scholarly journals TRANSMISSION EIGENVALUES FOR MULTIPOINT SCATTERERS

2021 ◽  
Vol 9 (4) ◽  
pp. 17-25
Author(s):  
Petr Grinevich ◽  
◽  
Roman Novikov ◽  
Keyword(s):  
Strong Sense ◽  
Positive Energy ◽  
Transmission Eigenvalues ◽  
Transmission Eigenvalue ◽  
Infinite Multiplicity

We study the transmission eigenvalues for the multipoint scatterers of the Bethe- Peierls-Fermi-Zeldovich-Beresin-Faddeev type in dimensions d = 2 and d = 3. We show that for these scatterers: 1) each positive energy E is a transmission eigenvalue (in the strong sense) of infinite multiplicity; 2) each complex E is an interior transmission eigenvalue of infinite multiplicity. The case of dimension d = 1 is also discussed.

Reconstruction of the refractive index from transmission eigenvalues for spherically stratified media

2017 ◽  
Vol 25 (1) ◽  
Author(s):  
Xiao-Chuan Xu ◽  
Chuan-Fu Yang
Keyword(s):  
Refractive Index ◽  
Eigenvalue Problem ◽  
Stratified Medium ◽  
Stratified Media ◽  
Transmission Eigenvalues ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem

AbstractThis work deals with the interior transmission eigenvalue problem for a spherically stratified medium supported in

Isospectral sets for transmission eigenvalue problem

2020 ◽  
Vol 28 (1) ◽  
pp. 63-69 ◽  
Author(s):  
Chuan-Fu Yang ◽  
Sergey A. Buterin
Keyword(s):  
Wave Equation ◽  
Eigenvalue Problem ◽  
Wave Speed ◽  
Spherically Symmetric ◽  
Variable Speed ◽  
Transmission Eigenvalues ◽  
Constructive Methods ◽  
Transmission Eigenvalue ◽  
Symmetric Variable ◽  
Transmission Eigenvalue Problem

AbstractWe consider the boundary value problem {R(a,q)}: {-y^{\prime\prime}(x)+q(x)y(x)=\lambda y(x)} with {y(0)=0} and {y(1)\cos(a\sqrt{\lambda})=y^{\prime}(1)\frac{\sin(a\sqrt{\lambda})}{\sqrt{% \lambda}}}. Motivated by the previous work [T. Aktosun and V. G. Papanicolaou, Reconstruction of the wave speed from transmission eigenvalues for the spherically symmetric variable-speed wave equation, Inverse Problems 29 2013, 6, Article ID 065007], it is natural to consider the following interesting question: how does one characterize isospectral sets corresponding to problem {R(1,q)}? In this paper applying constructive methods we answer the above question.

Nonconforming Finite Element Method for the Transmission Eigenvalue Problem

2016 ◽  
Vol 9 (1) ◽  
pp. 92-103 ◽  
Author(s):  
Xia Ji ◽  
Yingxia Xi ◽  
Hehu Xie
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Nonconforming Finite Element ◽  
Transmission Eigenvalues ◽  
Nonconforming Finite Element Method ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem ◽  
Eigenvalue And Eigenfunction ◽  
Theoretical Results ◽  
Element Method

AbstractIn this paper, we analyze a nonconforming finite element method for the computation of transmission eigenvalues and the corresponding eigenfunctions. The error estimates of the eigenvalue and eigenfunction approximation are given, respectively. Finally, some numerical examples are provided to validate the theoretical results.

scholarly journals Are Your Vitals OK? Revitalizing Vitality of Nurses through Relational Caring for Patients

Healthcare ◽  
2021 ◽  
Vol 9 (1) ◽  
pp. 46
Author(s):  
Jung Hwan Park ◽  
Young Kyun Chang ◽  
Sooyeol Kim
Keyword(s):  
Prosocial Behavior ◽  
Job Demands ◽  
Strong Sense ◽  
Job Resources ◽  
Positive Energy ◽  
Patient Centered ◽  
South Korean ◽  
Job Demand ◽  
Alternative Approach ◽  
Healthcare Employees

This study offers an alternative approach to address on-going concerns about burnout of healthcare employees. Departing from the existing job-demand based approach proposing that healthcare employees’ burnout can be resolved by reducing demands, we theorize that patient-centered prosocial behavior, even if it often increases job demands, could serve as potential job resources that fuel positive energy to vitalize nurses at work. We further theorize that this possibility could be more pronounced among a group of nurses with a strong sense of ethical membership regarding their hospital (i.e., moral identification). To test our hypotheses, we used a sample of 202 nurses from 104 South Korean hospitals. We found that, even controlling for workloads as an indicator of job demand, nurses who engage in patient-centered prosocial behavior (i.e., relational caring) are likely to feel vitalized, and this pattern is more salient among a group of nurses with high moral identification. Results indicate that prosocial behavior could be an alternative job resource that helps nurses flourish at work.

The interior transmission eigenvalue problem for a spherically-symmetric domain with anisotropic medium and a cavity

2015 ◽  
Vol 23 (4) ◽  
Author(s):  
Andreas Kirsch ◽  
Hayk Asatryan
Keyword(s):  
Inverse Problem ◽  
Anisotropic Medium ◽  
Acoustic Waves ◽  
Symmetric Domain ◽  
Spherically Symmetric ◽  
Scattering Problems ◽  
Transmission Eigenvalues ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem ◽  
Infinite Set

AbstractWe consider the scattering of spherically-symmetric acoustic waves by an anisotropic medium and a cavity. While there is a large number of recent works devoted to the scattering problems with cavities, existence of an infinite set of transmission eigenvalues is an open problem in general. In this paper we prove existence of an infinite set of transmission eigenvalues for anisotropic Helmholtz and Schrödinger equations in a spherically-symmetric domain with a cavity. Further in this paper we consider the corresponding inverse problem. Under some assumptions we prove the uniqueness in the inverse problem.

scholarly journals Important Issues on Spectral Properties of a Transmission Eigenvalue Problem

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Besiana Cobani ◽  
Aurora Simoni ◽  
Ledia Subashi
Keyword(s):  
Eigenvalue Problem ◽  
Inverse Scattering ◽  
Scattering Problem ◽  
Fredholm Property ◽  
Normal Derivative ◽  
Inhomogeneous Media ◽  
Transmission Eigenvalues ◽  
Transmission Eigenvalue ◽  
Transmission Eigenvalue Problem ◽  
The Difference

Nowadays, inverse scattering is an important field of interest for many mathematicians who deal with partial differential equations theory, and the research in inverse scattering is in continuous progress. There are many problems related to scattering by an inhomogeneous media. Here, we study the transmission eigenvalue problem corresponding to a new scattering problem, where boundary conditions differ from any other interior problem studied previously. more specifically, instead of prescribing the difference Cauchy data on the boundary which is the classical form of the problem, we consider the case when the difference of the trace of the fields is proportional to the normal derivative of the field. Typical concerns related to TEP (transmission eigenvalue problem) are Fredholm property and solvability, the discreteness of the transmission eigenvalues, and their existence. In this article, we provide answers for all these concerns in a given interior transmission problem for an inhomogeneous media. We use the variational method and a very important theorem on the existence of transmission eigenvalues to arrive at the conclusion of the existence of the transmission eigenvalues.

WAVE PROPAGATION AND LOCALIZATION VIA QUASI-NORMAL MODES AND TRANSMISSION EIGENCHANNELS

2012 ◽  
Vol 11 ◽  
pp. 1-11 ◽  
Author(s):  
JING WANG ◽  
ZHOU SHI ◽  
MATTHIEU DAVY ◽  
AZRIEL Z. GENACK
Keyword(s):  
Normal Modes ◽  
Destructive Interference ◽  
Strongly Correlated ◽  
Transmission Eigenvalues ◽  
Distinctive Features ◽  
Transmission Coefficients ◽  
Wave Transport ◽  
Transmission Eigenvalue ◽  
Random Samples ◽  
Speckle Patterns

Field transmission coefficients for microwave radiation between arrays of points on the incident and output surfaces of random samples are analyzed to yield the underlying quasi-normal modes and transmission eigenchannels of each realization of the sample. The linewidths, central frequencies, and transmitted speckle patterns associated with each of the modes of the medium are found. Modal speckle patterns are found to be strongly correlated leading to destructive interference between modes. This explains distinctive features of transmission spectra and pulsed transmission. An alternate description of wave transport is obtained from the eigenchannels and eigenvalues of the transmission matrix. The maximum transmission eigenvalue, τ1 is near unity for diffusive waves even in turbid samples. For localized waves, τ1 is nearly equal to the dimensionless conductance, which is the sum of all transmission eigenvalues, g = Στn. The spacings between the ensemble averages of successive values of ln τn are constant and equal to the inverse of the bare conductance in accord with predictions by Dorokhov. The effective number of transmission eigenvalues Neff determines the contrast between the peak and background of radiation focused for maximum peak intensity. The connection between the mode and channel approaches is discussed.

scholarly journals On local and global structures of transmission eigenfunctions and beyond

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Hongyu Liu
Keyword(s):  
Inverse Scattering ◽  
Wave Scattering ◽  
Eigenvalue Problems ◽  
Practical Importance ◽  
Intrinsic Properties ◽  
Eigenvalues And Eigenfunctions ◽  
Scattering Problems ◽  
Transmission Eigenvalues ◽  
Inverse Scattering Problems ◽  
Transmission Eigenvalue

AbstractThe (interior) transmission eigenvalue problems are a type of non-elliptic, non-selfadjoint and nonlinear spectral problems that arise in the theory of wave scattering. They connect to the direct and inverse scattering problems in many aspects in a delicate way. The properties of the transmission eigenvalues have been extensively and intensively studied over the years, whereas the intrinsic properties of the transmission eigenfunctions are much less studied. Recently, in a series of papers, several intriguing local and global geometric structures of the transmission eigenfunctions are discovered. Moreover, those longly unveiled geometric properties produce some interesting applications of both theoretical and practical importance to direct and inverse scattering problems. This paper reviews those developments in the literature by summarizing the results obtained so far and discussing the rationales behind them. There are some side results of this paper including the general formulations of several types of transmission eigenvalue problems, some interesting observations on the connection between the transmission eigenvalue problems and several challenging inverse scattering problems, and several conjectures on the spectral properties of transmission eigenvalues and eigenfunctions, with most of them are new to the literature.

Welsh Politics after the EU Referendum

2017 ◽  
Vol 26 (2) ◽  
pp. 212-228 ◽  
Author(s):  
John Osmond
Keyword(s):  
Effective Leadership ◽  
Strong Sense ◽  
Speaking Up ◽  
Common Cause ◽  
National Assembly ◽  
Working Together ◽  
Eu Referendum ◽  
Welsh Politics ◽  
Plaid Cymru ◽  
The Eu

This paper examines the electoral and ideological contest that has taken place between Welsh Labour and Plaid Cymru in the five National Assembly elections that have been held between 1999 and 2016. Both parties have found success when they have managed to combine effective leadership with a coherent programme and a strong sense of Welsh identity. However, the Welsh vote to leave the EU in the June 2016 referendum has dealt both parties a poor hand in speaking up for Welsh interests. Can they find a common cause in working together and also with Scotland to take Wales forward in a progressive constitutional direction?

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