scholarly journals Stability estimates for an inverse Steklov problem in a class of hollow spheres

2021 ◽  
pp. 1-55
Author(s):  
Germain Gendron
Keyword(s):  
Hollow Sphere ◽  
Continuous Dependence ◽  
Warped Product ◽  
Hollow Spheres ◽  
Stability Estimate ◽  
Warping Function ◽  
Stability Estimates ◽  
Steklov Problem ◽  
Calderón Problem ◽  
Steklov Spectrum

In this paper, we study an inverse Steklov problem in a class of n-dimensional manifolds having the topology of a hollow sphere and equipped with a warped product metric. Precisely, we aim at studying the continuous dependence of the warping function defining the warped product with respect to the Steklov spectrum. We first show that the knowledge of the Steklov spectrum up to an exponential decreasing error is enough to determine uniquely the warping function in a neighbourhood of the boundary. Second, when the warping functions are symmetric with respect to 1/2, we prove a log-type stability estimate in the inverse Steklov problem. As a last result, we prove a log-type stability estimate for the corresponding Calderón problem.

scholarly journals New global stability estimates for the Calderón problem in two dimensions

2012 ◽  
Vol 12 (3) ◽  
pp. 553-569 ◽  
Author(s):  
Matteo Santacesaria
Keyword(s):  
Global Stability ◽  
Electrical Impedance ◽  
Stability Estimate ◽  
Two Dimensions ◽  
Stability Estimates ◽  
Impedance Tomography ◽  
Inverse Boundary ◽  
Conductivity Type ◽  
Calderón Problem ◽  
The Stability

AbstractWe prove a new global stability estimate for the Gel’fand–Calderón inverse problem on a two-dimensional bounded domain. Specifically, the inverse boundary value problem for the equation ${- }\Delta \psi + v\hspace{0.167em} \psi = 0$ on $D$ is analysed, where $v$ is a smooth real-valued potential of conductivity type defined on a bounded planar domain $D$. The main feature of this estimate is that it shows that the smoother a potential is, the more stable its reconstruction is. Furthermore, the stability is proven to depend exponentially on the smoothness, in a sense to be made precise. The same techniques yield a similar estimate for the Calderón problem for electrical impedance tomography.

Synthesis of urchin-like Ni3Si2O5(OH)4 hierarchical hollow spheres/GO composite with enhanced electrochemical properties for high-performance hybrid supercapacitors

2019 ◽  
Vol 48 (31) ◽  
pp. 11749-11762 ◽  
Author(s):  
Xueying Dong ◽  
Yifu Zhang ◽  
Qiushi Wang ◽  
Xiaorong Zhang ◽  
Meng Gao ◽  
...  
Keyword(s):  
Electrochemical Performance ◽  
Electrochemical Properties ◽  
Hollow Sphere ◽  
High Performance ◽  
Hollow Spheres ◽  
Capacity Retention ◽  
Hybrid Supercapacitors ◽  
Enhanced Electrochemical Performance

Urchin-like Ni3Si2O5(OH)4 hierarchical hollow sphere/GO composites were synthesized, which showed an enhanced electrochemical performance of 165 F g−1 at 0.5 A g−1 and 84% capacity retention after 5000 cycles.

Magnetic trajectories corresponding to Killing magnetic fields in a three-dimensional warped product

2020 ◽  
Vol 17 (14) ◽  
pp. 2050212
Author(s):  
Zafar Iqbal ◽  
Joydeep Sengupta ◽  
Subenoy Chakraborty
Keyword(s):  
Magnetic Fields ◽  
Warped Product ◽  
Vector Fields ◽  
Killing Vector ◽  
Three Dimensional ◽  
Charged Particles ◽  
Open Interval ◽  
Product Formula ◽  
Warping Function ◽  
Killing Vector Fields

The aim of this paper is to investigate Killing magnetic trajectories of varying electrically charged particles in a three-dimensional warped product [Formula: see text] with positive warping function [Formula: see text], where [Formula: see text] is an open interval in [Formula: see text] equipped with an induced semi-Euclidean metric on [Formula: see text]. First, Killing vector fields on [Formula: see text] are characterized and it is observed that lifts to [Formula: see text] of Killing vector fields tangent to [Formula: see text] are also Killing on [Formula: see text]. Now, any Killing vector field on [Formula: see text] corresponds to a Killing magnetic field on [Formula: see text]. Magnetic trajectories (also known as magnetic curves) of charged particles which move under the influence of Lorentz force generated by Killing magnetic fields on [Formula: see text] are obtained in both Riemannian and Lorentzian cases. Moreover, some examples are exhibited with pictures determining Killing magnetic trajectories in hyperbolic [Formula: see text]-space [Formula: see text] modeled by the Riemannian warped product [Formula: see text]. Furthermore, some examples of spacelike, timelike and lightlike Killing magnetic trajectories are given with their possible graphs in the Lorentzian warped product [Formula: see text].

scholarly journals The rational design of hierarchical MoS2 nanosheet hollow spheres sandwiched between carbon and TiO2@graphite as an improved anode for lithium-ion batteries

2019 ◽  
Vol 1 (5) ◽  
pp. 1957-1964 ◽  
Author(s):  
Faze Wang ◽  
Fanggang Li ◽  
Maojun Zheng ◽  
Yanbo Li ◽  
Li Ma
Keyword(s):  
Lithium Ion Batteries ◽  
Amorphous Carbon ◽  
Hollow Sphere ◽  
Rational Design ◽  
Specific Capacity ◽  
Hollow Spheres ◽  
Lithium Ion ◽  
Carbon Shell ◽  
Lithium Storage ◽  
Mos2 Nanosheet

Hierarchical MoS2 nanosheet hollow sphere is sandwiched by graphite and amorphous carbon shell, showing high reversible specific capacity and cycling stability for lithium storage.

The synthesis and characterization of 3D mesoporous CeO2 hollow spheres as a modifier for the simultaneous determination of amlodipine, hydrochlorothiazide and valsartan

2020 ◽  
Vol 12 (13) ◽  
pp. 1767-1778 ◽  
Author(s):  
Najmeh Farvardin ◽  
Shohreh Jahani ◽  
Maryam Kazemipour ◽  
Mohammad Mehdi Foroughi
Keyword(s):  
Electrochemical Sensor ◽  
Glassy Carbon ◽  
Hollow Sphere ◽  
Hollow Spheres ◽  
Synthesis And Characterization ◽  
Carbon Electrode ◽  
Modified Glassy Carbon Electrode ◽  
Mesoporous Ceo2

Electrochemical sensor based on mesoporous CeO2 hollow sphere modified glassy carbon electrode for simultaneous detecting amlodipine, hydrochlorothiazide and valsartan was fabricated.

scholarly journals Energy- and Regularity-Dependent Stability Estimates for Near-Field Inverse Scattering in Multidimensions

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
M. I. Isaev
Keyword(s):  
Inverse Problem ◽  
Inverse Scattering ◽  
Near Field ◽  
Scattering Problem ◽  
Inverse Scattering Problem ◽  
Uniform Norm ◽  
Stability Estimate ◽  
Stability Estimates ◽  
Logarithmic Stability

We prove new global Hölder-logarithmic stability estimates for the near-field inverse scattering problem in dimensiond≥3. Our estimates are given in uniform norm for coefficient difference and related stability efficiently increases with increasing energy and/or coefficient regularity. In addition, a global logarithmic stability estimate for this inverse problem in dimensiond=2is also given.

LOCAL MINIMIZERS WITH VORTEX PINNING FOR A GINZBURG–LANDAU FUNCTIONAL FOR SUPERCONDUCTING HOLLOW SPHERES

2012 ◽  
Vol 14 (01) ◽  
pp. 1250004
Author(s):  
JIAN ZHAI ◽  
SHUAI XUE
Keyword(s):  
Hollow Sphere ◽  
Hollow Spheres ◽  
Vortex Pinning ◽  
Local Minimizers ◽  
Ginzburg Landau ◽  
Pinning Effect

In this paper, we consider the pinning effect for full Ginzburg–Landau functional on a superconducting hollow sphere. The existence of local minimizers with vortices locating in the pinning regions is obtained.

scholarly journals Semi-Slant Warped Product Submanifolds of a Kenmotsu Manifold

2012 ◽  
Vol 2012 ◽  
pp. 1-10 ◽  
Author(s):  
Falleh R. Al-Solamy ◽  
Meraj Ali Khan
Keyword(s):  
Fundamental Form ◽  
Warped Product ◽  
Shape Operator ◽  
Second Fundamental Form ◽  
Warping Function ◽  
Kenmotsu Manifold

We study semi-slant warped product submanifolds of a Kenmotsu manifold. We obtain a characterization for warped product submanifolds in terms of warping function and shape operator and finally proved an inequality for squared norm of second fundamental form.

On the topology of CR-warped product submanifolds

2018 ◽  
Vol 15 (02) ◽  
pp. 1850032 ◽  
Author(s):  
Fulya Şahin
Keyword(s):  
Fundamental Form ◽  
Homology Group ◽  
Warped Product ◽  
Second Fundamental Form ◽  
Necessary Condition ◽  
Warping Function ◽  
Euclidean Spaces ◽  
Homotopy Sphere

We obtain a necessary condition for homology group to be zero on CR-warped product submanifold in Euclidean spaces in terms of second fundamental form of the submanifold and warping function. By using this condition, we show that such CR-warped product submanifold is a homotopy sphere.

Sign in / Sign up

Export Citation Format

Share Document