Search results for "STABILITY"
showing 10 items of 3085 documents
The Calderón problem for the fractional wave equation: Uniqueness and optimal stability
2021
We study an inverse problem for the fractional wave equation with a potential by the measurement taking on arbitrary subsets of the exterior in the space-time domain. We are interested in the issues of uniqueness and stability estimate in the determination of the potential by the exterior Dirichlet-to-Neumann map. The main tools are the qualitative and quantitative unique continuation properties for the fractional Laplacian. For the stability, we also prove that the log type stability estimate is optimal. The log type estimate shows the striking difference between the inverse problems for the fractional and classical wave equations in the stability issue. The results hold for any spatial di…
The fractional Calderón problem: Low regularity and stability
2017
The Calder\'on problem for the fractional Schr\"odinger equation was introduced in the work \cite{GSU}, which gave a global uniqueness result also in the partial data case. This article improves this result in two ways. First, we prove a quantitative uniqueness result showing that this inverse problem enjoys logarithmic stability under suitable a priori bounds. Second, we show that the results are valid for potentials in scale-invariant $L^p$ or negative order Sobolev spaces. A key point is a quantitative approximation property for solutions of fractional equations, obtained by combining a careful propagation of smallness analysis for the Caffarelli-Silvestre extension and a duality argumen…
Volume preserving mean curvature flows near strictly stable sets in flat torus
2021
In this paper we establish a new stability result for the smooth volume preserving mean curvature flow in flat torus $\mathbb T^n$ in low dimensions $n=3,4$. The result says roughly that if the initial set is near to a strictly stable set in $\mathbb T^n$ in $H^3$-sense, then the corresponding flow has infinite lifetime and converges exponentially fast to a translate of the strictly stable (critical) set in $W^{2,5}$-sense.
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…
Increasing stability in the linearized inverse Schrödinger potential problem with power type nonlinearities
2022
We consider increasing stability in the inverse Schr\"{o}dinger potential problem with power type nonlinearities at a large wavenumber. Two linearization approaches, with respect to small boundary data and small potential function, are proposed and their performance on the inverse Schr\"{o}dinger potential problem is investigated. It can be observed that higher order linearization for small boundary data can provide an increasing stability for an arbitrary power type nonlinearity term if the wavenumber is chosen large. Meanwhile, linearization with respect to the potential function leads to increasing stability for a quadratic nonlinearity term, which highlights the advantage of nonlinearit…
Static instability analysis of an elastic band travelling in the gravitational field
2011
Static instability analysis is performed for an axially moving elastic band, which is travelling at a constant velocity in a uniform gravitational field between two supports. The buckling of the band is investigated with the help of admitting small transverse deflections. The model of a thin elastic beam (panel) subjected to bending, centrifugal forces and nonhomogeneous tension (including a gravitational term) is used. Buckling analysis and estimation of the critical velocities of elastic instability are based on variational principles and variational inequalities. As a result, explicit formulas for upper and lower limits for critical velocities are found. It is shown analytically that a c…
Isolated lip dermatitis (atopic cheilitis), successfully treated with topical tacrolimus 0.03%
2020
Background Exfoliative and erosive cheilitis, may be a source of speech and chewing discomfort, but may also be an aesthetic issue for the patients affected. Such a clinical presentation may implicate a variety of inflammatory conditions, including atopic (eczematous) cheilitis. Topical and systemic agents, e.g. corticosteroids, have been used to treat inflammatory lip conditions. Topical tacrolimus has also been used in some inflammatory lip conditions. Material and Methods We performed a retrospective clinical analysis of atopic cheilitis patients. Results Between 2015 and 2020, we addressed 7 (seven) patients with atopic dermatitis affecting only lips and were diagnosed as atopic-eczemat…
Apollon gene silencing induces apoptosis in breast cancer cells via p53 stabilisation and caspase-3 activation
2009
We analysed the effects of small interfering RNA (siRNA)-mediated silencing of Apollon, a member of the inhibitors of apoptosis protein family, on the proliferative potential and ability of human breast cancer cell lines to undergo apoptosis. In wild-type p53 ZR75.1 cells, Apollon knockdown resulted in a marked, time-dependent decline of cell growth and an increased rate of apoptosis, which was associated with p53 stabilisation and activation of the mitochondrial-dependent apoptotic pathway. Pre-incubation of cells with a p53-specific siRNA resulted in a partial rescue of cell growth inhibition, as well as in a marked reduction of the apoptotic response, indicating p53 as a major player in …
Longitudinal tests of the theory of planned behaviour : A meta-analysis
2023
In a meta-analysis of longitudinal analyses of the theory of planned behaviour, we tested a series of extended or auxiliary theory-consistent hypotheses: construct stability, theory predictions within and between occasions, consistency over time or stationarity in theory effects and reciprocal effects among constructs. We also tested the effects of moderators on theory effects: measurement lag, health behaviour type (protection, risk) and specific health behaviours (alcohol, dietary and physical activity). A systematic search identified 87 studies eligible for inclusion. Meta-analytic structural equation models supported construct stability and theory effects within and between occasions. O…
Added-Mass Based Efficient Fluid–Structure Interaction Model for Dynamics of Axially Moving Panels with Thermal Expansion
2020
The paper considers the analysis of a traveling panel, submerged in axially flowing fluid. In order to accurately model the dynamics and stability of a lightweight moving material, the interaction between the material and the surrounding air must be taken into account. The lightweight material leads to the inertial contribution of the surrounding air to the acceleration of the panel becoming significant. This formulation is novel and the case complements our previous studies on the field. The approach described in this paper allows for an efficient semi-analytical solution, where the reaction pressure of the fluid flow is analytically represented by an added-mass model in terms of the panel…