Results 31 to 40 of about 7,827 (246)

On Spectral Characterization of Nonuniform Hyperbolicity

Journal of Function Spaces, 2017
We give a complete functional theoretic characterization of tempered exponential dichotomies in terms of the invertibility of certain linear operators acting on a suitable Frechét space.
Muna Abu Alhalawa, Davor Dragičević
doaj   +1 more source

Exact bounds for exponential dichotomy roughness III. Semistrong dichotomy

Journal of Differential Equations, 1991
[For part II see the above review.] Consider the linear system (1) \(x'=A(t)x\) and its perturbation (2) \(x'=[A(t)+B(t)]x\). In an earlier paper [J. Differ. Equations 71, 63-71 (1988; Zbl 0651.34051)] the author obtained exact bounds for exponential dichotomy roughness by suitably restricting the perturbation term \(B(t)\).
openaire   +2 more sources

Nonuniform exponential dichotomies and admissibility

Discrete & Continuous Dynamical Systems - A, 2011
In this paper we consider the relation between the notions of exponential stability and admissibility, in the general context of nonuniform exponential behavior. In particular, we show that with respect to certain adapted norms related to the nonuniform behavior, if any $L^p$ space, with $p\in(1,\infty]$, is admissible for a given evolution process ...
Luis Barreira, Claudia Valls
openaire   +1 more source

On exponential dichotomy in Banach spaces [PDF]

Bulletin of the Australian Mathematical Society, 1981
In this paper we study the exponential dichotomy property for linear systems, the evolution of which can be described by a semigroup of class C0 on a Banach space. We define the class of (p, q) dichotomic semigroups and establish the connections between the dichotomy concepts and admissibility property of the pair (Lp, Lq) for linear control systems ...
Megan, Mihail, Preda, Petre
openaire   +1 more source

Genetic attenuation of ALDH1A1 increases metastatic potential and aggressiveness in colorectal cancer

Molecular Oncology, EarlyView.
Aldehyde dehydrogenase 1A1 (ALDH1A1) is a cancer stem cell marker in several malignancies. We established a novel epithelial cell line from rectal adenocarcinoma with unique overexpression of this enzyme. Genetic attenuation of ALDH1A1 led to increased invasive capacity and metastatic potential, the inhibition of proliferation activity, and ultimately ...
Martina Poturnajova, Zuzana Kozovska, Ondrej Pos, Kristina Pavlov, Sachin Gulati, Peter Makovicky, Kristina Jakic, Monika Burikova, Eva Sedlackova, Barbora Svitkova, Silvia Tyciakova, Vojtech Bystry, Nicolas Blavet, Boris Tichy, Matej Hrnciar, Jaroslav Budis, Miroslav Tomas, Peter Dubovan, Georgina Kolnikova, Veronika Repaska, Nikoleta Mojzesova, Eva Zomborska, Daniel Pindak, Michal Mego, Tomas Szemes, Miroslava Matuskova   +25 more
wiley   +1 more source

Shadowing for Nonautonomous Dynamics

Advanced Nonlinear Studies, 2019
We prove that whenever a sequence of bounded operators (Am)m∈ℤ{(A_{m})_{m\in\mathbb{Z}}} acting on a Banach space X admits an exponential dichotomy and a sequence of differentiable maps fm:X→X{f_{m}\colon X\to X}, m∈ℤ{m\in\mathbb{Z}}, has bounded and ...
Backes Lucas, Dragičević Davor
doaj   +1 more source

A complete characterization of exponential stability for discrete dynamics

, 2017
For a discrete dynamics defined by a sequence of bounded and not necessarily invertible linear operators, we give a complete characterization of exponential stability in terms of invertibility of a certain operator acting on suitable Banach sequence ...
Lupa, Nicolae, Popescu, Liviu Horia
core   +1 more source

Exact bounds for exponential dichotomy roughness I. Strong dichotomy

Journal of Differential Equations, 1988
The author considers the unperturbed and perturbed equations (1) \(x'=A(t)x\) and (2) \(y'=[A(t)+B(t)]y,\) where \(t\in {\mathbb{R}}_+\) and A and B are \(n\times n\) matrices. It is shown that if (1) has strong dichotomy on \({\mathbb{R}}_+\), then (2) also has a dichotomy and exact estimates on the exponential dichotomy roughness are obtained.
openaire   +1 more source

Single‐molecule DNA flow‐stretch assays for high‐throughput DNA–protein interaction studies

FEBS Open Bio, EarlyView.
We describe an optimised single‐molecule DNA flow‐stretch assay that visualises DNA–protein interactions in real time. Linear DNA fragments are tethered to a surface and stretched by buffer flow for fluorescence imaging. Using λ and φX174 DNA, this protocol enhances reproducibility and accessibility, providing a versatile approach for studying diverse ...
Ayush Kumar Ganguli, Mohammad Nour Alsamsam, Ugnė Bagdonaitė, Van Truc Vu, Chun‐Jen Huang, Polina Kuzhir, Mindaugas Zaremba, Aurimas Kopūstas, Marijonas Tutkus   +8 more
wiley   +1 more source

Nonlinear stability of source defects in oscillatory media [PDF]

, 2018
In this paper, we prove the nonlinear stability under localized perturbations of spectrally stable time-periodic source defects of reaction-diffusion systems. Consisting of a core that emits periodic wave trains to each side, source defects are important
Beck, Margaret, Nguyen, Toan, Sandstede, Bjorn, Zumbrun, Kevin   +3 more
core   +1 more source