Numerical stability of the intrinsic equations for beams in time domain

Klesa, Jan

Displaying similar documents to “Numerical stability of the intrinsic equations for beams in time domain”

Quantitative stability for sumsets in $ℝ^{n}$

Alessio Figalli, David Jerison (2015)

Journal of the European Mathematical Society

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Given a measurable set $A \subset ℝ^{n}$ of positive measure, it is not difficult to show that $| A + A | = | 2 A |$ if and only if $A$ is equal to its convex hull minus a set of measure zero. We investigate the stability of this statement: If $(| A + A | - | 2 A |) / | A |$ is small, is $A$ close to its convex hull? Our main result is an explicit control, in arbitrary dimension, on the measure of the difference between $A$ and its convex hull in terms of $(| A + A | - | 2 A |) / | A |$ .

Practical $h$ -stability behavior of time-varying nonlinear systems

Abir Kicha, Hanen Damak, Mohamed Ali Hammami (2023)

Commentationes Mathematicae Universitatis Carolinae

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We deal with the problem of practical uniform $h$ -stability for nonlinear time-varying perturbed differential equations. The main aim is to give sufficient conditions on the linear and perturbed terms to guarantee the global existence and the practical uniform $h$ -stability of the solutions based on Gronwall’s type integral inequalities. Several numerical examples and an application to control systems with simulations are presented to illustrate the applicability of the obtained results. ...

Theoretical and numerical studies of the $P_{N} P_{M}$ DG schemes in one space dimension

Abdulatif Badenjki, Gerald G. Warnecke (2019)

Applications of Mathematics

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We give a proof of the existence of a solution of reconstruction operators used in the $P_{N} P_{M}$ DG schemes in one space dimension. Some properties and error estimates of the projection and reconstruction operators are presented. Then, by applying the $P_{N} P_{M}$ DG schemes to the linear advection equation, we study their stability obtaining maximal limits of the Courant numbers for several $P_{N} P_{M}$ DG schemes mostly experimentally. A numerical study explains how the stencils used in the reconstruction affect...

Exponential stability conditions for non-autonomous differential equations with unbounded commutators in a Banach space

Michael Gil' (2023)

Czechoslovak Mathematical Journal

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We consider the equation $d y (t) / d t = (A + B (t)) y (t)$ $(t \geq 0)$ , where $A$ is the generator of an analytic semigroup ${(e^{A t})}_{t \geq 0}$ on a Banach space $𝒳$ , $B (t)$ is a variable bounded operator in $𝒳$ . It is assumed that the commutator $K (t) = A B (t) - B (t) A$ has the following property: there is a linear operator $S$ having a bounded left-inverse operator $S_{l}^{- 1}$ such that $∥ S e^{A t} ∥$ is integrable and the operator $K (t) S_{l}^{- 1}$ is bounded. Under these conditions an exponential stability test is derived. As an example we consider a coupled system of parabolic equations. ...

On Noether and strict stability, Hilbert exponent, and relative Nullstellensatz

Chia-chi Tung (2013)

Annales Polonici Mathematici

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Conditions characterizing the membership of the ideal of a subvariety arising from (effective) divisors in a product complex space Y × X are given. For the algebra $_{Y} [V]$ of relative regular functions on an algebraic variety V, the strict stability is proved, in the case where Y is a normal space, and the Noether stability is established under a weakened condition. As a consequence (for both general and complete intersections) a global Nullstellensatz is derived for divisors in $Y \times ℂ^{N}$ , respectively,...

Small and large time stability of the time taken for a Lévy process to cross curved boundaries

Philip S. Griffin, Ross A. Maller (2013)

Annales de l'I.H.P. Probabilités et statistiques

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This paper is concerned with the small time behaviour of a Lévy process $X$ . In particular, we investigate theof the times, ${\bar{T}}_{b} (r)$ and $T_{b}^{*} (r)$ , at which $X$ , started with $X_{0} = 0$ , first leaves the space-time regions ${(t, y) \in ℝ^{2} : y \leq r t^{b}, t \geq 0}$ (one-sided exit), or ${(t, y) \in ℝ^{2} : | y | \leq r t^{b}, t \geq 0}$ (two-sided exit), $0 \leq b l t; 1$ , as $r ↓ 0$ . Thus essentially we determine whether or not these passage times behave like deterministic functions in the sense of different modes of convergence; specifically convergence in probability, almost surely and in $L^{p}$ . In many instances these are...

Delay-dependent stability conditions for fundamental characteristic functions

Hideaki Matsunaga (2023)

Archivum Mathematicum

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This paper is devoted to the investigation on the stability for two characteristic functions $f_{1} (z) = z^{2} + p e^{- z τ} + q$ and $f_{2} (z) = z^{2} + p z e^{- z τ} + q$ , where $p$ and $q$ are real numbers and $τ > 0$ . The obtained theorems describe the explicit stability dependence on the changing delay $τ$ . Our results are applied to some special cases of a linear differential system with delay in the diagonal terms and delay-dependent stability conditions are obtained.

Stabilization of monomial maps in higher codimension

Jan-Li Lin, Elizabeth Wulcan (2014)

Annales de l’institut Fourier

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A monomial self-map $f$ on a complex toric variety is said to be $k$ -stable if the action induced on the $2 k$ -cohomology is compatible with iteration. We show that under suitable conditions on the eigenvalues of the matrix of exponents of $f$ , we can find a toric model with at worst quotient singularities where $f$ is $k$ -stable. If $f$ is replaced by an iterate one can find a $k$ -stable model as soon as the dynamical degrees $λ_{k}$ of $f$ satisfy $λ_{k}^{2} > λ_{k - 1} λ_{k + 1}$ . On the other hand, we give examples of monomial maps $f$ , where...

Stability of nonlinear $h$ -difference systems with $n$ fractional orders

Małgorzata Wyrwas, Ewa Pawluszewicz, Ewa Girejko (2015)

Kybernetika

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In the paper we study the subject of stability of systems with $h$ -differences of Caputo-, Riemann-Liouville- and Grünwald-Letnikov-type with $n$ fractional orders. The equivalent descriptions of fractional $h$ -difference systems are presented. The sufficient conditions for asymptotic stability are given. Moreover, the Lyapunov direct method is used to analyze the stability of the considered systems with $n$ -orders.

The universal tropicalization and the Berkovich analytification

Jeffrey Giansiracusa, Noah Giansiracusa (2022)

Kybernetika

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Given an integral scheme $X$ over a non-archimedean valued field $k$ , we construct a universal closed embedding of $X$ into a $k$ -scheme equipped with a model over the field with one element $𝔽_{1}$ (a generalization of a toric variety). An embedding into such an ambient space determines a tropicalization of $X$ by previous work of the authors, and we show that the set-theoretic tropicalization of $X$ with respect to this universal embedding is the Berkovich analytification $X^{an}$ . Moreover, using the scheme-theoretic...

Global behavior of the difference equation $x_{n + 1} = \frac{a x_{n - 3}}{b + c x_{n - 1} x_{n - 3}}$

Raafat Abo-Zeid (2015)

Archivum Mathematicum

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In this paper, we introduce an explicit formula and discuss the global behavior of solutions of the difference equation $x_{n + 1} = \frac{a x_{n - 3}}{b + c x_{n - 1} x_{n - 3}}, n = 0, 1, \dots$ where $a, b, c$ are positive real numbers and the initial conditions $x_{- 3}$ , $x_{- 2}$ , $x_{- 1}$ , $x_{0}$ are real numbers.

Simultaneous stabilization in $A_{ℝ} ()$

Raymond Mortini, Brett D. Wick (2009)

Studia Mathematica

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We study the problem of simultaneous stabilization for the algebra $A_{ℝ} ()$ . Invertible pairs $(f_{j}, g_{j})$ , j = 1,..., n, in a commutative unital algebra are called simultaneously stabilizable if there exists a pair (α,β) of elements such that $α f_{j} + β g_{j}$ is invertible in this algebra for j = 1,..., n. For n = 2, the simultaneous stabilization problem admits a positive solution for any data if and only if the Bass stable rank of the algebra is one. Since $A_{ℝ} ()$ has stable rank two, we are faced here with a different...