A Two-Dimensional Bisection Method for Solving Two-Parameter Eigenvalue Problems

1992 ◽  
Vol 13 (4) ◽  
pp. 1085-1093 ◽  
Author(s):  
Xingzhi Ji
Keyword(s):  
Eigenvalue Problems ◽  
Bisection Method ◽  
Two Dimensional ◽  
Two Parameter

scholarly journals MULTIVARIATE SAMPLING THEOREMS ASSOCIATED WITH MULTIPARAMETER DIFFERENTIAL OPERATORS

2005 ◽  
Vol 48 (2) ◽  
pp. 257-277 ◽  
Author(s):  
M. H. Annaby
Keyword(s):  
Lagrange Interpolation ◽  
Differential Operators ◽  
Eigenvalue Problems ◽  
Sampling Theory ◽  
Sampling Theorem ◽  
Second Order ◽  
Two Dimensional ◽  
Single Variable ◽  
Sampling Theorems ◽  
Two Parameter

AbstractWe investigate the multivariate sampling theory associated with multiparameter eigenvalue problems. A several-variable counterpart of the classical sampling theorem of Whittaker, Kotel’nikov and Shannon is given. It arose when the multiparameter system has order one. Two-dimensional sampling theorems associated with two-parameter systems of second-order differential operators will be established. The sampling formulae are of multivariate non-uniform Lagrange interpolation type. Unlike many of the known formulae, the interpolating functions are not necessarily products of single variable functions.

scholarly journals Finsler Geometry for Two-Parameter Weibull Distribution Function

2017 ◽  
Vol 2017 ◽  
pp. 1-6 ◽  
Author(s):  
Emrah Dokur ◽  
Salim Ceyhan ◽  
Mehmet Kurban
Keyword(s):  
Probability Density Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Density Function ◽  
Finsler Space ◽  
Finsler Geometry ◽  
Cumulative Probability ◽  
Two Dimensional ◽  
Energy Potential ◽  
Two Parameter

To construct the geometry in nonflat spaces in order to understand nature has great importance in terms of applied science. Finsler geometry allows accurate modeling and describing ability for asymmetric structures in this application area. In this paper, two-dimensional Finsler space metric function is obtained for Weibull distribution which is used in many applications in this area such as wind speed modeling. The metric definition for two-parameter Weibull probability density function which has shape (k) and scale (c) parameters in two-dimensional Finsler space is realized using a different approach by Finsler geometry. In addition, new probability and cumulative probability density functions based on Finsler geometry are proposed which can be used in many real world applications. For future studies, it is aimed at proposing more accurate models by using this novel approach than the models which have two-parameter Weibull probability density function, especially used for determination of wind energy potential of a region.

scholarly journals Perturbation of eigenvalues due to gaps in two-dimensional boundaries

2006 ◽  
Vol 463 (2079) ◽  
pp. 759-786 ◽  
Author(s):  
Anthony M.J Davis ◽  
Stefan G Llewellyn Smith
Keyword(s):  
Eigenvalue Problems ◽  
Numerical Solutions ◽  
Neumann Boundary ◽  
Diffusion Problem ◽  
Length Scale ◽  
Two Dimensional ◽  
Constructive Approach ◽  
Term Outcome ◽  
Long Term Outcome

Motivated by problems involving diffusion through small gaps, we revisit two-dimensional eigenvalue problems with localized perturbations to Neumann boundary conditions. We recover the known result that the gravest eigenvalue is O (|ln  ϵ | −1 ), where ϵ is the ratio of the size of the hole to the length-scale of the domain, and provide a simple and constructive approach for summing the inverse logarithm terms and obtaining further corrections. Comparisons with numerical solutions obtained for special geometries, both for the Dirichlet ‘patch problem’ where the perturbation to the boundary consists of a different boundary condition and for the gap problem, confirm that this approach is a simple way of obtaining an accurate value for the gravest eigenvalue and hence the long-term outcome of the underlying diffusion problem.

Similarity Solution for the Curved Two-Dimensional Jet

1972 ◽  
Vol 39 (4) ◽  
pp. 879-882
Author(s):  
G. K. Fleming ◽  
S. A. Alpay
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Nonlinear Equation ◽  
Similarity Solution ◽  
Separation Bubble ◽  
The Other ◽  
Wall Jet ◽  
Two Dimensional ◽  
Two Parameter ◽  
Outer Half

A similarity solution has been obtained for a fluid jet bounded on one side by a separation bubble and on the other by an unbounded region containing the same fluid. The inner boundary has been approximated by a porous pseudowall. The resulting mathematical model reduces to other cases such as the plane wall jet and the free curved jet. A two-parameter family of solutions to the resulting nonlinear equation for the outer half of the jet correlates well with experimental data.

A Two-Dimensional Nonorthogonal WLP-FDTD Method for Eigenvalue Problems

2013 ◽  
Vol 23 (10) ◽  
pp. 515-517
Author(s):  
Wei-Jun Chen ◽  
Wei Shao ◽  
Jia-Lin Li ◽  
Bing-Zhong Wang
Keyword(s):  
Eigenvalue Problems ◽  
Fdtd Method ◽  
Two Dimensional

scholarly journals To switch or not to switch – a machine learning approach for ferroelectricity

2020 ◽  
Vol 2 (5) ◽  
pp. 2063-2072 ◽  
Author(s):  
Sabine M. Neumayer ◽  
Stephen Jesse ◽  
Gabriel Velarde ◽  
Andrei L. Kholkin ◽  
Ivan Kravchenko ◽  
...  
Keyword(s):  
Machine Learning ◽  
Measured Signal ◽  
Learning Approach ◽  
Two Dimensional ◽  
Dimensional Representation ◽  
Machine Learning Methods ◽  
Machine Learning Approach ◽  
Signal Dependence ◽  
Two Parameter

The introduced two-dimensional representation of two-parameter signal dependence allows for clear interpretation and classification of the measured signal upon using machine learning methods.

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