybrid mutation operator consisting of a polynomial based operator with nonlinear curve tracking capabilities and the differential evolution’s original mutation operator, to be efficiently able to handle various interdependencies between decision variables. The resulting hybrid operator is straightforward to implement and can be used within most evoluti…

Operators on Partial Inner Product Spaces: Towards a Spectral Analysis

2014

Given a LHS (Lattice of Hilbert spaces) $V_J$ and a symmetric operator $A$ in $V_J$, in the sense of partial inner product spaces, we define a generalized resolvent for $A$ and study the corresponding spectral properties. In particular, we examine, with help of the KLMN theorem, the question of generalized eigenvalues associated to points of the continuous (Hilbertian) spectrum. We give some examples, including so-called frame multipliers.

Numerical range and positive block matrices

2020

We obtain several norm and eigenvalue inequalities for positive matrices partitioned into four blocks. The results involve the numerical range $W(X)$ of the off-diagonal block $X$, especially the distance $d$ from $0$ to $W(X)$. A special consequence is an estimate, $$\begin{eqnarray}\text{diam}\,W\left(\left[\begin{array}{@{}cc@{}}A & X\\ X^{\ast } & B\end{array}\right]\right)-\text{diam}\,W\biggl(\frac{A+B}{2}\biggr)\geq 2d,\end{eqnarray}$$ between the diameters of the numerical ranges for the full matrix and its partial trace.

Determination of the $X(3872)$ meson quantum numbers

2013

The quantum numbers of the X(3872) meson are determined to be J(PC) = 1(++) based on angular correlations in B+ -> X(3872)K+ decays, where X(3872) -> pi(+) pi(-) j/psi and J/psi -> pi(+) mu(-). The data correspond to 1.0 fb(-1) of pp collisions collected by the LHCb detector. The only alternative assignment allowed by previous measurements J(PC) = 2(-+) is rejected with a confidence level equivalent to more than 8 Gaussian standard deviations using a likelihood-ratio test in the full angular phase space. This result favors exotic explanations of the X(3872) state.