scholarly journals EIGEN VALUES OF INTERVAL MATRIX

2021 ◽  
Vol 1 (4) ◽  
Keyword(s):  
Interval Matrix ◽  
Eigen Values

Bounds for the Eigen Values and Energy of Degree Product Adjacency Matrix of A Graph

2019 ◽  
Vol 10 (3) ◽  
pp. 565-573
Author(s):  
Keerthi G. Mirajkar ◽  
Bhagyashri R. Doddamani
Keyword(s):  
Adjacency Matrix ◽  
Eigen Values

scholarly journals On Spectral Properties of Compact Toeplitz Operators on Bergman Space with Logarithmically Decaying Symbol and Applications to Banded Matrices

2021 ◽  
Author(s):  
Mahamet Koïta ◽  
Stanislas Kupin ◽  
Sergey Naboko ◽  
Belco Touré
Keyword(s):  
Spectral Analysis ◽  
Continuous Function ◽  
Bergman Space ◽  
Orthogonal Projection ◽  
Spectral Properties ◽  
Toeplitz Operators ◽  
Closed Subspace ◽  
Jacobi Matrices ◽  
Banded Matrices ◽  
Eigen Values

Abstract Let $L^2({{\mathbb{D}}})$ be the space of measurable square-summable functions on the unit disk. Let $L^2_a({{\mathbb{D}}})$ be the Bergman space, that is, the (closed) subspace of analytic functions in $L^2({{\mathbb{D}}})$. $P_+$ stays for the orthogonal projection going from $L^2({{\mathbb{D}}})$ to $L^2_a({{\mathbb{D}}})$. For a function $\varphi \in L^\infty ({{\mathbb{D}}})$, the Toeplitz operator $T_\varphi : L^2_a({{\mathbb{D}}})\to L^2_a({{\mathbb{D}}})$ is defined as $$\begin{align*} & T_\varphi f=P_+\varphi f, \quad f\in L^2_a({{\mathbb{D}}}). \end{align*}$$The main result of this article are spectral asymptotics for singular (or eigen-) values of compact Toeplitz operators with logarithmically decaying symbols, that is, $$\begin{align*} & \varphi(z)=\varphi_1(e^{i\theta})\, (1+\log(1/(1-r)))^{-\gamma},\quad \gamma>0, \end{align*}$$where $z=re^{i\theta }$ and $\varphi _1$ is a continuous (or piece-wise continuous) function on the unit circle. The result is applied to the spectral analysis of banded (including Jacobi) matrices.

Torsional oscillations of a fluid sphere with a rigid boundary in a uniform magnetic field

1966 ◽  
Vol 24 (2) ◽  
pp. 275-284
Author(s):  
R. A. Wentzell
Keyword(s):  
Magnetic Field ◽  
Exact Solution ◽  
Uniform Magnetic Field ◽  
Perfect Conductor ◽  
Rigid Boundary ◽  
Torsional Oscillations ◽  
Magnetic Viscosity ◽  
Eigen Values ◽  
Infinite Conductivity ◽  
Axis Of Symmetry

Plumpton & Ferraro (1955) considered the torsional oscillations of an infinitely conducting sphere in a uniform magnetic field. They showed that if the fluid and magnetic viscosity were assumed to be zero in the governing differential equations, then a continuous spectrum of eigenvalues could be obtained. This novel feature was clarified by Stewartson (1957) when he obtained the exact solution and showed that in the correct limit of a perfect conductor the eigen-values are discrete. Furthermore, in the limit of infinite conductivity the oscillations occur only on the axis of symmetry (figure 1).

scholarly journals Adaptation, linguistic and clinimetric validation of the Bangla version of Zarit Burden Interview

2016 ◽  
Vol 9 (4) ◽  
pp. 181 ◽  
Author(s):  
Farzana Rabin ◽  
Jhunu Shamsun Nahar ◽  
Mohammad S. I. Mullick ◽  
Helal Uddin Ahmed ◽  
Nafia Farzana
Keyword(s):  
Factor Analysis ◽  
Exploratory Factor Analysis ◽  
Caregiver Burden ◽  
Primary Diagnosis ◽  
Validity And Reliability ◽  
Zarit Burden Interview ◽  
Eigen Values ◽  
Diagnosis Of Dementia ◽  
Highly Correlated ◽  
Test Retest Reliability

<p>The aim of this study was to develop a culturally adapted and validated Bangla version of Zarit Burden Interview  (ZBI-B) questionnaire for use in Bangla speaking caregiver of patient with dementia. This study was conducted on 100 caregivers related to consecutively attending outpatients with a previously established primary diagnosis of dementia, according to DSM-IV criteria. Validity and reliability were evaluated by comparing with the caregiver burden inventory (CBI). An exploratory factor analysis with the principle component with varimax rotation was used to detect the factorial structure in observed measurements. To attain the best-fitting structure and the correct number of factors, the following criteria were used: Eigen values &gt;1.0, factor loadings &gt;0.30. The Cronbach’s alpha value was 0.847 for test and 0.839 retest. The intra-class correlation for the test-retest reliability was 0.89. The ZBI score was highly correlated with the CBI score (Pearson’s correlation coefficient, r=0.909, P=.001). From the exploratory factor analysis six factors comprising 20 items were extracted with Eigen values higher than 1.00 accounting for 69% of the total item variance. In conclusion, ZBI-B is valid, reliable and useful for use in clinical contexts and in future studies that could lead to a better understanding of caregiver burden in dementia.</p>

Comparative Evaluation of Mode Combination Methods in Seismic Analysis Using Response Spectrum Method for Tank Structure Using FEA - Seismic FEA

2011 ◽  
Vol 110-116 ◽  
pp. 5240-5248
Author(s):  
Sujay Shelke ◽  
H.V. Vankudre ◽  
Vinay Patil
Keyword(s):  
Seismic Analysis ◽  
Response Spectrum ◽  
Initial Step ◽  
Relative Displacement ◽  
Geometrical Parameters ◽  
Response Spectrum Method ◽  
Spectrum Method ◽  
Combination Methods ◽  
Eigen Values ◽  
Modes Of Vibration

Typical seismic analysis using response spectrum method involves several steps from the initial step of extracting the modes. At the initial stage Eigen values are extracted corresponding to the modes of vibration. These give us Eigen vectors which are a series of relative displacement shapes; however these do not correspond to real displacements or stresses. Participation factors asses these Eigen vectors and grades them according to contribution they will have to the overall solution. Based on the spectral seismic acceleration, participation factor is used to calculate the mode coefficient, which is more of a scaling factor to give physical meaning to the values. Once the modes are extracted, the key issue is of combining these modes to obtain the seismic response. The modes cannot be added algebraically in reality as all the modes do not occur at the same time. Hence we employ methods which can add the modes in a more realistic manner. The objective of this paper is to do a comparative study of various mode combination methods with a focus on tank structures and study the effect of various geometrical parameters on the combination methods

scholarly journals Excitonic States and Related Optical Susceptibility in InN/AlN Quantum Well Under the Effects of the Well Size and Impurity Position

2021 ◽  
Vol 4 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Fathallah Jabouti ◽  
Haddou El Ghazi ◽  
Redouane En-nadir ◽  
Izeddine Zorkani ◽  
Anouar Jorio
Keyword(s):  
Quantum Well ◽  
Heavy Hole ◽  
Binding Energies ◽  
Exciton Transition ◽  
Impurity Position ◽  
Optical Susceptibility ◽  
Peak Energy ◽  
Eigen Values ◽  
Excitonic States ◽  
Photoluminescence Peak

Based on the finite difference method, linear optical susceptibility, photoluminescence peak and binding energies of three first states of an exciton trapped by a positive charge donor-impurity ( ) confined in InN/AlN quantum well are investigated in terms of well size and impurity position. The electron, heavy hole free and bound excitons allowed eigen-values and corresponding eigen-functions are obtained numerically by solving one-dimensional time-independent Schrödinger equation. Within the parabolic band and effective mass approximations, the calculations are made considering the coupling of the electron in the n-th conduction subband and the heavy hole in the m-th valence subband under the impacts of the well size and impurity position. The obtained results show clearly that the energy, binding energy and photoluminescence peak energy show a decreasing behavior according to well size for both free and bound cases. Moreover, the optical susceptibility associated to exciton transition is strongly red-shift (blue-shifted) with enhancing the well size (impurity position).

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