scholarly journals Lower and upper bounds of Laplacian eigenvalue problem by weak Galerkin method on triangular meshes

2019 ◽  
Vol 24 (1) ◽  
pp. 403-413
Author(s):  
Qilong Zhai ◽  
◽  
Ran Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Galerkin Method ◽  
Upper Bounds ◽  
Triangular Meshes ◽  
Lower And Upper Bounds ◽  
Weak Galerkin ◽  
Laplacian Eigenvalue

scholarly journals Acceleration of Weak Galerkin Methods for the Laplacian Eigenvalue Problem

2018 ◽  
Vol 79 (2) ◽  
pp. 914-934
Author(s):  
Qilong Zhai ◽  
Hehu Xie ◽  
Ran Zhang ◽  
Zhimin Zhang
Keyword(s):  
Eigenvalue Problem ◽  
Galerkin Methods ◽  
Weak Galerkin ◽  
Laplacian Eigenvalue

The Perturbation Method for Stability Analysis of Uncertain Structures

2013 ◽  
Vol 367 ◽  
pp. 302-307
Author(s):  
Chang Rui Ji ◽  
Zao Ni
Keyword(s):  
Stability Analysis ◽  
Eigenvalue Problem ◽  
Perturbation Method ◽  
Stability Problem ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Interval Mathematics ◽  
Stiffness Matrices ◽  
Uncertain Structure ◽  
Uncertain Structures

This paper is concerned with the structural stability problem involving uncertain-but-bounded parameters, specified as bounds on these parameters. This produces interval stand and geometry stiffness matrices, and the problem is transformed into a interval buckling eigenvalue problem in interval mathematics. The perturbation method is proposed to determine the lower and upper bounds on the buckling eigenvalues and due to uncertain-but-bounded parameters. Moreover, the critical load of the uncertain structure can be obtained. The effectiveness of the presented method was demonstrated by comparison with conventional stability theory, using a typical numerical example.

Extension of the Spatial PDI Model to Three Dimensions

1997 ◽  
Vol 84 (1) ◽  
pp. 176-178
Author(s):  
Frank O'Brien
Keyword(s):  
Population Density ◽  
Dimensional Space ◽  
Finite Lattice ◽  
Three Dimensional ◽  
Upper Bounds ◽  
Three Dimensions ◽  
Lower And Upper Bounds ◽  
Density Index ◽  
Three Dimensional Space

The author's population density index ( PDI) model is extended to three-dimensional distributions. A derived formula is presented that allows for the calculation of the lower and upper bounds of density in three-dimensional space for any finite lattice.

Energy of spherical fuzzy graphs

2020 ◽  
pp. 321-332
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Adjacency Matrix ◽  
Upper Bounds ◽  
Fuzzy Graph ◽  
Lower And Upper Bounds ◽  
Fuzzy Graphs

In this paper, the notion of energy extended to spherical fuzzy graph. The adjacency matrix of a spherical fuzzy graph is defined and we compute the energy of a spherical fuzzy graph as the sum of absolute values of eigenvalues of the adjacency matrix of the spherical fuzzy graph. Also, the lower and upper bounds for the energy of spherical fuzzy graphs are obtained.

scholarly journals Relationship between Age and Value of Information for a Noisy Ornstein–Uhlenbeck Process

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 940
Author(s):  
Zijing Wang ◽  
Mihai-Alin Badiu ◽  
Justin P. Coon
Keyword(s):  
Value Of Information ◽  
Markov Models ◽  
Upper Bounds ◽  
Distribution Functions ◽  
Lower And Upper Bounds ◽  
Uhlenbeck Process ◽  
Source Data ◽  
Non Linear ◽  
Queue Model ◽  
Selection Of

The age of information (AoI) has been widely used to quantify the information freshness in real-time status update systems. As the AoI is independent of the inherent property of the source data and the context, we introduce a mutual information-based value of information (VoI) framework for hidden Markov models. In this paper, we investigate the VoI and its relationship to the AoI for a noisy Ornstein–Uhlenbeck (OU) process. We explore the effects of correlation and noise on their relationship, and find logarithmic, exponential and linear dependencies between the two in three different regimes. This gives the formal justification for the selection of non-linear AoI functions previously reported in other works. Moreover, we study the statistical properties of the VoI in the example of a queue model, deriving its distribution functions and moments. The lower and upper bounds of the average VoI are also analysed, which can be used for the design and optimisation of freshness-aware networks. Numerical results are presented and further show that, compared with the traditional linear age and some basic non-linear age functions, the proposed VoI framework is more general and suitable for various contexts.

The Lower and Upper Bounds of Turán Number for Odd Wheels

2021 ◽  
Vol 37 (3) ◽  
pp. 919-932
Author(s):  
Byeong Moon Kim ◽  
Byung Chul Song ◽  
Woonjae Hwang
Keyword(s):  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Turán Number
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