Search results for "Exponential function"
showing 10 items of 173 documents
Adaptive Control Design for Underactuated Cranes With Guaranteed Transient Performance: Theoretical Design and Experimental Verification
2022
For antiswing control of underactuated cranes, how to guarantee the converging speed of cranes through control design is essential but still remains unsolved. In this paper, the adaptive antiswing control for underactuated gantry cranes with guaranteed transient performance under unmodeled dynamics and external disturbances is investigated. To sovle this problem, a set of filters are proposed to make the backstepping technique applicable for the control of crane systems. Then through variable transformation the position error and swing angel could be guaranteed converging to the origin with a given exponential speed. Hardware experiments are conducted to show that the proposed scheme achiev…
Quasi-Modes and Spectral Instability in One Dimension
2019
In this section we describe the general WKB construction of approximate “asymptotic” solutions to the ordinary differential equation $$\displaystyle P(x,hD_x)u=\sum _{k=0}^m b_k(x)(hD_x)^ku=0, $$ on an interval α < x < β, where we assume that the coefficients bk ∈ C∞(]α, β[). Here h ∈ ]0, h0] is a small parameter and we wish to solve (above equation) up to any power of h. We look for u in the form $$\displaystyle u(x;h)=a(x;h)e^{i\phi (x)/h}, $$ where ϕ ∈ C∞(]α, β[) is independent of h. The exponential factor describes the oscillations of u, and when ϕ is complex valued it also describes the exponential growth or decay; a(x;h) is the amplitude and should be of the form $$\displaystyle a(x;h…
Varieties of Algebras with Superinvolution of Almost Polynomial Growth
2015
Let A be an associative algebra with superinvolution ∗ over a field of characteristic zero and let $c_{n}^{\ast }(A)$ be its sequence of corresponding ∗-codimensions. In case A is finite dimensional, we prove that such sequence is polynomially bounded if and only if the variety generated by A does not contain three explicitly described algebras with superinvolution. As a consequence we find out that no intermediate growth of the ∗-codimensions between polynomial and exponential is allowed.
Yet Another New Variant of Szász–Mirakyan Operator
2021
In this paper, we construct a new variant of the classical Szász–Mirakyan operators, Mn, which fixes the functions 1 and eax,x≥0,a∈R. For these operators, we provide a quantitative Voronovskaya-type result. The uniform weighted convergence of Mn and a direct quantitative estimate are obtained. The symmetry of the properties of the classical Szász–Mirakyan operator and of the properties of the new sequence is investigated. Our results improve and extend similar ones on this topic, established in the last decade by many authors.
On the existence of the exponential solution of linear differential systems
1999
The existence of an exponential representation for the fundamental solutions of a linear differential system is approached from a novel point of view. A sufficient condition is obtained in terms of the norm of the coefficient operator defining the system. The condition turns out to coincide with a previously published one concerning convergence of the Magnus series expansion. Direct analysis of the general evolution equations in the SU(N) Lie group illustrates how the estimate for the domain of existence/convergence becomes larger. Eventually, an application is done for the Baker-Campbell-Hausdorff series.
The Emergence of Chaos in Quantum Mechanics
2020
Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrö
MAC design on real 802.11 devices: From exponential to Moderated Backoff
2016
In this paper we describe how a novel backoff mechanism called Moderated Backoff (MB), recently proposed as a standard extension for 802.11 networks, has been prototyped and experimentally validated on a commercial 802.11 card before being ratified. Indeed, for performance reasons, the time critical operations of MAC protocols, such as the backoff mechanism, are implemented into the card hardware/firmware and cannot be arbitrarily changed by third parties or by manufacturers only for experimental reasons. Our validation has been possible thanks to the availability of the so called Wireless MAC Processor (WMP), a prototype of a novel wireless card architecture in which MAC protocols can be p…
Exponential Entropy Driven HUM on Knee MR Images
2007
A very important artifact corrupting Magnetic Resonance Images is the RF inhomogeneity. This kind of artifact generates variations of illumination which trouble both direct examination by the doctor and segmentation algorithms. Even if homomorphic filtering approaches have been presented in literature, none of them has developed a measure to determine the cut-off frequency. In this work we present a measure based on information theory with a large experimental setup aimed to demonstrate the validity of our approach.
Sequentially Forecasting Economic Indices Using Mixture Linear Combinations of EP Distributions
2021
This article displays an application of the statistical method moti- vated by Bruno de Finetti's operational subjective theory of probability. We use exchangeable forecasting distributions based on mixtures of linear com- binations of exponential power (EP) distributions to forecast the sequence of daily rates of return from the Dow-Jones index of stock prices over a 20 year period. The operational subjective statistical method for comparing distributions is quite different from that commonly used in data analysis, because it rejects the basic tenets underlying the practice of hypothesis test- ing. In its place, proper scoring rules for forecast distributions are used to assess the values o…
A laboratory analysis of falling head infiltration procedures for estimating the hydraulic conductivity of soils
2006
Abstract Falling head (FH) infiltration procedures can give rapid estimates of the field saturated hydraulic conductivity ( K fs ) of soils. The objectives of this investigation were to develop a procedure for estimating both the K fs and the α ⁎ parameter of the exponential hydraulic conductivity function from a FH experiment, and to compare FH procedures differing by experimental and computational demands. A total of 33 FH experiments were carried out on repacked, sandy loam and loam soil cores. A two level (TL) analysis was applied to determine a value of α ⁎ for each soil core. K fs was then calculated by three different approaches, ranging from the fitting approach (FA) that used the m…