The central heights of stability groups of series in vector spaces

Bertram A. F. Wehrfritz

Displaying similar documents to “The central heights of stability groups of series in vector spaces”

Numerical stability of the intrinsic equations for beams in time domain

Klesa, Jan

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Intrinsic equations represent promising approach for the description of rotor blade dynamics. They are the system of non-linear partial differential equations. Stability of numeric solution by the finite difference method is described. The stability is studied for various numerical schemes with different methods for the computation of spatial derivatives from time level $n + 0.5$ (i.e., mean values of old and new time step) to $n + 1$ (i.e., only from new time step). Stable solution was obtained only...

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. ...

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 $(| A + A | - | 2 A |) / | A |$ .

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.

A property which ensures that a finitely generated hyper-(Abelian-by-finite) group is finite-by-nilpotent

Fares Gherbi, Nadir Trabelsi (2024)

Czechoslovak Mathematical Journal

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Let $𝔐$ be the class of groups satisfying the minimal condition on normal subgroups and let $Ω$ be the class of groups of finite lower central depth, that is groups $G$ such that $γ_{i} (G) = γ_{i + 1} (G)$ for some positive integer $i$ . The main result states that if $G$ is a finitely generated hyper-(Abelian-by-finite) group such that for every $x \in G$ , there exists a normal subgroup $H_{x}$ of finite index in $G$ satisfying $〈 x, x^{h} 〉 \in 𝔐 Ω$ for every $h \in H_{x}$ , then $G$ is finite-by-nilpotent. As a consequence of this result, we prove that a finitely generated...

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,...

$𝒟_{n, r}$ is not potentially nilpotent for $n \geq 4 r - 2$

Yan Ling Shao, Yubin Gao, Wei Gao (2016)

Czechoslovak Mathematical Journal

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An $n \times n$ sign pattern $𝒜$ is said to be potentially nilpotent if there exists a nilpotent real matrix $B$ with the same sign pattern as $𝒜$ . Let $𝒟_{n, r}$ be an $n \times n$ sign pattern with $2 \leq r \leq n$ such that the superdiagonal and the $(n, n)$ entries are positive, the $(i, 1)$ $(i = 1, \dots, r)$ and $(i, i - r + 1)$ $(i = r + 1, \dots, n)$ entries are negative, and zeros elsewhere. We prove that for $r \geq 3$ and $n \geq 4 r - 2$ , the sign pattern $𝒟_{n, r}$ is not potentially nilpotent, and so not spectrally arbitrary.

Certain decompositions of matrices over Abelian rings

Nahid Ashrafi, Marjan Sheibani, Huanyin Chen (2017)

Czechoslovak Mathematical Journal

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A ring $R$ is (weakly) nil clean provided that every element in $R$ is the sum of a (weak) idempotent and a nilpotent. We characterize nil and weakly nil matrix rings over abelian rings. Let $R$ be abelian, and let $n \in ℕ$ . We prove that $M_{n} (R)$ is nil clean if and only if $R / J (R)$ is Boolean and $M_{n} (J (R))$ is nil. Furthermore, we prove that $R$ is weakly nil clean if and only if $R$ is periodic; $R / J (R)$ is $ℤ_{3}$ , $B$ or $ℤ_{3} \oplus B$ where $B$ is a Boolean ring, and that $M_{n} (R)$ is weakly nil clean if and only if $M_{n} (R)$ is nil clean for all $n \geq 2$ .

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. ...

A note on infinite $a S$ -groups

Reza Nikandish, Babak Miraftab (2015)

Czechoslovak Mathematical Journal

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Let $G$ be a group. If every nontrivial subgroup of $G$ has a proper supplement, then $G$ is called an $a S$ -group. We study some properties of $a S$ -groups. For instance, it is shown that a nilpotent group $G$ is an $a S$ -group if and only if $G$ is a subdirect product of cyclic groups of prime orders. We prove that if $G$ is an $a S$ -group which satisfies the descending chain condition on subgroups, then $G$ is finite. Among other results, we characterize all abelian groups for which every nontrivial quotient group...