Search results for "Exponent"
showing 10 items of 896 documents
Recovering a variable exponent
2021
We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements. The main technique is using the properties of a moment problem after reducing the inverse problem to determining a function from its $L^p$-norms.
Refined instability estimates for some inverse problems
2022
Many inverse problems are known to be ill-posed. The ill-posedness can be manifested by an instability estimate of exponential type, first derived by Mandache [29]. In this work, based on Mandache's idea, we refine the instability estimates for two inverse problems, including the inverse inclusion problem and the inverse scattering problem. Our aim is to derive explicitly the dependence of the instability estimates on key parameters. The first result of this work is to show how the instability depends on the depth of the hidden inclusion and the conductivity of the background medium. This work can be regarded as a counterpart of the depth-dependent and conductivity-dependent stability estim…
Rheological Properties of Different Film Blowing Polyethylene Samples Under Shear and Elongational Flow
2005
Summary: The rheological behavior of polyethylenes ismainly dominated by the molecular weight, the molecularweight distribution and by the type, the amount and thedistribution of the chain branches. In this work a linearmetallocenecatalyzedpolyethylene(m-PE),abranchedme-tallocene catalyzed polyethylene (m-bPE), a conventionallinear low density polyethylene (LLDPE) and a low densitypolyethylene (LDPE) have been investigated in order tocompare their rheological behavior in shear and in elonga-tional flow. The four samples have similar melt flow indexand in particular a value typical of film blowing grade.The melt viscosity has been studied both in shear and inisothermal and non-isothermal elonga…
Growth of central polynomials of algebras with involution
2021
Let A be an associative algebra with involution ∗ over a field of characteristic zero. A central ∗-polynomial of A is a polynomial in non- commutative variables that takes central values in A. Here we prove the existence of two limits called the central ∗-exponent and the proper central ∗-exponent that give a measure of the growth of the central ∗-polynomials and proper central ∗-polynomials, respectively. Moreover, we compare them with the PI-∗-exponent of the algebra.
On the spatial configuration of scatterers for given delay-angle distributions
2014
Published version of an article in the journal: Engineering Letters. Also available from the publisher at: http://www.engineeringletters.com/issues_v22/issue_1/EL_22_1_05.pdf. Open access This paper investigates the distribution of scatterers located around the mobile station (MS) for given delay-angle distributions. The delay-angle distribution function represents the joint probability density function (PDF) of the time-ofarrival (TOA) and angle-of-arrival (AOA). Given such a joint PDF, we first derive a general expression for the distribution of the scatterers in both polar and Cartesian coordinates. We then analyze an important special case in which the TOA and the AOA follow the multipl…
Stability of stochastic nonlinear systems with state-dependent switching
2013
In this paper, the problem of stability on stochastic systems with state-dependent switching is investigated. To analyze properties of the switched system by means of Itô’s formula and Dynkin’s formula, it is critical to show switching instants being stopping times. When the given active-region set can be replaced by its interior, the local solution of the switched system is constructed by defining a series of stopping times as switching instants, and the criteria on global existence and stability of solution are presented by Lyapunov approach. For the case where the active-region set can not be replaced by its interior, the switched systems do not necessarily have solutions, thereby quasi-…
Poincare Inequalities and Spectral Gap, Concentration Phenomenon for G-Measures
2002
We produce a new approach based upon inequalities of Poincare’s type for giving constructive estimates of the mixing rate for a family of mixing stationary processes continuously depending on their past called g-measures. We establish also exponential inequalities of Hoeffding’s type leading to a concentration phenomenon for a large class of observables; this last property permits in particular to give the typical behaviour of the n-orbits of a g-measure.
Truncation, Information, and the Coefficient of Variation
1989
The Fisher information in a random sample from the truncated version of a distribution that belongs to an exponential family is compared with the Fisher information in a random sample from the un- truncated distribution. Conditions under which there is more information in the selection sample are given. Examples involving the normal and gamma distributions with various selection sets, and the zero-truncated binomial, Poisson, and negative binomial distributions are discussed. A property pertaining to the coefficient of variation of certain discrete distributions on the non-negative integers is introduced and shown to be satisfied by all binomial, Poisson, and negative binomial distributions.
The Complex WKB Method
2019
In this chapter we shall study the exponential growth and asymptotic expansions of exact solutions of second-order differential equations in the semi-classical limit. As an application, we establish a Bohr-Sommerfeld quantization condition for Schrodinger operators with real-analytic complex-valued potentials.
Robust H<inf>&#x221E;</inf> control of Markovian jump systems with mixed time delays
2010
In this paper, the problem of stability analysis and control synthesis for Markovian jump linear systems with time delays and norm-bounded uncertainties is studied. The model under consideration consists of different time-invariant discrete, neutral and distributed delays. Delay-dependent sufficient conditions for the design of a mode-dependent delayed state feedback H ∞ control are given in terms of linear matrix inequalities (LMIs). A controller which guarantees stochastic stability and a prescribed level of H ∞ performance for the closed-loop system is then developed. A Lyapunov-Krasovskii functional (LKF) method underlies the control design. A numerical example with simulation results i…